Abstract
A new efficient Chebyshev–Petrov–Galerkin (CPG) direct solver is presented for the second order elliptic problems in square domain where the Dirichlet and Neumann boundary conditions are considered. The CPG method is based on the orthogonality property of the kth-derivative of the Chebyshev polynomials. The algorithm differs from other spectral solvers by the high sparsity of the coefficient matrices: the stiffness and mass matrices are reduced to special banded matrices with two and four nonzero diagonals respectively. The efficiency and the spectral accuracy of CPG method have been validated.
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Elbarbary, E.M.E. Efficient Chebyshev–Petrov–Galerkin Method for Solving Second-Order Equations. J Sci Comput 34, 113–126 (2008). https://doi.org/10.1007/s10915-007-9161-9
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DOI: https://doi.org/10.1007/s10915-007-9161-9