Domain Embedding/Controllability Methods for the Conjugate Gradient Solution of Wave Propagation Problems
The main goal of this paper is to discuss the numerical simulation of propagation phenomena for time harmonic electromagnetic waves by methods combining controllability and fictitious domain techniques. These methods rely on distributed Lagrangian multipliers, which allow the propagation to be simulated on an obstacle free computational region using regular finite element meshes essentially independent of the geometry of the obstacle and on a controllability formulation which leads to algorithms with good convergence properties to time-periodic solutions. This novel methodology has been validated by the solutions of test cases associated to non trivial geometries, possibly non-convex. The numerical experiments show that the new method performs as well as the method discussed in Bristeau et al.  where obstacle fitted meshes were used.
KeywordsDirect Numerical Simulation Conjugate Gradient Algorithm Wave Problem Saddle Point Problem Forward Wave
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- V. Bokil. Computational methods for wave propagation problems in unbounded domains. PhD thesis, University of Houston, Texas, USA, 2004.Google Scholar
- M. Fortin and R. Glowinski. Lagrangiens Augmentés. Dunod, Paris, 1982.Google Scholar
- R. Glowinski. Finite element methods for incompressible viscous flow, volume IX of Handbook of Numerical Analysis. North-Holland, Amsterdam, 2003.Google Scholar
- R. Glowinski and J. L. Lions. Exact and approximate controllability for distributed parameter systems (II). Acta Numerica, pages 159–333, 1995.Google Scholar
- R. Glowinski, T. Pan, T. Hesla, D. Joseph, and J. Periaux. A fictitious domain approach to the direct numerical simulation of incompressible fluid flow past moving rigid bodies: Application to particulate flow. J. Comp. Phys., pages 363–426, 2001.Google Scholar