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A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation

Part of: Integral equations, integral transforms Partial differential equations, boundary value problems

Published online by Cambridge University Press:  09 January 2017

Hu Li  and
Jin Huang
Hu Li*
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
Jin Huang
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
*
*Corresponding author. Email:lihuxiwangzhixing@163.com (H. Li)
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Abstract

In this article, we consider the numerical solution for Poisson's equation in axisymmetric geometry. When the boundary condition and source term are axisymmetric, the problem reduces to solving Poisson's equation in cylindrical coordinates in the two-dimensional (r,z) region of the original three-dimensional domain S. Hence, the original boundary value problem is reduced to a two-dimensional one. To make use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular solution, which can be subtracted off, so that MQM can be used to solve the resulting Laplace problem, which possesses high accuracy order and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths hi is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by the splitting extrapolation algorithm (SEA). Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

Keywords

Mechanical quadrature methodsplitting extrapolation algorithmPoisson's equationa posteriori estimate

MSC classification

Secondary: 65N38: Boundary element methods 65R20: Integral equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 393 - 406
Copyright
Copyright © Global-Science Press 2017 

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