Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 27, Issue 4, Pages 1141-1167Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040604728
Keywords
wave equation; stability; accuracy; embedded boundary
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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 TMz 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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