Related papers: A Reduced Order Model for Finite Element Method in…
Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…
In many industries, including aerospace and defense, waveform analysis is commonly conducted to compute the resonance of physical objects, with the Finite Element Method (FEM) being the standard approach. The Finite Difference Method (FDM)…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
We propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the…
In this work, we propose to use the Reduced-Basis Method (RBM) as a model order reduction approach to solve Maxwell's equations in electromagnetic (EM) scatterers based on plasma to build a metasurface, taking into account a parameter,…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
The continuous casting tundish plays a critical role as a metallurgical reactor in the continuous casting process, with its flow characteristics serving as a key parameter in the production of high-quality steel. These characteristics are…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
A Finite-Difference Time-Domain (FDTD) scheme with Perfectly Matched Layers (PMLs) is considered for solving the time-dependent Schr\"{o}dinger equation, and simulate the ionization of an electron initially bound to a one-dimensional…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…
We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
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 paper proposes an efficient FDTD technique for determining electromagnetic fields interacting with a finite-sized 2D and 3D periodic structures. The technique combines periodic boundary conditions---modelling fields away from the edges…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…