Parallel Computing Research On Fast Multipole Boundary Element Method For The Geodynamics

Boundary Element Method(called BEM for short) is a newly numerical method, which has many merits. Firstly, it can reduce the dimension of the problem(only for boundary discrete). Secondly it can keep precision of calculate and is appropriate for the solution of infinite field problem. Traditional science and engineering computing problems are based on the local spatial schemes like finite element and finite difference, of which discrete coefficient matrix are mostly banded-parse. It has a quasi- linear relationship between its storage and its amount of calculation. Fitting for large-scale parallel computing is better. However, the discrete problem of BEM always has global dependency at the same time of dimension reduction. That is to say, the coefficient matrix of linear system is full matrix. And the amount of storage and calculation will increase rapidly with the development of problem size and is usually hard for parallelization.In 1987, the Fast Multipole Method(called FMM for short) is presented. This method can be used to relieve computational bottleneck and storage of BEM in larger engineering and science problems. It lighten the development and application of BEM. Usually we called the combination of FMM and BEM as the Fast Mulitipole Boundary Element Method(called FMBEM for short). Compared with BEM‘s, FMBEM can cut off calculation time and storage amount for nearly order of magnitude. Recently, FMBEM has been applied to acoustics, elastostatics, elastodynamics, solid mechanics, electromagnetic and other fields. Especially in the electromagnetic field, business software of FMBEM has been developed. Although BEM has already widely used for scientific problems in geodynamics, the application of FMBEM in this field is still very limited. Thus it‘s urgent to research the numerical method and parallel computing of FMBEM in geodynamics.This paper is based on the traditional serial boundary element software which is developed by the Institute of Geology, C hinese Academy of Geological Sciences(called IGC-BEM for short). Following work about fast parallel algorithm research and parallel software were involved:Firstly, hybrid parallel computing based on MPI/Open MP mode for the IGC-BEM are achieved;Secondly, based on the traditional model of boundary element geodynamics, the numerical model of geodynamics of the FMBEM, was completed and developd the corresponding version of parallel software. Testing result showed good scalability of the parallel FMBEM geodynamics software;Thirdly, parallel algorithm and optimization of FMM on Many- integrated Cores(called MIC for short) was involved. And as a result, we got a performance speedup of 1.95 on a single MIC card comparing to double CPUs.