Geodesic
Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction
Gigante, Giacomo1 ; Vergara, Christian2
1 Dipartimento di Ingegneria gestionale, dell’informazione e della produzione, Università degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italy
2 MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1597-1615

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In this work, we focus on the Optimized 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 Gigante and Vergara (Numer. Math. 131 (2015) 369–404). 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.

DOI : 10.1051/m2an/2018039
Classification : 65N12, 65B99
Keywords: Optimized Schwarz Method, cylindrical domains, geometric multiscale, Bessel functions

Gigante, Giacomo 1 ; Vergara, Christian 2

1 Dipartimento di Ingegneria gestionale, dell’informazione e della produzione, Università degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italy
2 MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy 
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     author = {Gigante, Giacomo and Vergara, Christian},
     title = {Optimized {Schwarz} methods for the coupling of cylindrical geometries along the axial direction},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1597--1615},
     publisher = {EDP-Sciences},
     volume = {52},
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     year = {2018},
     doi = {10.1051/m2an/2018039},
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Gigante, Giacomo; Vergara, Christian. Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1597-1615. doi: 10.1051/m2an/2018039

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