3 papers
math.NA2026
Multiscale Mixed-Dimensional Simulation via Domain Decomposition and Non-Intrusive Neural Model Order Reduction
Nunzio Dimola, Piermario Vitullo, Paolo Zunino
Many computational models arising in science and engineering exhibit a multiscale structure that makes the assembly or direct solution of the global problem computationally prohibi…
math.NA2025
Neural Preconditioning via Krylov Subspace Geometry
Nunzio Dimola, Alessandro Coclite, Paolo Zunino
We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differ…
math.NA2025
Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner
Nunzio Dimola, Nicola Rares Franco, Paolo Zunino
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenge…