Towards efficient interface conditions for a Schwarz domain decomposition algorithm for an advection equation with biharmonic diffusion

Authors:
Elise Nourtier-Mazauric;Eric Blayo
Affiliations:
Laboratoire Jean Kuntzmann, INRIA Rhône-Alpes and Université Joseph Fourier, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France;Laboratoire Jean Kuntzmann, INRIA Rhône-Alpes and Université Joseph Fourier, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

This paper addresses the problem of deriving efficient interface conditions for solving biharmonic diffusion-advection equations using a Schwarz global-in-time domain decomposition algorithm. General interface conditions are proposed, which lead to well-posed problems on each subdomain. The equation is then studied in the simplified 1D case. Exact non-local absorbing boundary conditions are derived, and are approximated by optimized local interface conditions, the efficiency of which is illustrated by numerical experiments.