Time Integration Utilities

mustardarchaeologistMechanics

Feb 22, 2014 (3 years and 7 months ago)

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Time Integration Utilities


on an FPGA

Cris A. Kania

with

Olaf O. Storaasli, Ph. D.

NASA Langley

Traditional Computing


Hardware development
has struggled to keep
pace with analysis
needs


Computing speed
reaching asymptotic
limit


Clusters offer means of
faster computing

Moore’s Law

Computing Alternative


FPGAs offer means to achieve
faster execution


Design is inherently parallel
whereas CPUs are sequential


“Field Programmable” where the
circuitry is optimized to best suit
the demands of the application


CPU circuitry 1% active while
FPGA circuitry 80% active

Purpose


Legacy software is incompatible


Basic engineering utilities must be developed to begin
transition


Critical to many analysis methodologies is the solution to
time
-
dependent PDEs


Key disciplines which would benefit from an FPGA are
CSM and CFD


Two
-
fold purpose: Demonstrate the advantages of the
FPGA and provide time integration routines

Methods


Learn Viva programming environment for FPGAs


Implement time integration schemes for scalar ODEs


Apply methodology to representative ODE for
verification


Extend utilities for vector PDEs


Test vector utilities on problems in CFD & CSM


Compare execution speeds of traditional CPU vs
FPGA on identical problems

C/C++ programming environment

VIVA programming environment

Expected 50 to 300 times faster

Accomplishments


Spring
-
mass system with damping


four
-
stage Runge
-
Kutta integration scheme


Newmark method


compare analytical solution with numerical solutions

Accomplishments


Computational Structural Mechanics


time dependent solution of cantilever beam


Computational Fluid Dynamics


time dependent solution quasi
-
2D flow with area
change

Spring
-
Mass Results


Spring
-
Mass System with damping


verified integration schemes on both CPU and FPGA


numerical solutions agree with analytical solution


700 C++ lines, 36 Viva sheets

Displacement vs. Time
-10
-5
0
5
10
0
2
4
6
8
10
Time (sec)
Displacement
Analytical Solution

Numerical Solutions

Cantilever Beam Results


Cantilever Beam


solved structural problem using a finite element
approach


used Newmark integration scheme


1200 C++ lines, 56+ Viva sheets

Elements
CPU Solution Time (sec)
FPGA Solution Time (sec)
20
109
*
40
723
*
60
1705
*
Quasi
-
2D Flow Results


Quasi
-
2D Flow


solved fluid dynamics problem involving three
simultaneous equations


used Runge
-
Kutta integration scheme


700 C++ lines, 49+ Viva sheets

Nodes
CPU Solution Time (sec)
FPGA Solution Time (sec)
60
40
*
80
55
*
100
66
*
140
830
*
200
1188
*
Conclusions/Relevancy


FPGA demonstrates x
-
fold increase in efficiency over
Pentium class CPU


FPGAs represent next generation hardware


Numerical integration utilities will aid in transition to
FPGA hardware

Acknowledgements


Dr. Olaf Storaasli, NASA Langley Research Center


Dr. Arthur Johnson, NASA Langley Research Center


Mrs. Sue Greiner, New Horizons Governor’s School

Citations


Meirovitch,

L
.

1967
.

Analytical

Methods

in

Vibrations
.

Macmillan,

New

York
.

555
p
.


Anonymous
.

Unknown

Date
.

The

Runge
-
Kutta

Method
.

<http
:
//www
.
sst
.
ph
.
ic
.
ac
.
uk/angus/Lectures/compphys/node
11
.
html>


Baddourah,

M
.
,

Storaasli,

O
.
,

and

Bostic,

S
.

Unknown

Date
.

Linear

Static

Structural

and

Vibration

Analysis

on

High

Performance

Computers
.

International

Journal

of

Computing

Systems

in

Engineering,

Vol
.

4
,

No
.

4
-
6
,

Dec
.

1993
,

pp
.

41
-
49
.


Beckett,

P
.

and

Jennings,

A
.

2002
.

Towards

Nanocomputer

Architecture
.

Proceedings

of

the

7
th

Asia
-
Pacific

Computer

Systems

Architectures

Conference,

Melbourne,

Australia,

2002
.


Cook,

R
.
,

Malkus,

D
.
,

and

Plesha,

M
.

1972
.

Concepts

and

Applications

of

Finite

Element

Analysis

3
rd

Edition
.

John

Wiley

&

Sons,

Inc
.

324
p
.


Durbeck,

L
.

and

Macias,

N
.

2001
.

The

Cell

Matrix
:

an

architecture

for

nanocomputing
.

Nanotechnology,

Vol
.

12

(
2001
),

pp
.

217
-
230
.


Hoffmann,

K
.

and

Chiang,

S
.

2000
.

Computational

Fluid

Dynamics

4
th

Edition
.

Engineering

Education

System
.

486
p
.


Singleterry,

R
.
,

Sobieszczanski
-
Sobieski,

J
.
,

and

Brown,

S
.

2002
.

Field
-
programmable

Gate

Array

Computer

in

Structural

Analysis
:

An

Initial

Exploration
.


Storaasli,

O
.
,

Singleterry,

R
.
,

and

Brown,

S
.

Unknown

Date
.

Scientific

Computations

on

a

NASA

Reconfigurable

Hypercomputer
.


Storaasli,

O
.
,

Singleterry,

R
.
,

Sobieski,

J
.
,

Rutishauser,

D
.

2002
.

Importance

of

Ultrafast

Computing

for

NASA

Missions
.


Warsi,

S
.

and

Kania,

L
.

1998
.

Hybrid

Grid

Navier
-
Stokes

Solver

with

H
-
Refinement

Adaptation
.

AIAA

paper

98
-
0545
.


Watson,

W

and

Storaasli,

O
.

Unknown

Date
.

Application

of

NASA

General
-
Purpose

Solver

to

Large
-
Scale

Computations

in

Aeroacoustics
.

Fifth

Symposium

on

the

Large
-
Scale

Analysis

and

Design

and

ISE,

Williamsburg,

VA

Oct
.

12
-
15
,

1999
.


Anonymous
.

Unknown

Date
.

Chipping

Away
.

<http
:
//www
.
forbes
.
com/forbes/
2003
/
0414
/
206
.
html