| Boundary Element Method (BEM) is an important numerical method in the fieldof scientific research and engineering applications. Compared to Finite Element Method(FEM), BEM has the advantage of dimensional reduction which can shorten thepre-processing time of analysis modeling. BEM has been widely used and studied forstructural performance simulation. But the computation of BEM is intensive, especially thesolving process of nonsymmetric and dense system equation which costs considerablememory and time. In this thesis, the systematic analysis and research on how to efficientlysolve the system equations of BEM was conducted.Typically, GMRES algorithm based on Krylov subspace methods is most effective forthe solution of system equations. The classical GMRES algorithm is based on global Krylovsubspace, and the restarted version of GMRES algorithm is commonly introduced. Thedisadvantage with restarting is that some valuable information is discarded when iterationrestarts, and this affects the convergence. In order to improve the convergence, GMRES-DC(GMRES with Dual Compensation) algorithm which utilizes approximate eigenvectors anderror vectors as compensation information is proposed to save lost valuable information.Parallel technology is an important method to achieve high performance computation.The CUDA architecture provides a way to use CPU/GPU collaborative heterogeneouscomputing model, which is a cost-effective means of parallel computing. As to acceleratethe solving process of system equations by exerting the parallel computing power of GPU,GMRES-DC algorithm is implemented with CUDA based on the parallel analysis.Finally, the system equations of BEM analyzing three-dimensional elasticity problemswere solved by CUDA based GMRES-DC algorithm. The solving efficiency was comparedwith relative algorithm. The example results show that the GMRES-DC algorithm can moreefficiently accomplish solving process of BEM and the CUDA based algorithm reach asatisfactory speedup. |
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