Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE
نویسنده
چکیده
Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this same approach to time-independent PDE of the form Lu = f , where L is an elliptic differential operator. Numerical results demonstrate the effectiveness of this approach for Poisson’s equation and the Helmholtz equation in two dimensions.
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A Multigrid Block Krylov Subspace Spectral Method for Variable-Coefficient Elliptic PDE
Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...
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