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.
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The work of the first author is supported in part by National Basic Research Project of China N.2005CB321701, NSF of China, N.10771142, Science and Technology Commission of Shanghai Municipality Grant, N.075105118, Shuguang Project of Shanghai Education Commission, N.08SG45, Shanghai Leading Academic Discipline Project N.S30405 and The Fund for E-institute of Shanghai Universities N.E03004.
The work of the second author is partially supported by AcRF Tier 1 Grant RG58/08, Singapore MOE Grant # T207B2202, and Singapore # NRF2007IDM-IDM002-010.
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Wang, ZQ., Wang, LL. A Collocation Method with Exact Imposition of Mixed Boundary Conditions. J Sci Comput 42, 291–317 (2010). https://doi.org/10.1007/s10915-009-9325-x
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DOI: https://doi.org/10.1007/s10915-009-9325-x