Autonomic Dynamic Load Balancing of Parallel SAMR Applications

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Dec 8, 2013 (3 years and 7 months ago)

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UPTEC F 11041
Examensarbete 30 hp
Juni 2011
Autonomic Dynamic Load Balancing
of Parallel SAMR Applications
Karl Ljungkvist



Teknisk- naturvetenskaplig fakultet
UTH-enheten

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Ångströmlaboratoriet
Lägerhyddsvägen 1
Hus 4, Plan 0

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Box 536
751 21 Uppsala

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018 – 471 30 03

Telefax:
018 – 471 30 00

Hemsida:
http://www.teknat.uu.se/student

Abstract
Autonomic Dynamic Load Balancing of Parallel SAMR
Applications
Karl Ljungkvist
When solving partial differential equations using finite difference methods on
structured meshes, adaptive refinement can be used to increase the accuracy of the
solution in an efficient manner. When implementing solvers using structured adaptive
mesh refinement for modern parallel computer systems, an important task is the
partitioning of the grid hierarchy over the available processors. The Meta-partitioner
is an autonomic framework which can dynamically select between a large number of
grid-partitioning algorithms at run time.
In this thesis we investigate which modifications that are necessary in order to
connect the Meta-partitioner to the existing SAMR-framework Chombo, and begin
the process of performing this connection. We conclude that although significant
changes to both Chombo and the Meta-partitioner are necessary, a connection
definitely seams feasible. We estimate that that the major work of the connection has
been done, and that with the experience gained from this project, the continuation is
straightforward.
We also connect a patch-based partitioning algorithm to Chombo and evaluate it for
the first time as part of a real SAMR-based simulation. The results are promising and
we conclude that it is a viable candidate for inclusion in the Meta-partitioner.
ISSN: 1401-5757, UPTEC F 11041
Examinator: Tomas Nyberg
Ämnesgranskare: Sverker Holmgren
Handledare: Michael Thuné, Jarmo Rantakokko

  
   
     
                               
                           
                                   
   
                                
                     
                          
                  
                            
     
      
                          
          
                                    
                                    
                                 
        
                          
                              
  
   

 

  
            
           
            
        
           
               
         
               


              
            
         
             
                
          
 n+1         n   
            
n + 1          n + 1    
              
          
          
                

            
            

      

           

          
               
           
              
            
  
            
               
               
           
              
           
            
             
          
         
          
          
        
     
             
             
            
            
                  
          
           
            
  
        
           
            
           
     
          
          
             
               
             
            
 
           
         
          
           
            
            
             

             

           
             
              
   
    
           
               
             
             
               
            
               
            
              
            
          
   
       
              
              
      
             
           
            
        

  
            
   L+1   0  L       
              
         
       l        l 1 
    l          l 1     
         
     l             
l 1             l 1   
              
     


           
             
         
            
                
           r
l
 
           (2;3;2)
     h         (
h
2
;
h
6
;
h
12
) 
           
     
         
             
           
              
   
          
            
            

          
            
  h  k            
 Q     q         
        k  h  
   
k
h
=   Q
h
  Q     
h  k =  h  
     Q
h
2
u      
    h    Q
2h
u    
       2h        
  
 
Q
h
2
u(x;t) Q
2h
u(x;t)
2
q+1
2

             
               
   
            
             
             
                
  
              
             
     l      l +2      
          l +1   
  l +2 
         
              
              
                
             
          
              
             
             
            
           
 
             
             
                
           
             
              
          

            
               
                 
        
             
               
                
          
             
              
               
              
                
               
      
           
             
            
              
             I
x;y
 
     x   
S(x) =
X
y
I(x;y):
             
              
        
             
            
            
        
           
    
               
             
            
           
             
            
              

  
            
              
          
            
                
            

             
             
   l k
  k      l
 l == L 


    l  l +1
 i = 1:r
l+1

 l +1 k=r
l+1

 
     l +1  l
 
           k    
  r
l+1
= 2
     L + 1    r
l
 
l > 0      k
0
        
      0 k
0
     l    
         l    
             L  
          l < L     
 
             
             
    l +1           l
         l + 1      
          l        
                
     
        l + 1   
         

k
h
;
              
           

              
            
             
             
l +1      r
l+1
  
k
r
l+1
      
      l + 1       k
l

         l         
 
            l
        l + 1     
             
              
     
             
             
              
                
               
                
                
  
              
               
              
            
              
               
            
                
       
             
            
               
          Z
D
     
         Z
D
   
         
            
            
         
                
          
        
        
            
           
              
          

        
         
           
             
         

  
 
           
           
            
              
            
              
              
           
            
            
  
          
              
             
           
             
             
                    
      p
S
p
=
T
1
T
p
:
            
              
            
             P   
     (1 P)         
      
S
p
=
1
(1 P) +
P
p
;
              
         p     
              
            
              
       
           
                 

             
           
             
            
                
   
          
           
                
             
      
            
            
          
             
          
             
              
         
             
           
     
            
             
             
             
       
           
              
                
             
            
             

        
         
            
           
          
           
            
                
            
    

              
           
     
           
            
               
           
           
               
           
             
            
          
                  
            
         l +1       
  l        l   l +1  r
l+1
  
         r
l+1
   
          l   
               
       
             
           
              
                 
          
              
            
            
               
          
             
    
           
              
               
               
             
            
            
            
          
            
   
            
            
              
               

  
         
         
          
     
           
              
                
       
            
               
              
              
            
    
            
           
              
              
     
            
          
                 
            
              
       d    1
              
                 
          
            
               
                
         
           p 
                
                 
       
          
          
           

            
           
               
             
             
            
            
         
            
           
               
                 
             
             
              
              
  
         
         
                
          
           
               
           
              
             
            
               
  
            
             

          
   
                
               
              
        
         
               
              
         
               
              
                 
        
          
            
              
           
               
               
              
            
  
         
          
              
  m > p  p              
           
                  
             
        p    
            
             
           
           
  
         
            
             

         
   
            
        
            
           
            
            
     
         
            
          
          
         
           
          
            
           
             
            
              
          
            
          
          = 2   
 
           
              
         
  
     
           
           
             
               
         
             
             
               
            

         
        
                
              
             
          
          

          
 
          
              
           
            
      
  
           
 
            
          
            
             
          

          
             
             
         
             
            
     
          
           
          
         
           
         
          
         
            
  
           
              
      
           
            
           
       
          
           
         
                  
     
             
          

     
             
             
            
              
               
             
         
              
               
              
              
           
            
             
      
         
            
             
               
             
              
         
              
               
           
              
          
            v
    
v
norm:
=
v 
v

v
:

 
v
 
v
        v  
        
              
           
           
 
v
log:
=
1
1 +e
v
norm:
                
            
              
  
         
          
            
  
            
               
           
               
             
             
               
    
            
             
       
 
 
 
 
 
 
 
 
          
         
           
              
            
          
              
              
          
          
           
           
            

           
             
              
             
         
               
       
           
           
           
          
              
              
        
      
              
         
             
            
         
           
           
          
          
           
              
          
          
             
            
          
              
             
          
         
        
            
            
              
          
            
          
             
               
 = 20%             = 25%
  
       

          
    
 


  

   
   

   

    
   

    
   

    
    
   
        
            
               
              
         
          
             
              
            
           
       
          
             
      
          
               
           
             
          
             
           

           
           
         
          
         
            
             
           
          
             
              

           
             
             
             
            
          
            
             
            
         
         
            
          
             
              
             
           
  
  
     
                 
            
            
            
            
 
   
            
                
        
         

tt
= 
xx
+
yy

   
= [0;1] [0;1]      
(x;y) =
1

2
e
(x0:5)
2
+(y0:5)
2

2
;

t
(x;y) = 0;
            
            
      

00
i;j
=

i1;j
2
i;j
+
i+1;j
h
2
+

i;j1
2
i;j
+
i;j+1
h
2
=:f(
i;j
);

        

n+1
= 
n
+
k
6
(
1
+2
2
+2
3
+
4
);


1
= f(
n
);

2
= f(
n
+k 
1
=2);

3
= f(
n
+k 
2
=2);

4
= f(
n
+k 
3
):
          
            
              
            
             
   
           

       
   
      
      
    128 128
   
     = 0:025
             
                 
             
              
              
               
             
                   
  
            
                
             
               
                
                
            
               
   

          

N
proc
   

   
  
   
           

      
   
        
            
           
              
             
          
      
  
             
            
            
             
       
             
           

            
            
          
             
        
  
               
              
           
          
             
              
 
  
        
          
              

             
          
            
             
           
             
       
             
      
  N
proc:
   

   
   
  
   
   
 
   
   

          
          
             
             
                
              
                 
           
           
     
         
  N
proc:
   

   
   
  
   
   
 
   
   
                
               
              
               
             
            
             
           
                 

       
             
    
       
               
            
            
           
             
        
            
     
            
              
                 
             
           
     
            
               
               
             
      
             
         

          
              
        
          
                
            
              
          
          
            
            
    
            
            
          
         
           
     
                
            
           
    
     
       
            
          
             
              
                
            
 
             
            
          
            
             
         
                 
   
          
              
          
            
        
              

                
       
            
              
             
            
          
  
             
            
            
               
           
      

             
            
          
             
            
        

           
         
 
              
         
              
         
 
              
         

           
       
    
              
           
    
            
        

        
    
                 
              
           
   
 
         
       
          
           
         
        
    
          
         
  
          
         
       
 
         
        
       
  
           
        
       
 
           
          
      
             
           
 
            
       
           
     
            
         
 

              
         
          
   
          
   
          
        

          
        
  
            
           
          
            
          
        
      
 
           
       
   
           
        

  
          

          
          

           
           

           
