THE ACCELERATION OF THE FINITE ELEMENT METHOD BY USING GRAPHICS CARD

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Dec 2, 2013 (3 years and 8 months ago)

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Symposium on Applied Electromagnetics


Sopron, Hungary, June 3
-
6, 2012



1


THE ACCELERATION OF THE

FINITE
ELEMENT METHOD BY USING GRAPHICS
CARD



P
.

Prukner
, M
.

Kuczmann
, Z. Pólik



Széchenyi István U
niversity, Faculty of Engineering Science
s
,

Department of
Automation

Egyetem tér 1, H
-
9026

Győr
,
Hungary


e
-
mail:
pruknerpeter@maxwell.sze.hu



Calculation with the finite element

method

[1]
can be

a

time
-
consuming

task
. In some
cases
,

like complicated geometry or
fine

grid
,

it can take hours or even days. The time of the
calculat
ion process can be reduced by using a computer with stronger resources, but there are
other efficient and cost
-
effective solutions as well, for example calculation by using graphics
card.

During
our

research, the problem of a 1D planar capacitor

[2]

has be
en solved by finite
element method implemented in MATLAB software environment, which requires processor,
memory and time consuming matrix operations. The aim of
this

work is to shorten the time of
the simulation process by parallel computation and by apply
ing an
nVidia GeForce GTX 560
Ti

(Fig. 1
) graphics card.




Fig
.

1
:

The

nVidia GeForce GTX 560 Ti graphics card

Symposium on Applied Electromagnetics


Sopron, Hungary, June 3
-
6, 2012



2


This graphics card has a GPU

which has
448 CUDA cores. The GPU
is the central unit of the
graphics cards. During the calculation process, the
GPU takes over the performation of the
mathematic
al

operations from the CPU.
By using this graphics card,
the time of the
calculation process can be reduced
,
because the Graphi
cs Processing Unit’s calculation

performance is higher than
the performance of
C
entral Processing Unit
s
.

During the work

a significant acceleration of the calculation process

has been
experienced

by using MATLAB
[3]
and JACKET

[4]
,

as well.
The data

in

Table I.

show us
the time differences
between the
length of the
operations with a r
andom matrix using CPU or
GPU.

Table I.

The time

differences between using CPU and GPU


C
alculation time using
CPU
[sec]

C
alculation time using
GPU
[sec]

Speed up

rand(2^16,200)

0.3462

0.0846

4.0914

2*sin(x)

0.2605

0.0114

22.8063

fft(x)

0.8128

0.0292

27.8
167

Our

future plans include the examination of the complex geometrics’s electric and
magnetic fields using the finite element method and the
acceleration

of this process by using
graphics card and with the multi GPU solution
,

as well.




References:

[1]
Kuczmann M., Iványi A.,
The Finite Element Method in Magnetics
, Budapest: Academic Press, 2008

[2]

Jackson, J. D.

Classical Electrodynamics
. J. Wiley, New York, 1962

[3]
http://www.mathworks.com/

(last visible 20
12
-
03
-
18)

[4]
http://www.accelereyes.com/

(last visible 2012
-
03
-
18)