Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow
| Autor: | Orlando Astudillo, Ingeborg Bischoff-Gauss, Melitta Fiebig-Wittmaack, Wolfgang Börsch-Supan |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Poisson-like equation
Biconjugate gradient method 010504 meteorology & atmospheric sciences Tridiagonal matrix Operator (physics) Applied Mathematics Linear system Geometry Preconditioning 010103 numerical & computational mathematics 01 natural sciences Computational Mathematics Conjugate gradient method Convergence (routing) Convergence acceleration Applied mathematics Dynamic pressure 0101 mathematics Condition number Atmospheric model 0105 earth and related environmental sciences Mathematics Flat grids |
| Zdroj: | Journal of Computational and Applied Mathematics. 236(6):1435-1441 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2011.09.007 |
| Popis: | The convergence of many iterative procedures, in particular that of the conjugate gradient method, strongly depends on the condition number of the linear system to be solved. In cases with a large condition number, therefore, preconditioning is often used to transform the system into an equivalent one, with a smaller condition number and therefore faster convergence. For Poisson-like difference equations with flat grids, the vertical part of the difference operator is dominant and tridiagonal and can be used for preconditioning. Such a procedure has been applied to incompressible atmospheric flows to preserve incompressibility, where a system of Poisson-like difference equations is to be solved for the dynamic pressure part. In the mesoscale atmospheric model KAMM, convergence has been speeded up considerably by tridiagonal preconditioning, even though the system matrix is not symmetric and, hence, the biconjugate gradient method must be used. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect