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A preconditioned Krylov subspace iterative methods for inverse source problem by virtue of a regularizing LM-DRBEM. (English) Zbl 07322718
Summary: In this paper, we investigate an effectual methodology to solve the problem of identifying the source term standing on a combined discontinuous dual reciprocity boundary element method with a regularized Levenberg-Marquardt algorithm. The mathematical model is described by optimizing the variation between the measured potential in some points within the problem domain and the estimated one by the discontinuous dual reciprocity boundary element approximation. To provide a qualitative evaluation, the derived dense and non symmetric matrix system of the forward problem is solved by virtue of the LU factorization and using some preconditioned Krylov subspace iterative algorithms, expressly the biconjugate gradient stabilized, the generalized minimum residual and the squared conjugate gradient method. Due to noise interference, a regularized Levenberg-Marquardt algorithm is adopted to retrieve the unknown source term. Extensive experiments evince greater effectiveness and stability criteria of the proposed approach.
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65F05 Direct numerical methods for linear systems and matrix inversion
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