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Numerical Algorithms

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14-08-2020 | Original Paper

A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension

Authors: Kamal Shanazari, Siamak Banei

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

We present a truly meshless method based on the thin plate splines for the numerical solution of the two dimensional forward-backward heat equation and give a robust formulation for the proposed method. The physical domain is divided into two subdomains each of which defines a forward or a backward subproblem. The resulting subproblems are treated by a radial basis function method for spatial dimension and a finite difference scheme for the time derivative followed by an iterative domain decomposition method to achieve a desired accuracy. In addition, we propose a combined use of an interpolation and the collocation method, in the iterations to update the interface boundary solution. Furthermore, we show that the time discretization scheme is unconditionally stable and convergent. Finally, some numerical examples will be presented to demonstrate the efficiency of the proposed method and some computational aspects will be discussed.

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Title: A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension
Authors: Kamal Shanazari
Siamak Banei
Publication date: 14-08-2020
Publisher: Springer US
Published in: Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-020-00952-3

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