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Matrix equation solving of PDEs in polygonal domains using conformal mappings

  • Yue Hao und Valeria Simoncini EMAIL logo
Veröffentlicht/Copyright: 25. September 2021

Abstract

We explore algebraic strategies for numerically solving linear elliptic partial differential equations in polygonal domains. To discretize the polygon by means of structured meshes, we employ Schwarz–Christoffel conformal mappings, leading to a multiterm linear equation possibly including Hadamard products of some of the terms. This new algebraic formulation allows us to clearly distinguish between the role of the discretized operators and that of the domain meshing. Various algebraic strategies are discussed for the solution of the resulting matrix equation.

MSC 2010: 65F10; 65N22

Acknowledgment

We thank two anonymous reviewers for their careful reading and for several helpful remarks. The second author is a member of Indam-GNCS. Its support is gratefully acknowledged. Part of this work was also supported by the Grant AlmaIdea 2017-2020 – Università di Bologna. The first author is funded by the China Scholarship Council (Contract No. 201906180033) and by the National Natural Science Foundation of China (Grant Nos. 11471150, 11401281). Her work was performed during her visit at the Università di Bologna, Italy.

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Received: 2020-04-28
Revised: 2020-10-29
Accepted: 2020-10-29
Published Online: 2021-09-25
Published in Print: 2021-09-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 26.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jnma-2020-0035/pdf
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