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Recovering the source term in a linear diffusion problem by the method of fundamental solutions. (English) Zbl 1159.65354
Summary: This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed.

MSC:
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
80A23 Inverse problems in thermodynamics and heat transfer
80M25 Other numerical methods (thermodynamics) (MSC2010)
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