The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems

The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems

Year:    2022

Author:    Youngmok Jeon, Son-Young Yi

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 336–359

Abstract

We propose several immersed interface hybridized difference methods (IHDMs), combined with the Crank-Nicolson time-stepping scheme, for parabolic interface problems. The IHDM is the same as the hybrid difference method away from the interface cells, but the finite difference operators on the interface cells are modified to maintain the same accuracy throughout the entire domain. For the modification process, we consider virtual extensions of two sub-solutions in the interface cells in such a way that they satisfy certain jump equations between them. We propose several different sets of jump equations and their resulting discrete methods for one- and two-dimensional problems. Some numerical results are presented to demonstrate the accuracy and robustness of the proposed methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2021-0154

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 336–359

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Parabolic interface problem hybrid difference method immersed interface.

Author Details

Youngmok Jeon

Son-Young Yi