A Legendre Spectral Galerkin Method for the Biharmonic Dirichlet Problem
Copyright policy )A Legendre Spectral Galerkin Method for the Biharmonic Dirichlet Problem
The authors consider the Dirichlet problem for the biharmonic equation on a square. They use a Galerkin method based on tensor products of Legendre polynomials for stress and displacement. The matrix equation is solved by using the Schur complement, with the solution of a clamped-plate problem as a preconditioner.
- Colorado School of Mines United States
- University of Cyprus Cyprus
Schur complement matrix, Iterative numerical methods for linear systems, spectral Galerkin method, Numerical computation of matrix norms, conditioning, scaling, biharmonic Dirichlet problem, Linear systems, Polynomials, clamped-plate problem, Mathematical techniques, Galerkin methods, Spectral Galerkin method, Gradient methods, preconditioned conjugate gradient method, Boundary value problems for higher-order elliptic equations, Preconditioned conjugate gradient method, Spectral and related methods applied to problems in solid mechanics, Convergence of numerical methods, Biharmonic Dirichlet problem, Schur complement, Spectral, collocation and related methods for boundary value problems involving PDEs, Cholesky method, Plates, Algorithms
Schur complement matrix, Iterative numerical methods for linear systems, spectral Galerkin method, Numerical computation of matrix norms, conditioning, scaling, biharmonic Dirichlet problem, Linear systems, Polynomials, clamped-plate problem, Mathematical techniques, Galerkin methods, Spectral Galerkin method, Gradient methods, preconditioned conjugate gradient method, Boundary value problems for higher-order elliptic equations, Preconditioned conjugate gradient method, Spectral and related methods applied to problems in solid mechanics, Convergence of numerical methods, Biharmonic Dirichlet problem, Schur complement, Spectral, collocation and related methods for boundary value problems involving PDEs, Cholesky method, Plates, Algorithms
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