相关论文: POD-Galerkin Model Order Reduction for Parametrize…

We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the…

We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…

This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…

We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully…

A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…

The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-Cahn equation using distributed controls that satisfy…

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…

In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of…

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space-time ROM for linear dynamical problems has been developed, which further reduces the…

This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in…

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…

We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general…

We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with…

Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…