Application Of Parallel Processing In Structural Engineering

Abstract

Today's computing environments are becoming more multifaceted, exploiting the ca- pabilities of a range of multi-core microprocessors, Central Processing Units (CPUs), digital signal processors, and graphic processing units (GPUs). Due to heterogeneity in hardware, the process of developing efficient software for such a wide array of ar- chitectures poses a number of challenges to the programming community. Solution of linear equations is a major mathematical process to solve many problems of solid mechanics, uid dynamics, structural engineering and so on. Since the size of problems increases to achieve accuracy, number of linear equations to be solved also increases and so is the time, to solve equations increases. Advancement of new par- allel computation technology using inexpensive graphic card processors (multi-core GPUs) and multi-core CPUs speed up the solution of various problems of structural engineering. In the present study, computationally intensive problems of structural engineering are implemented on High Performance Computing Platforms like multi-core processors and graphic processing units (GPUs). Direct methods like, Gaussian Elimination and Modified Cholesky solver, for solving linear equations in form of [A]fxg=fBg are used. GPUs and CPUs are used for parallel computations with help of OpenCL programming language. It is a step in the direction of heterogeneous computing for smarter, faster and better analysis of problem. The main purpose of using this paral- lel computation is to minimize the time of structural analysis of problem that involves large number of linear equations. For parallel implementation of Gaussian Elimination solver, linear equations sys- tem representing equilibrium equations of finite element problem is used. Equa- tions in form of [A]fxg=fBg are generated from finite element analysis of axial bar using 3-node bar element where A=Square Stifeness Matrix, B=Load Vector and x=Displacement vector. For solution of equations Matrix-[A] is inverted using se- quential and parallel implementation of Gaussian Elimination. Sequential program is developed using C++ and parallel program is developed using OpenCL language. For comparing computational e ciency of parallel code, speedup factor which is ra- tio of sequential execution time to parallel execution time is calculated for di erent number of linear equations ranging 101 to 10001. Parallel execution time includes processing time and communication time. As data is transferred between various memories, communication time increases total computational time. Code is executed on diferent CPUs and GPUs for parametric study. For parallel implementation of Half-Band solver, which is based on modified cholesky method, Direct Stifeness Method program of Plane Frame and Space Frame are used for generating set of linear equation system. Here stifeness matrix is stored in banded form to reduce memory requirements. Programs for sequential and parallel solution of banded equations are developed using C++ and OpenCL languages. Problems of varying size from 7650 Degrees of Freedom to 1,88,250 Degrees of Freedom are solved using sequential and parallel Half-Band solver. The computational efficiency of parallel code is studied based on speedup factor. Further to understand the efficiency of program on different hardware platform, the parallel code is executed on multi- core CPUs like Intel R CoreTMi3, i5, i7 processors with different specifications and NVIDIA GPU. Major factors affecting computational effciency of parallel program are hardware specifications, algorithms used, size of problem, communication time. When parallel code is implemented on multi-core CPUs, communication time is less compared to implementation on GPU. In case of GPU, computational time is reduced because of parallel operations on large number of cores.