Some preconditioners for the iterative solution of Helmholtz's equation discretized with spectral Legendre collocation methods are introduced and studied. The preconditioners are based either on a finite element discretization of Helmholtz's equation on the spectral collocation mesh or on replacing the Sommerfeld-like boundary condition on a subset of the boundary with either Neumann or Dirichlet boundary conditions. The convergence rate of the resulting iterative methods is only mildly dependent on the spectral degree N and the wave number k.
Preconditioners for spectral discretizations of Helmholtz's equation with Sommerfeld boundary conditions / L.F. Pavarino, E. Zampieri. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - 190:40-41(2001), pp. 5341-5356.
Preconditioners for spectral discretizations of Helmholtz's equation with Sommerfeld boundary conditions
L.F. Pavarino;E. Zampieri
2001
Abstract
Some preconditioners for the iterative solution of Helmholtz's equation discretized with spectral Legendre collocation methods are introduced and studied. The preconditioners are based either on a finite element discretization of Helmholtz's equation on the spectral collocation mesh or on replacing the Sommerfeld-like boundary condition on a subset of the boundary with either Neumann or Dirichlet boundary conditions. The convergence rate of the resulting iterative methods is only mildly dependent on the spectral degree N and the wave number k.File | Dimensione | Formato | |
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