Related papers: Efficient and certified solution of parametrized o…
This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…
The discrete empirical interpolation method (DEIM) is a well-established approach, widely used for state reconstruction using sparse sensor/measurement data, nonlinear model reduction, and interpretable feature selection. We introduce the…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…
The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM…
Discrete Empirical Interpolation Method (DEIM) is a simple and effective method for reconstructing a function from its incomplete pointwise observations. However, applying DEIM to functions with physically constrained ranges can produce…
Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
The present contribution aims at developing a non-overlapping Domain Decomposition (DD) approach to the solution of acoustic wave propagation boundary value problems based on the Helmholtz equation, on both bounded and unbounded domains.…
This work investigates transmission conditions for the domain decomposition-based coupling of subdomain-local models using the non-overlapping Schwarz alternating method (NO-SAM). Building on prior efforts involving overlapping SAM (O-SAM),…
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…
In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be…
Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type diffuse interface model in an optimised way using model order…
Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…
In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…
The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…
For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
Modelling of physical systems may be a challenging task when it requires solving large sets of numerical equations. This is the case of photovoltaic (PV) systems which contain many PV modules, each module containing several silicon cells.…