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We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a…
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…
In the context of estimating material properties of porous walls based on in-site measurements and identification method, this paper presents the concept of Optimal Experiment Design (OED). It aims at searching the best experimental…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Backward parabolic equations, such as the backward heat equation, are classical examples of ill-posed problems where solutions may not exist or depend continuously on the data. In this work, we study a least squares finite element method to…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…
In this paper, we develop an optimization-based systematic approach for the challenging, less studied, and important problem of optimal partitioning of multi-thermal zone buildings for the decentralized control. The proposed method consists…
The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas…