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The optimized order 2 method: Application to convection-diffusion problems. (English) Zbl 1050.65124
Summary: We present an iterative, non-overlapping domain decomposition method for solving the convection-diffusion equation. A reformulation of the problem leads to an equivalent problem where the unknowns are on the boundary of the subdomains. The solving of this interface problem by a Krylov-type algorithm is done by the solving of independent problems in each subdomain, so it permits to use efficiently parallel computation. In order to have very fast convergence, we use differential interface conditions of order 1 in the normal direction and of order 2 in the tangential direction to the interface, which are optimized approximations of absorbing boundary conditions [C. Japhet, Méthode de décomposition de domaine et conditions aux limites artificielles en mécanique des fluides: méthode optimisée d’ordre 2, Thèse de Doctorat, Université Paris XIII (1998); F. Nataf and F. Rogier, Math. Models Methods Appl. Sci. 5, 67–93 (1995; Zbl 0826.65102)] . Numerical tests illustrate the efficiency of the method.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y05 Parallel numerical computation
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