A Model Reduction Method for Boundary Element Method
Shengze Li  1@  , Jon Trevelyan  2@  , Zhang Weihua  1@  
1 : National University of Defense Technology (CHINA)  (NUDT)  -  Website
109 Deya Road, Hunan, Changsha -  China
2 : School of Engineering and Computing Sciences  -  Website
South Road, DH1 3LE Durham -  United Kingdom

The aim of this work is to provide a promising way to improve the computational efficiency for BEM. This study introduces 'a priori' model reduction method in BEM analysis aiming to narrow calculation scale and enhance efficiency. Here, the problem is treated as a state evolution process, it is proceed by approximating the problem solution using the most appropriate set of approximation functions, which depend on Karhunen-Lo\`{e}ve decomposition. The calculation process will be proceeded depending on the previous basis if the norm of the residual is small enough, if not, it need to enrich the approximation basis and compute again some of the previous steps using the Krylov subspaces. Finally, an example is proposed in this article which allow to accurate and fast resolution of BEM problem and proves the potentiality of this numerical technique. This provides a proper condition that structure optimization bases on.

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