LubichのCQMを用いた時間域境界積分方程式法のACAによる高速化について

Abstract

Time domain boundary integral equation method(TD-BIEM) with Lubich convolution quadrature method is considered. In TD-BIEM with Lubich CQM, the convolution integrals with respect to time in the boundary integral equation are approximated as the products of the boundary values and the sum of the Laplace transform of the fundamental solution. Because the influence coefficient matrices become dense in TD-BIEM with Lubich CQM, a lot of computational time and large memory are required in TD-BIEM with Lubich CQM. We therefore change the timing of the matrix-vector products in the algebra equations in TD-BIEM with Lubich CQM in order to reduce the computational time. We also apply Adaptive Cross Approximation to the influence coefficient matrices in TD-BIEM with Lubich CQM. Because the influence coefficient matrices are calculated approximately and become sparse using ACA, the reduction of the computational time and memory requirements is expected. We solved some simple wave scattering problems with the conventional TD-BIEM with Lubich CQM and with the proposed method. We also compared the computational time and memory requirements in each method. Using our proposed method, we can reduce the computational time and memory requirements in TD-BIEM with Lubich CQM.