Name
Title | ||
|---|---|---|
Matrix Decomposition Algorithms for Modified Spline Collocation for Helmholtz Problems |
Abstract | ||
|---|---|---|
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 modifications 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(N2 log N) operations on an N × 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. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1137/S106482750139964X | SIAM Journal on Scientific Computing |
Keywords | Field | DocType |
matrix decomposition algorithms,n uniform partition,unit square,collocation equation,dirichlet problem,nodal cubic spline collocation,periodic boundary condition,modified spline collocation,various boundary value problem,helmholtz equation,n2 log,computational study,helmholtz problems,matrix decomposition,superconvergence,boundary conditions,fast fourier transforms,tensor product | Boundary value problem,Mathematical optimization,Dirichlet problem,Mathematical analysis,Orthogonal collocation,Matrix decomposition,Algorithm,Helmholtz equation,Unit square,Collocation method,Mathematics,Collocation | Journal |
Volume | Issue | ISSN |
24 | 5 | 1064-8275 |
Citations | PageRank | References |
7 | 1.36 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Bialecki | 1 | 114 | 18.61 |
| Graeme Fairweather | 2 | 142 | 33.42 |
| Andreas Karageorghis | 3 | 204 | 47.54 |