2022-05-26T19:01:19Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000326492021-10-01T06:24:20ZDiscussion of Fast Multipole Boundary Element Method for Simulating Wide-area Seismic Ground Motions高速多重極境界要素法による広域地震動シミレーションに関する考察福井, 貞雄126530453seismic ground motionsimulationboundary element methodfast multipole methodpreconditioning of iterative solverapplication/pdfA quantitative simulation scheme to analyze wide-area seismic ground motions is discussed in the present paper. The ground is assumed to be a multi-zone elastic material as the first order approximation. The problem has a large number of freedom parameters and a large wavenumber because the area covers at least hundreds of wavelengths. The region is approximately semi-infinite. The boundary element method in the frequency domain elastodynamics is proposed to analyze this problem. To solve a large quantitative model the fast multipole method, which reduces the computing complexity of matrix-vector product to O (N) by doing all computations on a tree structure, is introduced to accelerate the boundary element method with an iterative solver. To reduce computing time of large wavenumber problems the diagonal form of the fast multipole method is combined with the conventional fast multipole method. The boundary integral equation of Burton and Muller is introduced to avoid fictitious eigen-values in exterior problems. For the iterative solver of the boundary element method, a preconditioning scheme using the Haar wavelet transformation and an algorithm on the tree structure is proposed. A block preconditioning for the boundary element equation in a multi-zone region is also proposed. The proposed method is expected to analyze problems of millions of elements with parallel computing. This method is applicable to viscoelastic ground motion analysis with complex wavenumbers.departmental bulletin paper東京大学地震研究所2000-12-22application/pdf東京大學地震研究所彙報 = Bulletin of the Earthquake Research Institute, University of Tokyo275197228AN0016225800408972https://repository.dl.itc.u-tokyo.ac.jp/record/32649/files/ji0752007.pdfjpn