Seminar Details
2026-03-24 (14:00) : Alternating low-rank optimization for solving PDEs depending on geometric parameters
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Javier Bevia Ripoll (KU Leuven)
Abstract :
We seek an efficient computation of the solutions to a PDE posed on a domain dependent on geometric parameters, as encountered in, for example, multiscale topology optimization. The domain geometry adds an extra complexity to the problem, as the parametrization is implicitly present in the domain shape, but not explicitly in the PDE coefficients. We address this by introducing a smooth change of variables that maps each parameterized domain to a fixed reference domain, yielding a PDE with analytically parameterized coefficients. The analytic dependence guarantees that the matrix containing the discretization of the solutions across parameter values has exponentially decaying singular values, so the family of solutions admits a low‑rank representation. We compute this representation with an alternating least squares (ALS) scheme and present numerical experiments for a PDE depending on one and two geometric parameters to illustrate the effectiveness of the approach.