The Static Condensation Reduced Basis Element Method for Parabolic Problems

We present a new approach for fast, flexible and reliable simulations of parameterdependent parabolic problems with a component-based geometry. The static condensation reduced basis element (SCRBE) is a domain decomposition method with reduced basis (RB) approximation at the intradomain level to populate a Schur complement at the interdomain level. In the Offline stage, for a library of archetype subdomains we train RB spaces for a family of time-dependent problems; in the Online stage we assemble instantiated subdomains and solve the transient problem for the full system using static condensation. We provide system-level a posteriori error bounds and we present various numerical results to demonstrate the accuracy, flexibility and computational efficiency of our approach.