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

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dc.contributor.authorLi, Chuan
dc.contributor.authorLong, Guangqing
dc.contributor.authorLi, Yiquan
dc.contributor.authorZhao, Shan
dc.contributor.otherNanning Normal University
dc.contributor.otherUniversity of California System
dc.contributor.otherUniversity of California Los Angeles
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2021-08-25T19:47:36Z
dc.date.available2021-08-25T19:47:36Z
dc.date.issued2021
dc.description.abstractThe 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.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationLi, C., Long, G., Li, Y., Zhao, S. (2021): Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients. Computation. 9(7).
dc.identifier.doi10.3390/computation9070079
dc.identifier.orcidhttps://orcid.org/0000-0002-3023-2107
dc.identifier.orcidhttps://orcid.org/0000-0003-2414-4781
dc.identifier.urihttp://ir.ua.edu/handle/123456789/8051
dc.languageEnglish
dc.language.isoen_US
dc.publisherMDPI
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectparabolic interface problem
dc.subjectvariable coefficient with discontinuity
dc.subjectalternating direction implicit (ADI)
dc.subjectghost fluid method (GFM)
dc.subjectmatched interface and boundary (MIB)
dc.subjectFINITE-ELEMENT METHODS
dc.subjectGHOST-FLUID METHODS
dc.subjectDISCONTINUOUS COEFFICIENTS
dc.subjectELLIPTIC-EQUATIONS
dc.subjectBOUNDARY METHOD
dc.subjectHEAT-EQUATION
dc.subjectDOMAINS
dc.subjectMathematics, Interdisciplinary Applications
dc.subjectMathematics
dc.titleAlternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficientsen_US
dc.typetext
dc.typeArticle

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