The Fast BEM Simulation And Application For The Question Of Elastic Waves Scattering By 3-D Complex Alluvial Basin

A lot of earthquake damage shows that the earthquake damage varies in different sites,and the alluvial basin,a typical complex field,has significant amplification effect for seismic wave.This paper focuses on the elastic waves scattering problems of 3-D homogeneous alluvial basin and 3-D layered alluvial basin,and solved it by using the indirect boundary element method(IBEM).IBEM has less discrete elements and higher precision,and it also automatically satisfies the infinite boundary conditions in the meanwhile.Through precision test,the accuracy of the method is verified.However,since the large matrix is a non-symmetric dense matrix when solving the virtual load density using the IBEM,the solution of this equation requires a lot of calculation and storage,it can not be used to effectively calculate problem with large scale and high frequency.In order to improve the computational speed and reduce the computational memory,this paper introduces a substructure parallel algorithm,which improves the computational speed and reduces the computational memory to a certain extent.But when the algorithm is used to calculate problems with large scale and high frequency,the storage capacity is still very large,it can not be used to the problems with large scale and high frequency actual problems.Therefore,this paper introduces the fast multipole algorithm(FMM),which is regarded as one of the top ten algorithm in twentieth century,FMM can classified the effect of the source points to the boundary points through the tree structure,and then get s iterative solution to get the virtual wave source density without solving and storing large matrix,the method can greatly reduced the calculation and storage which the problem solving required.At present,it is limited to theoretical analysis for the majority of many domestic scholars study of the problem of scattering of elastic waves in alluvial basins,the analysis for actual sites is rare,however,many foreign scholars have applied the research results to the actual sites,in order to provide a theoretical basis for the seismic zoning and actual engineering construction,therefore,the fast multipole indirect boundary element method(FM-IBEM)is applied to the seismic response solution of a 3-D complex shape homogeneous alluvial basin under the action of SV wave and the broadband solution of the 3-D non-horizontal layered alluvial basins under the action of P and SV waves in this paper,some laws of the surface seismic response of the alluvial basins are obtained,and the applicability of the method for all kinds of complex sites is verified,the results can also provide reference for other numerical methods.The research results show that the FM-IBEM is a new efficient algorithm and practical procedure,which is suitable for solving the problem of elastic waves scattering by alluvial basins,it can greatly improve the computational efficiency,it is beneficial to further application of the algorithm to solve real problem with large scale and high frequency.In addition,it can provide important theoretical basis and reference for seismic zonation,urban earthquake risk assessment,urban planning and important engineering seismic fortification.