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Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
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DOI：10.1137/S106482750139964X.png)
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摘要
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We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modi. cations of it which produce optimal (fourth-) order approximations. For the solution of the collocation equations, we formulate matrix decomposition algorithms, fast direct methods which employ fast Fourier transforms and require O(N-2 logN) operations on an N x N uniform partition of the unit square. A computational study confirms the published analysis for the Dirichlet problem and indicates that similar results hold for Neumann, mixed, and periodic boundary conditions. The numerical results also exhibit superconvergence phenomena not reported in earlier studies.
Keyword:
spline collocation
Helmholtz equation
boundary conditions
tensor product
fast Fourier transforms
convergence rates
superconvergence
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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