Numerical solution to the interface problem in a general domain using Moser’s deformation method

Eunhye Hong, Eunjung Lee, Younghoon Jung, Mikyoung Lim

Research output: Contribution to journalArticlepeer-review

Abstract

When seeking a solution to the interface problem, the potential theory to represent solution has been widely used. As the solution representation of the interface problem is only well-known for domains with simple inclusion, such as a disk, conformal mapping is often used to transform the arbitrary inclusion to a manageable inclusion to utilize the known solution representation. This paper proposes the construction of a conformal mapping based on Moser’s grid deformation method that generates a transformation with positive Jacobian determinant. By establishing an optimal control problem that minimizes the dissimilarity between transformed and reference images with desired constraints, we constructed an appropriate conformal mapping. Several numerical results prove the validity of our approach.

Original languageEnglish
Pages (from-to)379-401
Number of pages23
JournalJournal of Applied Mathematics and Computing
Volume65
Issue number1-2
DOIs
Publication statusPublished - 2021 Feb

Bibliographical note

Funding Information:
This work was funded by the National Research Foundation of Korea, NRF-2015R1A5A1009350 and NRF-2018R1D1A1B07042973.

Publisher Copyright:
© 2020, Korean Society for Informatics and Computational Applied Mathematics.

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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