105 citations · 168 across the 10 of their papers we have counts for
12 papers
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…
Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains
Luca Heltai, Paolo Zunino
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the smal…
Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression
Ludovica Cicci, Stefania Fresca, Mengwu Guo +2
Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving t…
Approximation bounds for convolutional neural networks in operator learning
Nicola Rares Franco, Stefania Fresca, Andrea Manzoni +1
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy…
Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical op…
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations
Nicola R. Franco, Andrea Manzoni, Paolo Zunino
Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map.…
Iterative splitting schemes for a soft material poromechanics model
Jakub W. Both, Nicolas A. Barnafi, Florin A. Radu +2
We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering t…
Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers
Miroslav Kuchta, Federica Laurino, Kent-Andre Mardal +1
Coupled partial differential equations defined on domains with different dimensionality are usually called mixed dimensional PDEs. We address mixed dimensional PDEs on three-dimens…
A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model
Ilona Ambartsumyan, Eldar Khattatov, Ivan Yotov +1
We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is…
Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid
Giovanni P. Galdi, Giusy Mazzone, Paolo Zunino
We study inertial motions of the coupled system, S, constituted by a rigid body containing a cavity that is completely filled with a viscous liquid. We show that for data of arbitr…
Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
Martina Bukac, Ivan Yotov, Rana Zakerzadeh +1
We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these…
Explicit partitioning strategies for the interaction between a fluid and a multilayered poroelastic structure: an operator-splitting approach
Martina Bukac, Paolo Zunino, Ivan Yotov
We study the interaction between an incompressible, viscous, Newtonian fluid and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material.…