抛物界面问题的浸入界面杂交差分法

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI:10.4208/nmtma.oa-2021-0154

Youngmok Jeon null, Son-Young Yi

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引用次数: 0

摘要

针对抛物型界面问题，我们提出了几种浸入式界面混合差分方法（IHDM），并结合Crank-Nicolson时间步进方案。IHDM与远离界面单元的混合差分方法相同，但对界面单元上的有限差分算子进行了修改，以在整个域中保持相同的精度。对于修改过程，我们考虑界面单元中两个子解的虚拟扩展，使它们满足它们之间的某些跳跃方程。针对一维和二维问题，我们提出了几种不同的跳跃方程组及其离散方法。给出了一些数值结果，以证明所提出方法的准确性和稳健性。AMS受试者分类：65N30、65N38、65N50

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The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems

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 oneand two-dimensional problems. Some numerical results are presented to demonstrate the accuracy and robustness of the proposed methods. AMS subject classifications: 65N30, 65N38, 65N50

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.