Next Article in Journal
Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm
Previous Article in Journal
Wavelet Power Spectral Domain Functional Principal Component Analysis for Feature Extraction of Epileptic EEGs
Article

Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients

1
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
2
Department of Mathematics, Nanning Normal University, Nanning 530001, China
3
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
4
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Ravi P. Agarwal
Received: 2 June 2021 / Revised: 30 June 2021 / Accepted: 11 July 2021 / Published: 17 July 2021
The matched interface and boundary method (MIB) and ghost fluid method (GFM) are two well-known methods for solving elliptic interface problems. Moreover, they can be coupled with efficient time advancing methods, such as the alternating direction implicit (ADI) methods, for solving time-dependent partial differential equations (PDEs) with interfaces. However, to our best knowledge, all existing interface ADI methods for solving parabolic interface problems concern only constant coefficient PDEs, and no efficient and accurate ADI method has been developed for variable coefficient PDEs. In this work, we propose to incorporate the MIB and GFM in the framework of the ADI methods for generalized methods to solve two-dimensional parabolic interface problems with variable coefficients. Various numerical tests are conducted to investigate the accuracy, efficiency, and stability of the proposed methods. Both the semi-implicit MIB-ADI and fully-implicit GFM-ADI methods can recover the accuracy reduction near interfaces while maintaining the ADI efficiency. In summary, the GFM-ADI is found to be more stable as a fully-implicit time integration method, while the MIB-ADI is found to be more accurate with higher spatial and temporal convergence rates. View Full-Text
Keywords: parabolic interface problem; variable coefficient with discontinuity; alternating direction implicit (ADI); ghost fluid method (GFM); matched interface and boundary (MIB) parabolic interface problem; variable coefficient with discontinuity; alternating direction implicit (ADI); ghost fluid method (GFM); matched interface and boundary (MIB)
Show Figures

Figure 1

MDPI and ACS Style

Li, C.; Long, G.; Li, Y.; Zhao, S. Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients. Computation 2021, 9, 79. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9070079

AMA Style

Li C, Long G, Li Y, Zhao S. Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients. Computation. 2021; 9(7):79. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9070079

Chicago/Turabian Style

Li, Chuan, Guangqing Long, Yiquan Li, and Shan Zhao. 2021. "Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients" Computation 9, no. 7: 79. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9070079

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop