An Investigation of Radial Basis Function-Finite Difference (RBF-FD) Method for Numerical Solution of Elliptic Partial Differential Equations

Suranon Yensiri and Ruth J. Skulkhu
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Suranon Yensiri: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Ruth J. Skulkhu: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Mathematics, 2017, vol. 5, issue 4, 1-14

Abstract: The Radial Basis Function (RBF) method has been considered an important meshfree tool for numerical solutions of Partial Differential Equations (PDEs). For various situations, RBF with infinitely differentiable functions can provide accurate results and more flexibility in the geometry of computation domains than traditional methods such as finite difference and finite element methods. However, RBF does not suit large scale problems, and, therefore, a combination of RBF and the finite difference (RBF-FD) method was proposed because of its own strengths not only on feasibility and computational cost, but also on solution accuracy. In this study, we try the RBF-FD method on elliptic PDEs and study the effect of it on such equations with different shape parameters. Most importantly, we study the solution accuracy after additional ghost node strategy, preconditioning strategy, regularization strategy, and floating point arithmetic strategy. We have found more satisfactory accurate solutions in most situations than those from global RBF, except in the preconditioning and regularization strategies.

Keywords: numerical partial differential equations (PDEs); radial basis function-finite difference (RBF-FD) method; ghost node; preconditioning; regularization; floating point arithmetic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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