Hierarchical multigrid strategy for efficiency improvement of the GPST inversion algorithm
type: Item
instance of: scholarly article
title: Hierarchical multigrid strategy for efficiency improvement of the GPST inversion algorithm
zbMATH Open document ID: 0707.65085
DOI: 10.1016/0168-9274(90)90002-W
author: Elsie Sterbin Gottlieb
published in: Applied Numerical Mathematics
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 4162205
zbMATH Keywords: evolution equations
zbMATH Keywords: efficiency
zbMATH Keywords: generalized pulse-spectrum technique
zbMATH Keywords: inversion algorithm
zbMATH Keywords: hierarchical multigrid strategy
zbMATH Keywords: inverse problems
zbMATH Keywords: iteration
reviewed by: Zongyi Hou
MaRDI profile type: Publication
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cites work: A numerical algorithm for solving inverse problems of two-dimensional wave equations
cites work: An iterative numerical algorithm for solving multi-parameter inverse problems of evolutional partial differential equations
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cites work: A numerical algorithm for remote sensing of density profiles of a simple ocean model by acoustic pulses
cites work: An iterative method for simultaneous determination of bulk and shear moduli and density variations
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cites work: An Iterative Method for Solving Inverse Problems of a Nonlinear Wave Equation
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cites work: A modified pulse-spectrum technique for solving inverse problems of two- dimensional elastic wave equation
full work available at URL: 0168-9274(90)90002-w
OpenAlex ID: W2007883714
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description: scientific article; zbMATH DE number 4162205