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

Journal Article · Tue Mar 02 04:00:00 EST 2004 · SIAM Journal on Scientific Computing

OSTI ID:883751

Kreiss, H O; Petersson, N A

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 883751
• Report Number(s): UCRL-JRNL-202686
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 4 Vol. 27; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ACCURACY
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
FLEXIBILITY
MAGNETIC FIELDS
STABILITY
WAVE EQUATIONS