Parallelism by hierarchy of GPST inversion algorithm for elastic wave equation
The Generalized Pulse-Spectrum Technique (GPST) is a versatile and efficient iterative numerical algorithm for solving multi-parameter inverse problems of a system of nonlinear partial differential equations. Here parallelism is introduced into the hierarchy of GPST to further improve is efficiency for solving the multi-parameter inverse problems with a large number of unknown parameters in some geophysical applications. Its implementation is quite easy and it achieves large speedup with almost no communication overhead even on a single-processor computer. Effectively, this parallelism in GPST reduces the computational effort for solving any multi-parameter inverse problem approximately to that of the corresponding single-parameter inverse problem. A simple computational complexity analysis is performed for the parallel structured GPST to estimate its speedup. At the present, the feasibility and capability of the parallel structure GPST are only tested in a limited sense by performing numerical simulations for a three-parameter and two-dimensional inverse problem of the isotropic linear elastic wave equation on a single-processor computer sequentially. It is found that the parallel structured GPST is not only as robust as the standard GPST but also shows a speedup per iteration close to its estimated value.
system of Fredholm integral equations of first kind
ill- conditioned linear algebraic system
system of nonlinear partial differential equations
scientific article; zbMATH DE number 4024878