Name
Abstract | ||
|---|---|---|
Quadratic spline collocation methods are formulated for the numerical solution of the Helmholtz equation in the unit square subject to non-homogeneous Dirichlet, Neumann and mixed boundary conditions, and also periodic boundary conditions. The methods are constructed so that they are: (a) of optimal accuracy, and (b) compact; that is, the collocation equations can be solved using a matrix decomposition algorithm involving only tridiagonal linear systems. Using fast Fourier transforms, the computational cost of such an algorithm is O(N^2logN) on an NxN uniform partition of the unit square. The results of numerical experiments demonstrate the optimal global accuracy of the methods as well as superconvergence phenomena. In particular, it is shown that the methods are fourth-order accurate at the nodes of the partition. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcp.2010.12.041 | J. Comput. Physics |
Keywords | Field | DocType |
matrix decomposition algorithm,collocation equation,compact optimal quadratic spline,numerical experiment,periodic boundary condition,quadratic spline collocation method,nxn uniform partition,helmholtz equation,optimal accuracy,mixed boundary condition,optimal global accuracy,numerical solution,fast fourier transforms,linear system,fast fourier transform,superconvergence,collocation method,matrix decomposition | Spline (mathematics),Boundary value problem,Mathematical optimization,Mathematical analysis,Orthogonal collocation,Superconvergence,Periodic boundary conditions,Helmholtz equation,Unit square,Mathematics,Collocation | Journal |
Volume | Issue | ISSN |
230 | 8 | Journal of Computational Physics |
Citations | PageRank | References |
4 | 0.46 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Graeme Fairweather | 1 | 165 | 40.42 |
| Andreas Karageorghis | 2 | 204 | 47.54 |
| Jon Maack | 3 | 4 | 0.46 |