On the influence of curvature on transmission conditions
نویسندگان
چکیده
Domain decomposition methods are both highly successful parallel solvers and also important modeling tools, since problems in subdomains can be treated by adapted methods to the physics in each subdomain. Subdomain boundaries are therefore rarely straight lines. The focus of this paper is to study the influence of curvature on transmission conditions used in optimized Schwarz methods. For straight interfaces and simple geometries, optimized interface conditions are typically determined using Fourier analysis, see for example [4] and references therein. Asymptotically, these optimized conditions are still valid for curved interfaces, as shown in [5, 6]. Since however the curvature is the most important information for a smooth curve, we want to study in this paper if and how the interface curvature influences the constants in the optimized parameters. We consider the model problem
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