The numerical solution of forward and inverse Robin problems for Laplace’s equation

The Robin boundary value problem for Laplace’s equation in the elliptic region (which is a forward problem) and its related inverse problem can be used to reconstruct Robin coefficients from measurements on a partial boundary (inverse problem). We present a numerical solution of the forward problem...

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Bibliographic Details
Published in:Boundary value problems Vol. 2019; no. 1; pp. 1 - 13
Main Authors: Qu, Dan, Ma, Yan-Bo
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.07.2019
Hindawi Limited
SpringerOpen
Subjects:
Analysis
Approximations and Expansions
Boundary element method
Boundary integral equations
Boundary integral method
Boundary value problems
Difference and Functional Equations
Forward problem
Integral equations
Inverse problems
Laplace equation
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Preconditioned Krylov subspace method
Robin inverse problem
Subspace methods
Preconditioned Krylov subspace method
Robin inverse problem
Laplace equation
45Q05
65N21
Boundary integral equations
ISSN:1687-2770, 1687-2762, 1687-2770
Online Access:Get full text
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Summary:The Robin boundary value problem for Laplace’s equation in the elliptic region (which is a forward problem) and its related inverse problem can be used to reconstruct Robin coefficients from measurements on a partial boundary (inverse problem). We present a numerical solution of the forward problem that uses a boundary integral equation method, and we propose a fast solver based on one that reduces the computational complexity to O ( N log ( N ) ) , where N is the size of the data. We compute the solution of the inverse problem using a preconditioned Krylov subspace method where the preconditioner is based on a block matrix decomposition. The structure of the matrix is then exploited to solve the direct problem. Numerical examples are presented to illustrate the effectiveness of the proposed approach.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-019-1229-6