Summary
In this paper we consider the numerical solution of a linear wave equation with discontinuous coefficients. We divide the computational domain into two subdomains and use explicit time difference scheme along with piecewise linear finite element approximations on semimatching grids. We apply boundary supported Lagrange multiplier method to match the solution on the interface between subdomains. The resulting system of linear equations of the “saddle-point” type is solved efficiently by a conjugate gradient method.
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References
M. O. Bristeau, E. J. Dean, R. Glowinski, V. Kwok, and J. Périaux. Exact controllability and domain decomposition methods with non-matching grids for the computation of scattering waves. In R. Glowinski, J. Périaux, and Z. Shi, editors, Domain Decomposition Methods in Sciences and Engineering, pages 291–307. John Wiley & Sons, 1997.
R. Dautray and J.-L. Lions. Mathematical Analysis and Numerical Methods for Science and Technology, volume 5. Springer-Verlag, 1992.
R. Glowinski and P. LeTallec. Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia, PA, 1989.
R. Glowinski. Finite element methods for incompressible viscous flow. In P. G. Ciarlet and J.-L. Lions, editors, Handbook of Numerical Analysis, Vol. IX, pages 3–1176. North-Holland, Amsterdam, 2003.
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Lapin, S., Lapin, A., Périaux, J., Jacquart, PM. (2008). A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients. In: Glowinski, R., Neittaanmäki, P. (eds) Partial Differential Equations. Computational Methods in Applied Sciences, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8758-5_7
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DOI: https://doi.org/10.1007/978-1-4020-8758-5_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8757-8
Online ISBN: 978-1-4020-8758-5
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