 A generalized finite difference method for solving elliptic interface problemsYanan Xing, Lina Song, Xiaoming He and Changxin Qiu Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 109-124 Abstract: In this article a generalized finite difference method (GFDM), which is a meshless method based on Taylor series expansions and weighted moving least squares, is proposed to solve the elliptic interface problem. This method turns the original elliptic interface problem to be two coupled elliptic non-interface subproblems. The solutions are found by solving coupled elliptic subproblems with sparse coefficient matrix, which significantly improves the efficiency for the interface problem, especially for the complex geometric interface. Furthermore, based on the key idea of GFDM which can approximate the derivatives of unknown variables by linear summation of nearby nodal values, we further develop the GFDM to deal with the elliptic problem with the jump interface condition which is related to the derivative of solution on the interface boundary. Four numerical examples are provided to illustrate the features of the proposed method, including the acceptable accuracy and the efficiency. Keywords: Meshless method; Generalized finite difference method; Elliptic interface problems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:109-124 DOI: 10.1016/j.matcom.2020.06.006 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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