Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform

This paper is concerned with a heat diffusion problem in a half-space which is motivated by the detection of material defects using thermal measurements. This problem is solved by inverting the Laplace transform with respect to time on a contour in the complex plane using an exponentially convergent quadrature rule. This leads to a finite number of time-independent problems, which can be solved in parallel using boundary integral equation methods. We provide a full numerical analysis of this scheme on compact time intervals. Our results are formulated in a way that they can easily be used for other diffusion problems in exterior or interior domains.

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