Hierarchical multigrid strategy for efficiency improvement of the GPST inversion algorithm
The efficiency of the generalized pulse-spectrum technique (GPST) inversion algorithm is further improved by the introduction of a hierarchical multigrid strategy in combination with the existing re- structuralization of the algorithm. This hierarchical multigrid strategy for solving inverse problems of partial differential equations has nothing in common with the standard multigrid algorithms for solving direct problems of equations except that in both cases multiple grids are utilized. Here it is used to solve one-parameter inverse problems of two- dimensional linear evolutional partial differential equations. It is found that the floating point arithmetic operation count per iteration for this new scheme is of the same order as that for solving the direct problem of the corresponding partial differential equation. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this hierarchical multigrid strategy with algorithm re-structuralization. Indeed, this new computational scheme makes the GPST inversion algorithm much more efficient.
scientific article; zbMATH DE number 4162205
scientific article