Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction. (English) Zbl 1407.65260
Summary: In this work, we focus on the otimized Schwarz method for circular flat interfaces and geometric heterogeneous coupling arising when cylindrical geometries are coupled along the axial direction. In the first case, we provide a convergence analysis for the diffusion-reaction problem and jumping coefficients and we apply the general optimization procedure developed in [the authors, Numer. Math. 131, No. 2, 369–404 (2015; Zbl 1326.65169)]. In the numerical simulations, we discuss how to choose the range of frequencies in the optimization and the influence of the finite element and projection errors on the convergence. In the second case, we consider the coupling between a three-dimensional and a one-dimensional diffusion-reaction problem and we develop a new optimization procedure. The numerical results highlight the suitability of the theoretical findings.
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
Citations:
Zbl 1326.65169Software:
FreeFem++References:
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