Perfectly Matched Layers Formulation and Stability Analysis of Heat Conduction Equation
Journal Title: 河南科技大学学报（自然科学版） - Year 2017, Vol 38, Issue 5
Abstract
In order to solve heat-conduction equation in unbounded space, a perfectly matched layer ( PML) formulation by introducing several auxiliary variables was proposed based on the Laplace transform. The stability of the PML equations was obtained by analyzing the sign of the real part of the eigenvalue of the partial differential operator and the completeness of eigenvectors. The Cauchy problem for the PML formulation with constant coefficient in two-dimension space is weakly stable. The Cauchy problem for the PML formulation with constant coefficient in three-dimension space is strongly stable. The numerical experiment results show that the the maximum value of absolute error of the PML formulation of heat-conduction equation is about 1. 5 × 10-3.The maximum value of absolute errors of the classical Dirichlet boundary condition and the Neumann boundary condition are about 2. 5 × 10-2and 3. 0 × 10-2respectively. Hence, the PML formulation of heat-conduction equation improves the accuracy of the numerical solution.
Authors and Affiliations
Xiaohua WANG, Wenfeng PAN
Keywords
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