Efficient Solvers of a Large Dimensional Linear Equation System with Multiple Right-Hand Side (RHS) Vectors for 3D Geophysical Modelling

Abstract

3D geophysical modelling, such as 3D resistivity, geo-electromagnetic and seismic wave modelling require simulating the physical fields in geological structures using the finite element or finite difference methods. The resultant equations of the numerical methods give rise to a linear equation involving a large dimensional sparse matrix with one right-hand-side source vector. Hence, the solution for the system is often computationally expensive for a practical 3D geological model. However, the sources used in geophysical explorations are usually much more than one in number and can be as many as over 1000 sources to cover a surface area. Therefore, solving the resulting equation becomes much more computationally intensive for such multiple right-hand-side vectors. Two standard solvers namely direct (matrix) and iterative methods have been often used to solve similar equations involving geophysical and engineering problems over years. Some new generations of the matrix solver and iterative solver packages are developed recently by many mathematicians and computer scientists. This research investigates the computational efficiencies of these new solver variants for 41 Right Hand Sides (RHS) 3D GQG resistivity model problems with respect to model size, resolution, topography, and anisotropy. MUMPS Direct Solver was determined to be the fastest solver, Parallelized Preconditioned Conjugate Gradient(P-PCG) Iterative Solver required the least memory to compute accurate solutions while PETSc Iterative Solver scaled efficiently across problems modification showing better flexibility than MUMPS and P-PCG.

Date of Award	Jul 2022
Original language	American English