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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…
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…
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…
Robust Preconditioning of mixed-dimensional PDEs on 3d-1d domains coupled with Lagrange multipliers
Nunzio Dimola, Miroslav Kuchta, Kent-Andre Mardal +1
In the context of micro-circulation, the coexistence of two distinct length scales - the vascular radius and the tissue/organ scale - with a substantial difference in magnitude, po…
Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics
Nunzio Dimola, Alessandro Coclite, Giuseppe Fanizza +1
Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-B…