MPI并行的节点大地电磁三维有限元正演

Three dimensional modeling of magnetotelluric data using finite element method and MPI parallel computation

用fortran语言编程实现了有限元三维大地电磁正演,通过层状介质模型、二维棱柱体模型及三维低阻体模型结果的对比,验证了所编写程序的正确性。首先通过加入第一类边界条件,减少了最终求解方程组的维数,同时对系数矩阵的存储采用非零存储技术,大大降低了对计算机内存的需求;最后在串行程序的基础上,基于MPI实现了频点间的并行,并对一个三维模型进行计算,并行后开启4进程时加速比达到了2.328,有效地减少了所需时间。

This paper deals with the forward modeling of three-dimensional（3D）magnetotelluric problem by using the finite element method with fortran language.The validity of this FEM approach is investigated and confirmed by comparing modeling results with a layered medium model,a 2Dprism model and a 3D model.The bi-conjugate gradient method is applied in solving the governed equations,which reduced the dimensions of the linear system under the first boundary condition.In addition,the memory requirement is reduced obviously in which only nonzero elements stored.The solution of the linear system is obtained by using a massive parallel program based on MPI between frequencies which massively reduced the computing time.A 3D model has been calculated,and the speed-up ratio is up to 2.328 when 4processes used.