GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computational methods for integral equations
Computational methods for integral equations
Matrix computations (3rd ed.)
GMRES computation of high frequency electrical field propagation in land mine detection
Journal of Computational Physics
Numerical solution of a parabolic inverse problem in optical tomography using experimental data
SIAM Journal on Applied Mathematics
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.