T-小波配点边界元法

T-wavelet Collocation Boundary Element Method

现有T-小波边界元法都基于Galerkin法,要计算二重边界积分,比较复杂。工程中需要一种简便高效的边界元算法。基于δ-函数构造了T-小波,将其应用于边界元系数矩阵压缩,形成T-小波配点边界元法。算例表明,采用T-小波配点边界元法在保持较高精度的同时,计算时间为O(NlgN),内存消耗为O(N)。

Existing T-wavelet boundary element method（BEM） uses Galerkin scheme to discretize boundary integral equations,in which the evaluation of double integrals is complication and time-consuming.A method for constructing T-wavelet using Dirac δ-function is first proposed.By adopting these new wavelets as test functions in weighted residual method,a T-wavelet collocation BEM is then established.The method only involves single-layer integrals,thus easy to realize.Two representative real-world examples clearly show the O（NlgN） computational time and O（N） memory requirements of the method.