Poisson approach for evaluating numerical methods for the two-dimensional wave equation constrained to absorbing boundary conditions

• Published in: Applied mathematics and computation 2009-03, Vol.209 (2), p.273-284
• Main Authors: Oliveira, Jáuber C., Viloche Bazán, Fermín S.
• Format: Article
• Language: English
• Subjects: Chebyshev pseudospectral methods; Exact sciences and technology; Mathematical analysis; Mathematics; Measure and integration; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Partial differential equations; Poisson’s formulae; Real functions; Sciences and techniques of general use; Semi-exact solution; Wave equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2008.12.043

In order to assess the accuracy of several Chebyshev pseudospectral methods proposed in the literature for solving the two-dimensional wave equation, we propose a numerical procedure that produces a highly accurate numerical solution based on integration of Poisson’s formula by Gauss quadratures. The motivation for this procedure is that this solution has no errors due to reflections as it happens with all numerical techniques used to solve this problem. The only source of errors is the integration error, which decays quickly to zero if the integrand is smooth and the number of integration points is large enough. Based on this solution, we can evaluate easily the effects of introducing artificial boundary conditions. Many numerical methods depend on this approximation as a consequence of domain truncation.