Some Recent Advances in Wavelet Boundary Element Method

摘要

Wavelet boundary element method (BEM), as one of the powerful fast BEMs, has attracted much attention in recent years. However, the conventional wavelet BEM needs the patch-wise parameterization of boundary as well as information about the topological connectedness of the patches, thus its efficiency in treating problems with complicate boundaries is limited. T-wavelet BEM, which was proposed in [1], overcomes this drawback by constructing boundary wavelets directly on the usual boundary element partitions, and has shown great potential in dealing with large-scale problems with complex geometries. This paper presents some recent achievements on T-wavelet BEM in our group, mainly including the T-wavelet with quasi-vanishing moments and the a-posteriori compression for the non-standard form. The former can largely reduce both the computational time and memory requirements of T-wavelet BEM, and the latter can further reduce the memory requirement for saving the system matrix. The performance of the improved method is comfirmed by large-scale numerical examples involving complex geometries. To show the efficiency of the method, we compare the memory requirement of the compressed non-standard form with the near-field matrix of a fast multipole BEM transformed from the T-wavelet BEM [2]. We find that the a-posteriori compression reduces the memory usage of the non-standard form to be even lower than for the fast multipole BEM.