Abstract
The paper proposes the concept of eliminating the explicit computation of singular integrals appearing in the parametric integral equation system (PIES) used to simulate the steady-state temperature field distribution. These singularities can be eliminated by regularizing the PIES formula with the auxiliary regularization function. Contrary to existing regularization methods that only eliminate strong singularities, the proposed approach is definitely more comprehensive due to the fact that it eliminates all strong and weak singularities. As a result, all singularities associated with PIES's integral functions can be removed. A practical aspect of the proposed regularization is the fact that all integrals appearing in the resulting formula can be evaluated numerically with a standard Gauss-Legendre quadrature rule. Simulation results indicate the high accuracy of the proposed algorithm.
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Szerszeń, K., Zieniuk, E., Bołtuć, A., Kużelewski, A. (2021). Comprehensive Regularization of PIES for Problems Modeled by 2D Laplace’s Equation. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_38
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DOI: https://doi.org/10.1007/978-3-030-77961-0_38
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