Related papers: A reduced order model for domain decompositions wi…

We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…

In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…

Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

In this paper, we revisit the nonoverlapping domain decomposition methods for solving elliptic problems with high contrast coefficients. Some interesting results are discovered. We find that the Dirichlet-Neumann algorithm and Robin-Robin…

We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture…

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and…

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…

We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…

In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…

The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…