Bounded Error Schemes for the Wave Equation on Complex Domains

Abstract

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular waveguide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) we achieve a decrease of two orders of magnitude in the level of the L2 error.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1998
Accession Number
ADA356639

Entities

People

  • Adi Ditkowski
  • Amir Yefet
  • Saul Abarbanel

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Eigenvalues
  • Elastic Waves
  • Electric Fields
  • Engineering
  • Equations
  • Errors
  • Frequency
  • Geometry
  • Magnetic Fields
  • Mathematics
  • Shape
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)