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Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…
This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast…
Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the…
In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…
The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the…
Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any…
An innovative and accurate dynamic Compact Thermal Model extraction method is proposed for multi-chip power electronics systems. It accounts for thermal coupling between multiple heat sources. Transient electro-thermal coupling can easily…
The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…
A thermal simulation methodology derived from the proper orthogonal decomposition (POD) and the Galerkin projection (GP), hereafter referred to as PODTherm-GP, is evaluated in terms of its efficiency and accuracy in a multi-core CPU. The GP…
This work develops a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two dimensional continua. The method employs Wachspress rational basis functions to construct conforming…
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations (PDEs) on polytopal meshes. We consider the Virtual Element Method (VEM) and different Discontinuous…
This paper develops a new 2D/3D stochastic closed-loop geothermal system with a random hydraulic conductivity tensor. We use the finite element method (FEM) and the Monte Carlo method (MCM) to discrete physical and probability spaces,…
An overall objective of energy efficiency in the built environment is to improve building and systems performances in terms of durability, comfort and economics. In order to predict, improve and meet a certain set of performance…
A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
This paper presents a method to simulate the thermal behavior of 3D systems using a graph neural network. The method discussed achieves a significant speed-up with respect to a traditional finite-element simulation. The graph neural network…