Abstract
Due to their rapid - often exponential - convergence as the number N of interpolation/collocation points is increased, polynomial pseudospectral methods are very efficient in solving smooth boundary value problems. However, when the solution displays boundary layers and/or interior fronts, this fast convergence will merely occur with very large N. To address this difficulty, we present a method which replaces the polynomial ansatz with a rational function r and considers the physical domain as the conformal map g of a computational domain. g shifts the interpolation points from their classical position in the computational domain to a problem-dependent position in the physical domain. Starting from a map by Bayliss and Turkel we have constructed a shift that can in principle accomodate an arbitrary number of fronts. Its parameters as well as the poles of r are optimized. Numerical results demonstrate how g best accomodates interior fronts while the poles also handle boundary layers.
Original language | English (US) |
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Pages (from-to) | 292-301 |
Number of pages | 10 |
Journal | Journal of Computational Physics |
Volume | 204 |
Issue number | 1 |
DOIs | |
State | Published - Mar 20 2005 |
Keywords
- Linear rational collocation
- Mesh generation
- Point shift optimization
- Pole optimization
- Two-point boundary value problems
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics