A Fictitious Domain Method with Operator Splitting for Wave Problems in Mixed Form
We propose a novel operator splitting scheme for time discretization, combined with a new fictitious domain method involving a distributed Lagrange multiplier for the solution of a wave scattering problem. The symmetrized operator splitting scheme decouples the propagation of the wave, and the enforcement of the Dirichlet boundary condition on the obstacle. We employ mixed finite elements for the substeps which propagate the wave. The accuracy of the method is demonstrated via a numerical example.
KeywordsDirichlet Boundary Condition Mixed Finite Element Wave Problem Finite Element Space Fictitious Domain
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- 1.V. Bokil. Computational methods for wave propagation problems on unbounded domains. PhD thesis, Department of Mathematics, University of Houston, In preparation.Google Scholar
- 2.M. O. Bristeau, V. Girault, R. Glowinski, T. W. Pan, J. Périaux, and Y. Xiang. On a fictitious domain method for flow and wave problems. In R. Glowinski, editor, Domain Decompostition methods in Sciences and Engineering, pages 361–386, 1997.Google Scholar
- 5.R. Glowinski, T. Hesla, D. D. Joseph, T. W. Pan, and J. Périaux. Distributed Lagrange multiplier methods for particulate flows. In M. O. Bristeau, G. Etgen, F. Fitzgibbin, J. L. Lions, Périaux J., and M. F. Wheeler, editors, Computational Science for the 21st century, pages 270–279, 1997.Google Scholar