One-step boundary knot method for discontinuous coefficient elliptic equations with interface jump conditions

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• 作者：Linlin Sun ; Wen Chen and Alexander H.-D. Cheng
• 刊名：Numerical Methods for Partial Differential Equations
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：32
• 期：6
• 页码：1509-1534
• 全文大小：3213K
• ISSN：1098-2426

文摘

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.