Heterogeneous optimized Schwarz methods for heat conduction in composites with thermal contact resistance

17.06.2025 15:00 – 16:00

In this talk, we analyze the optimized Schwarz Method (OSM) for solving the heterogeneous heat conduction problems with Thermal Contact Resistance (TCR), which significantly influences the heat transfer in composite materials. The OSM approach avoids ill-conditioned systems caused by high heterogeneity contrast and interface jumps through iterative subproblem solving. We evaluate three transmission conditions for OSM: standard Robin, scaled Robin, and two-sided Robin, by optimizing the free parameters via detailed analysis. Theoretical results reveal many new findings: (1) Large TCR accelerates OSM algorithm for all transmission conditions, leading to mesh independent convergence, which is very different from the case without TCR; (2) Heterogeneity contrast and thermal conductivity now simultaneously enhance convergence, unlike scenarios without TCR where only contrast matters and the heterogeneity contrast deteriorates the convergence behavior of the standard TCR. These insights extend to the many-subdomain case. Numerical experiments illustrate the theory and demonstrate the method’s potential for nonlinear engineering problems on irregular domains.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre