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An efficient reformulation of the difference potentials method for interface problems with a jump in the source term

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Abstract

This study proposes a new approach to reformulate the method of difference potentials (DPM) for linear interface problems whose solutions or their derivatives may be discontinuous due to singular sources across the interface. Eliminating the need to construct and solve the overdetermined system, which is required in the standard DPM, is the main advantage of this efficient reformulation of the difference potentials method (ERDPM), which decreases the computational cost and complexity of the method for governing interface problems. We use the proposed method to solve the steady-state convection–diffusion equation in two-dimensional geometries. Numerical results are obtained by ERDPM and compared with solutions obtained by DPM to validate the robustness, accuracy, convergence rates, and efficiency of the proposed method.

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Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

This work is based upon research funded by Iran National Science Foundation (INSF) under project No. 4004903.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 350, Hafez Ave, Valiasr Square, Tehran, 1591634311, Iran

    Mahboubeh Tavakoli Tameh & Fatemeh Shakeri

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  1. Mahboubeh Tavakoli Tameh
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  2. Fatemeh Shakeri
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Contributions

M.T. and F.Sh. contributed to the design and implementation of the research, to the analysis of the results, and to the writing of the manuscript.

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Correspondence to Fatemeh Shakeri.

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Tavakoli Tameh, M., Shakeri, F. An efficient reformulation of the difference potentials method for interface problems with a jump in the source term. Z. Angew. Math. Phys. 75, 119 (2024). https://doi.org/10.1007/s00033-024-02263-2

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  • DOI: https://doi.org/10.1007/s00033-024-02263-2

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