Related papers: Optimisation-Based Coupling of Finite Element Mode…

We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…

This paper is concerned with the finite element discretization of the data driven approach according to arXiv:1510.04232 for the solution of PDEs with a material law arising from measurement data. To simplify the setting, we focus on a…

We present a domain decomposition method for the fast simulation of large lattice structures described by level set functions. The method does not rely on homogenization or multiscale techniques, and therefore avoids their underlying…

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a…

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of…

This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…

A dynamical low-rank approximation is developed for reduced-order modeling (ROM) of the filtered density function (FDF) transport equation, which is utilized for large eddy simulation (LES) of turbulent reacting flows. In this methodology,…

We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

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…

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…