A Collocation Method with Exact Imposition of Mixed Boundary Conditions

Authors:
Zhong-Qing Wang;Li-Lian Wang
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, People's Republic of China 200234 and Scientific Computing Key Laboratory, Shanghai Universities, Shanghai, People's Republic of Ch ...;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371
Venue:
Journal of Scientific Computing
Year:
2010

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Abstract

In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Dirichlet boundary conditions. We apply the collocation method to some model PDEs and the time-harmonic Helmholtz equation, and demonstrate its spectral accuracy and efficiency by various numerical examples.