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PIMOL: The Finite Difference Method of Lines Based on the Precise Integration Method for an Arbitrary Irregular Domain

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Abstract

The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines (PIMOL), which is developed and used to solve the ordinary differential equation (ODE) systems based on the finite difference method of lines and the precise integration method. The irregular domain problem is mainly discussed in this paper. Three classical examples of Poisson’s equation problems are given, including one regular and two irregular domain examples. The PIMOL reduces a semi-discrete ODE problem to a linear algebraic matrix equation and does not require domain mapping for treating the irregular domain problem. Numerical results show that the PIMOL is a powerful method.

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  1. Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Yongjun Xu

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  1. Yongjun Xu
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Correspondence to Yongjun Xu.

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Xu, Y. PIMOL: The Finite Difference Method of Lines Based on the Precise Integration Method for an Arbitrary Irregular Domain. Acta Mech. Solida Sin. 33, 823–835 (2020). https://doi.org/10.1007/s10338-020-00165-0

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  • DOI: https://doi.org/10.1007/s10338-020-00165-0

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