Solution of biharmonic equations with application to radar imaging
type: Item
instance of: scholarly article
title: Solution of biharmonic equations with application to radar imaging
zbMATH Open document ID: 0933.65128
DOI: 10.1016/S0377-0427(98)00079-X
author: L.-E. Andersson
author: T. Elfving
author: Gene H. Golub
published in: Journal of Computational and Applied Mathematics
publication date: 2000-04-04T00:00:00Z
review text: This paper is concerned with the mathematical inverse problem to be resolved in order to recover the ground topography height function from radar data. It is proved that this problem amounts to solve Poisson's equation with the following difficulties: -- the solution has to be looked over a very large rectangular grid; -- boundary values are not known. To obtain suitable solutions, the authors propose two different methods. Both methods consist to introduce a minimizing criterion involving Sobolev norms of the solution; in this way, they propose two possible choices of criteria. In both cases, they prove that these formulations amount to solve biharmonic problems with appropriate boundary data. Then, fast numerical techniques are investigated to solve these biharmonic problems. Finally, some numerical experiments prove the efficiency of such methods. This is a very nice paper giving very well analyzed and powerful methods to solve difficult and important technical problems.
reviewed by: Michel Bernadou
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1326545
zbMATH Keywords: radar imaging
zbMATH Keywords: inverse problem
zbMATH Keywords: Poisson's equation
zbMATH Keywords: biharmonic problems
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
cites work: On the Determination of a Function from Spherical Averages
cites work: Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations
cites work: Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles
cites work: On Direct Methods for Solving Poisson’s Equations
cites work: Q4113326
cites work: Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
cites work: A Note on the Generalized Conjugate Gradient Method
cites work: Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
cites work: The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems
cites work: An inverse method for the processing of synthetic aperture radar data
cites work: Q5628582
cites work: Q4003887
cites work: Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators
cites work: On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations
cites work: The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”
cites work: Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners
cites work: The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. II
cites work: Q4692936
cites work: The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
cites work: A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
cites work: Q5604166
full work available at URL: s0377-0427(98)00079-x
OpenAlex ID: W1964603532
description: scientific article; zbMATH DE number 1326545