A characteristic domain decomposition and space-time local refinement method for first-order linear hyperbolic equations with interfaces

Hong Wang, Mohamed Al-Lawatia, Robert C. Sharpley

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We develop a characteristic-based domain decomposition and space-time local refinement method for first-order linear hyperbolic equations. The method naturally incorporates various physical and numerical interfaces into its formulation and generates accurate numerical solutions even if large time-steps are used. The method fully utilizes the transient and strongly local behavior of the solutions of hyperbolic equations and provides solutions with significantly improved accuracy and efficiency. Several numerical experiments are presented to illustrate the performance of the method and for comparison with other domain decomposition and local refinement schemes.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalNumerical Methods for Partial Differential Equations
Volume15
Issue number1
Publication statusPublished - Jan 1999

Fingerprint

Linear Hyperbolic Equation
Local Refinement
Domain Decomposition
Space-time
First-order
Decomposition
Hyperbolic Equations
Experiments
Numerical Experiment
Numerical Solution
Formulation

Keywords

  • Adaptive refinement; advection
  • Lagrangian methods; linear hyperbolic problems; local refinement techniques
  • Reaction equations; characteristic methods; domain decomposition methods; Eulerian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

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N2 - We develop a characteristic-based domain decomposition and space-time local refinement method for first-order linear hyperbolic equations. The method naturally incorporates various physical and numerical interfaces into its formulation and generates accurate numerical solutions even if large time-steps are used. The method fully utilizes the transient and strongly local behavior of the solutions of hyperbolic equations and provides solutions with significantly improved accuracy and efficiency. Several numerical experiments are presented to illustrate the performance of the method and for comparison with other domain decomposition and local refinement schemes.

AB - We develop a characteristic-based domain decomposition and space-time local refinement method for first-order linear hyperbolic equations. The method naturally incorporates various physical and numerical interfaces into its formulation and generates accurate numerical solutions even if large time-steps are used. The method fully utilizes the transient and strongly local behavior of the solutions of hyperbolic equations and provides solutions with significantly improved accuracy and efficiency. Several numerical experiments are presented to illustrate the performance of the method and for comparison with other domain decomposition and local refinement schemes.

KW - Adaptive refinement; advection

KW - Lagrangian methods; linear hyperbolic problems; local refinement techniques

KW - Reaction equations; characteristic methods; domain decomposition methods; Eulerian

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