Publications

C. Teng, M. Min, J. Wang, "Pseudospectral and Runge-Kutta-Nystrom Methods for Second-Order Wave Equations: Stable and Accurate Boundary Treatments," Preprint ANL/MCS-P4008-1212, December 2012. [pdf]

In this study we propose pseudospectral schemes for second-order wave equations subject to general boundary conditions, including Dirichlet, Neumann, Robin, and materials interface conditions. The boundary conditions are enforced in the schemes through a penalty method, and special attention is paid to analyzing the stability of the schemes. In addition we discuss how to consistently impose boundary conditions at the intermediate stages of the Runge-Kutta-Nystr ̈om method, to avoid order reduction. The proposed schemes can be used in multidomain computational frameworks for simulating wave problems on complex domains. Numerical validations are conducted, and the expected convergence is observed.