An embedded boundary method for the wave equation with discontinuous coefficients

Kreiss, H O; Petersson, N A

Title: An embedded boundary method for the wave equation with discontinuous coefficients

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Abstract

A second order accurate embedded boundary method for the two-dimensional wave equation with discontinuous wave propagation speed is described. The wave equation is discretized on a Cartesian grid with constant grid size and the interface (across which the wave speed is discontinuous) is allowed to intersect the mesh in an arbitrary fashion. By using ghost points on either side of the interface, previous embedded boundary techniques for the Neumann and Dirichlet problems are generalized to satisfy the jump conditions across the interface to second order accuracy. The resulting discretization of the jump conditions has the desirable property that each ghost point can be updated independently of all other ghost points, resulting in a fully explicit time-integration method. Numerical examples are given where the method is used to study electro-magnetic scattering of a plane wave by a dielectric cylinder. The numerical solutions are evaluated against the analytical solution due to Mie, and point-wise second order accuracy is confirmed.

Authors:: Kreiss, H O; Petersson, N A

Publication Date:: Mon Sep 26 00:00:00 EDT 2005

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 899432

Report Number(s):: UCRL-JRNL-215702
TRN: US200708%%288

DOE Contract Number:: W-7405-ENG-48

Resource Type:: Journal Article

Journal Name:: SIAM Journal of Scientific Computing, vol. 28, n/a, December 5, 2006, pp. 2054-2074

Additional Journal Information:: Journal Name: SIAM Journal of Scientific Computing, vol. 28, n/a, December 5, 2006, pp. 2054-2074

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 58 GEOSCIENCES; 42 ENGINEERING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; ANALYTICAL SOLUTION; DIELECTRIC MATERIALS; DIRICHLET PROBLEM; NUMERICAL SOLUTION; SCATTERING; VELOCITY; WAVE EQUATIONS; WAVE PROPAGATION

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                    Kreiss, H O, and Petersson, N A. An embedded boundary method for the wave equation with discontinuous coefficients.  United States: N. p., 2005. 
        Web.

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                    Kreiss, H O, & Petersson, N A. An embedded boundary method for the wave equation with discontinuous coefficients.  United States.

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                    Kreiss, H O, and Petersson, N A. 2005.  
        "An embedded boundary method for the wave equation with discontinuous coefficients".  United States.  https://www.osti.gov/servlets/purl/899432.

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@article{osti_899432,

  title        = {An embedded boundary method for the wave equation with discontinuous coefficients},

  author       = {Kreiss, H O and Petersson, N A},

  abstractNote = {A second order accurate embedded boundary method for the two-dimensional wave equation with discontinuous wave propagation speed is described. The wave equation is discretized on a Cartesian grid with constant grid size and the interface (across which the wave speed is discontinuous) is allowed to intersect the mesh in an arbitrary fashion. By using ghost points on either side of the interface, previous embedded boundary techniques for the Neumann and Dirichlet problems are generalized to satisfy the jump conditions across the interface to second order accuracy. The resulting discretization of the jump conditions has the desirable property that each ghost point can be updated independently of all other ghost points, resulting in a fully explicit time-integration method. Numerical examples are given where the method is used to study electro-magnetic scattering of a plane wave by a dielectric cylinder. The numerical solutions are evaluated against the analytical solution due to Mie, and point-wise second order accuracy is confirmed.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/899432},
  journal      = {SIAM Journal of Scientific Computing, vol. 28, n/a, December 5, 2006, pp. 2054-2074},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Mon Sep 26 00:00:00 EDT 2005},

  month        = {Mon Sep 26 00:00:00 EDT 2005}

}

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