Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems

Jean Paul Berrut, Hans Mittelmann

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageEnglish (US)
Pages (from-to)292-301
Number of pages10
JournalJournal of Computational Physics
Volume204
Issue number1
DOIs
StatePublished - 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

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