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Speaker: Rishi Pawar, Program in Applied Mathematics
Title: Surrogate-based Partitioned Scheme for a Model Advection-Diffusion Transmission Problem
Abstract: In this presentation we develop and demonstrate a new surrogate-based partitioned scheme for a model advection-diffusion transmission problem. The work is motivated by the Implicit Value Recovery (IVR) partitioned method in which the interface flux is approximated by the dual Schur complement of a discrete monolithic formulation of the coupled problem. Unless the discretized equations employ lumped mass matrices, forming and solving the Schur complement equation for the flux adds nontrivial computational cost at every time step.
To reduce the computational cost we replace the Schur complement equation by an efficient flux surrogate. The latter is based on the Operator Inference algorithm (OpInf) which learns the dynamic behavior of the interface flux from a suitable training set during an offline training phase. The inferred operator is then used during the online stage to provide accurate flux approximations for each subdomain problem. Numerical examples illustrate the potential of the approach.