A Collocation Method with Exact Imposition of Mixed Boundary Conditions | Zendy

Zhongqing Wang | Zendy; Li-Lian Wang | Zendy

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A Collocation Method with Exact Imposition of Mixed Boundary Conditions

Author(s) -

Zhongqing Wang,

Li-Lian Wang

Publication year - 2009

Publication title -

journal of scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.53

H-Index - 80

eISSN - 1573-7691

pISSN - 0885-7474

DOI - 10.1007/s10915-009-9325-x

Subject(s) - mathematics , collocation method , orthogonal collocation , gaussian quadrature , quadrature (astronomy) , collocation (remote sensing) , singular boundary method , mathematical analysis , boundary value problem , dirichlet boundary condition , helmholtz equation , spectral method , boundary (topology) , nyström method , boundary element method , differential equation , computer science , finite element method , ordinary differential equation , physics , engineering , machine learning , electrical engineering , thermodynamics

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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