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Within the environmental context, numerical modeling is a promising approach to assessing the energy efficiency of buildings. Resilient buildings need to be designed, and capable of adapting to future extreme heat. Simulations are required…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…
This paper offers an approach to deal with parametrized nonlinear strongly coupled thermo-poroelasticity problems. The approach uses the LATIN-PGD method and extends previous work in multiphysics problems. Proper Generalized Decomposition…
We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…
A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…
Thermal tomography is an imaging technique for deducing information about the internal structure of a physical body from temperature measurements on its boundary. This work considers time-dependent thermal tomography modeled by a parabolic…
The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard…
This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…
This work introduces an ensemble parameter estimation framework that enables the Lumped Parameter Linear Superposition (LPLSP) method to generate reduced order thermal models from a single transient dataset. Unlike earlier implementations…
In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric…
A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the…
The estimation of wall thermal properties by \emph{in situ} measurement enables to increase the reliability of the model predictions for building energy efficiency. Nevertheless, retrieving the unknown parameters has an important…
An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations,…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…