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Volume 15, Issue 2
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems

Youngmok Jeon & Son-Young Yi

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 336-359.

Published online: 2022-03

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  • 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.

  • AMS Subject Headings

65N30, 65N38, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-336, author = {Jeon , Youngmok and Yi , Son-Young}, title = {The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0154}, url = {http://global-sci.org/intro/article_detail/nmtma/20355.html} }
TY - JOUR T1 - The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems AU - Jeon , Youngmok AU - Yi , Son-Young JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 336 EP - 359 PY - 2022 DA - 2022/03 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0154 UR - https://global-sci.org/intro/article_detail/nmtma/20355.html KW - Parabolic interface problem, hybrid difference method, immersed interface. AB -

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.

Youngmok Jeon & Son-Young Yi. (2022). The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems. Numerical Mathematics: Theory, Methods and Applications. 15 (2). 336-359. doi:10.4208/nmtma.OA-2021-0154
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