Application Of Graphics Processing Unit For Parallel Processing In Structural Engineering

Abstract

Multicore machines and hyper-threading technology have enabled scientists and en- gineers to speed up computationally intensive applications. However, the use of these advanced computing technology requires parallel programming techniques. Solution of linear equation is a computational intensive process in analysis of structural sys- tem. With increase in size of problems more linear equations need to be solved which increases execution time of structural analysis dramatically. To overcome this prob- lem parallel programming can be implemented in structural engineering applications. Objective of this project is to use the concept of parallel programming in Finite Ele- ment Analysis of structure using NVIDIA GPU as Hardware. Parallel programming on GPU is carried out using CUDA C language which is based on platform developed by NVIDIA. Unlike CPU, advantage of using GPU is that its architecture allow us to execute many parallel threads slowly, rather than executing a single thread very quickly. In a few years, many standard software products will be based on concepts of par- allel programming. Thus, the need for parallel programming will extend to all areas of software development. The application area for parallel computing will be much larger than scientific computing, which will be main area of parallel computing for many years. In present study computationally intensive problems of structure engineering are im- plemented on Graphics Processing Unit(GPU) using concept of parallel computing. For implementation of parallel program on GPU , computational intensive parts of Finite Element Analysis like Matrix multiplication and solution of linear equation are considered. To measure performance of parallel program with respect to sequential program speed up factor is calculated which is ratio of sequential execution time to parallel execution time. For parallel implementation of Gaussian Elimination solver, linear equation of system representing equilibrium equations of Finite Element Analysis is used. For generation of equation in form of [A]fxg=fBg, Finite Element Analysis of Axially loaded bar using 3 node element is considered. Data generated from Finite Element Analysis are always in form of [K]fxg=fFg, which is similar to [A]fxg=fBg, where K=sti ness matrix, x=displacement vector and F= Force vector. For Solution of displacement vector x, inversion of K matrix is done using Gaussian Elimination method. Sequen- tial program is developed using C language and parallel program is developed using CUDA C language. To compare performance of program, speed up factor is calcu- lated for di erent number of equation ranging from 100 to 1000. For parallel implementation of Half Band solver, Finite Element problem used in Gaussian Elimination method is used but in this case a matrix stored in Half Band Form. Data generated from Finite Element analysis are in form of [K]fxg=fFg is converted in to [A]fxg=fBg, where A= Half Band sti ness matrix , x= displacement vector and F=Force vector. For solution of displacement vector x, inversion of Half Band matrix is done using Gaussian Elimination method. Sequential program is de- veloped using c language and parallel program is developed using CUDA c language. To compare performance of program speed up factor is calculated for equation rang- ing from 100 to 10000. Literature survey shows that parallelization whole Finite Element method rather than focusing equation solver leads to better performance. For parallel implementation Fi- nite Element method, Finite Element analysis of rectangular beam using CST element is developed. Parallel program is developed using CUDA C language. To compare performance of parallel program speed up factor is calculated for number of elements ranging from 10 to 10240.