Roghayeh Sarah Ebrahim Nataj, University of Southern Denmark, will present her work on "Stable high-order methods for multi-physics problems"

Abstract:
Multi-physics problems arise in many engineering applications, such as conjugate heat transfer (CHT), thermal management, and simulation-driven design of thermal systems. In this talk, I present stable high-order methods for such problems, with particular emphasis on CHT problems. I first discuss a partitioned coupling framework based on summation-by-parts operators and simultaneous approximation terms (SBP-SAT) for coupled advection--diffusion and diffusion equations, in which interface and boundary conditions are imposed weakly to obtain provably stable scheme. I then turn to transient topology optimization, where the goal is to determine an optimal material distribution in a domain governed by heat equation and design constraints. Since each optimization step requires repeated forward and adjoint solves over the full time horizon, the problem leads to large linear systems and needs significant computational cost. To address this challenge, I present a space--time spectral element SBP-SAT method that treats time as an additional dimension and solves for all time levels simultaneously. The resulting framework provides an accurate and efficient approach for simulation-driven design, with improved accuracy and a more favorable time-to-solution than conventional time-marching methods.