Solution of Evolutionary Partial Differential Equations Using Adaptive Finite Differences with Pseudospectral Post-processing
| Autor: | L. S. Mulholland, Y. Qiu, D. M. Sloan |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Numerical Analysis
Partial differential equation Physics and Astronomy (miscellaneous) Applied Mathematics Coordinate system Mathematical analysis Finite difference Legendre pseudospectral method Computer Science Applications Computational Mathematics Transformation (function) Gauss pseudospectral method Modeling and Simulation Chebyshev pseudospectral method Pseudospectral optimal control Mathematics |
| Zdroj: | Journal of Computational Physics. 131:280-298 |
| ISSN: | 0021-9991 |
| Popis: | A coordinate transformation approach is described that enables pseudospectral methods to be applied efficiently to unsteady differential problems with steep solutions. The work is an extension of a method presented by Mulholland, Huang, and Sloan for the adaptive pseudospectral solution of steady problems. A coarse grid is generated by a moving mesh finite difference method that is based on equidistribution, and this grid is used to construct a time-dependent coordinate transformation. A sequence of spatial transformations may be generated at discrete points in time, or a single transformation may be generated as a continuous function of space and time. The differential problem is transformed by the coordinate transformation and then solved using a method that combines pseudospectral discretisation in space with a suitable integrator in time. Numerical results are presented for unsteady problems in one space dimension. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect