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This work builds on the previous introduction [1] of a coupled experimental-computational system devised to fully characterize the thermal behavior of complex 3D submicron electronic devices. The new system replaces the laser-based surface…
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic…
This work presents a novel three-dimensional Crack Element Method (CEM) designed to model transient dynamic crack propagation in quasi-brittle materials efficiently. CEM introduces an advanced element-splitting algorithm that enables…
We analyze a discontinuous Galerkin FEM-BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart-Thomas finite elements…
We develop a locally conservative, finite element method for simulation of two-phase flow on quadrilateral meshes that minimize the number of degrees of freedom (DoFs) subject to accuracy requirements and the DoF continuity constraints. We…
This paper proposes a computationally efficient simulation strategy for cold thermal energy storage (TES) systems based on phase change material (PCM). Taking as a starting point the recent design of a TES system based on PCM, designed to…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
Numerical models based on the finite-element method (FEM) are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the $T$-$A$…
This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM…
We propose a reduced space mixed finite element method (MFEM) built on a Skinning Eigenmode subspace and material-aware cubature scheme. Our solver is well-suited for simulating scenes with large material and geometric heterogeneities in…
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method (DG-FEM) for…
An efficient time-stepping algorithm is proposed based on operator-splitting and the space-time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates…
Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics that also has fundamental implications for condensed matter physics. In this work, we use minimally…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
We report a new computational model for simulations of electromagnetic interactions with semiconductor quantum well(s) (SQW) in complex electromagnetic geometries using the finite difference time domain (FDTD) method. The presented model is…
Hyperbolic-parabolic partial differential equations are widely used for the modeling of complex, multiscale problems. High-order methods such as the discontinuous Galerkin (DG) scheme are attractive candidates for their numerical…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…