A second order accurate embedded boundary method for the wave equation with Dirichlet data

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The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also ... continued below

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Kreiss, H O & Petersson, N A March 2, 2004.

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The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.

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PDF-file: 29 pages; size: 1.3 Mbytes

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  • Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 27; Journal Issue: 4

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  • Report No.: UCRL-JRNL-202686
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 883751
  • Archival Resource Key: ark:/67531/metadc892242

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • March 2, 2004

Added to The UNT Digital Library

  • Sept. 23, 2016, 2:42 p.m.

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  • Dec. 1, 2016, 7:17 p.m.

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Kreiss, H O & Petersson, N A. A second order accurate embedded boundary method for the wave equation with Dirichlet data, article, March 2, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc892242/: accessed April 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.