One‐step boundary knot method for discontinuous coefficient elliptic equations with interface jump conditions |
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| Authors: | Linlin Sun Wen Chen Alexander H.‐D. Cheng |
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| Affiliation: | 1. State Key Laboratory of Hydrology‐Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, China;2. Department of Computing Science and Statistics, School of Sciences, Nantong University, Nantong, People's Republic of China;3. Department of Civil Engineering, School of Engineering, University of Mississippi, University, MS |
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| Abstract: | This study makes the first attempt to apply the boundary knot method (BKM), a meshless collocation method, to the solution of linear elliptic problems with discontinuous coefficients, also known as the elliptic interface problems. The additional jump conditions are usually required to be prescribed at the interface which is used to maintain the well‐posedness of the considered problem. To solve the problem efficiently, the original governing equation is first transformed into an equivalent inhomogeneous modified Helmholtz equation in the present numerical formulation. Then the computational domain is divided into several subdomains, and the solution on each subdomain is approximated using the BKM approach. Unlike the conventional two‐step BKM, this study presents a one‐step BKM formulation which possesses merely one influence matrix for inhomogeneous problems. Several benchmark examples with various discontinuous coefficients have been tested to demonstrate the accuracy and efficiency of the present BKM scheme. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1509–1534, 2016 |
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| Keywords: | anisotropic coefficients boundary knot method discontinuous coefficient elliptic equation variable coefficients |
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