A Scalable Parallel Algorithm for 3-D Magnetotelluric Finite Element Modeling in Anisotropic Media - Zhu, Xiaoxiong; Liu, Jie; Cui, Yian; Gong, Chunye (IEEE transactions on geoscience and remote sensing, 2022)
3-D magnetotelluric (MT) forward modeling has always been faced with the problems of high memory requirements and long computing time. In this article, we design a scalable parallel algorithm for 3-D MT finite element modeling in anisotropic media. The parallel algorithm is based on the distributed mesh storage, including multiple parallel granularities, and is implemented through multiple tools. Message-passing interface (MPI) is used to exploit process parallelisms for subdomains, frequencies, and solving equations. Thread parallelisms for merge sorting, element analysis, matrix assembly, and imposing Dirichlet boundary conditions are developed by Open Multi-Processing (OpenMP). We validate the algorithm through several model simulations and study the effects of topography and conductivity anisotropy on apparent resistivities and phase responses. Scalability tests are performed on the Tianhe-2 supercomputer to analyze the parallel performance of different parallel granularities. Three parallel direct solvers Supernodal LU (SUPERLU), MUltifrontal Massively Parallel sparse direct Solver (MUMPS), and Parallel Sparse matriX package (PASTIX) are compared in solving sparse systems of equations. As a result, reasonable parallel parameters are suggested for practical applications. The developed parallel algorithm is proven to be efficient and scalable.