Abstract
The research is focused on the numerical analysis of the inverse Poisson problem, namely the identification of the unknown (input) load source function, being the right-hand side function of the second order differential equation. It is assumed that the additional measurement data of the solution (output) function are available at few isolated locations inside the problem domain. The problem may be formulated as the non-linear optimisation problem with inequality constrains.
The proposed solution approach is based upon the well-known Monte Carlo concept with a random walk technique, approximating the solution of the direct Poisson problem at selected point(s), using series of random simulations. However, since it may deliver the linear explicit relation between the input and the output at measurement locations only, the objective function may be analytically differentiated with the respect to unknown load parameters. Consequently, they may be determined by the solution of the small system of algebraic equations. Therefore, drawbacks of traditional optimization algorithms, computationally demanding, time-consuming and sensitive to their parameters, may be removed. The potential power of the proposed approach is demonstrated on selected benchmark problems with various levels of complexity.
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Milewski, S. (2021). Semi-analytical Monte Carlo Optimisation Method Applied to the Inverse Poisson Problem. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12745. Springer, Cham. https://doi.org/10.1007/978-3-030-77970-2_19
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