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Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…
In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by…
The envelope theory is a simple technique to obtain approximate, but reliable, solutions of many-body systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
Pipeline transport of dense-phase CO2-rich mixtures is a crucial component in carbon capture and storage (CCS). Accurate modeling requires coupling of fluid dynamics and thermodynamics, especially during transient events such as…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
In this Letter we present a new method, called chain equation method (CEM), for computing a cascade of distinct modes in a two-dimensional weakly nonlinear wave system generated by narrow frequency band excitation. The CEM is a means for…
The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological,…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
We examine volume computation of general-dimensional polytopes and more general convex bodies, defined as the intersection of a simplex by a family of parallel hyperplanes, and another family of parallel hyperplanes or a family of…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
Two primary types of numerical instabilities often occur in low-order finite element method (FEM) analyses of thermo-hydro-mechanical (THM) phenomena: (1) pressure oscillations arising improper interpolation of pressure and displacement…
Multiphase systems are ubiquitous in engineering, biology, and materials science, where understanding their complex interactions and rheological behavior is crucial for advancing applications ranging from emulsion stability to cellular…
In conventional molecular simulation, metastable structures often survive over considerable computational time, resulting in difficulties in simulating equilibrium states. In order to overcome this difficulty, here we propose a newly…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
We used numerical simulations based on the finite element method (FEM) to calculate both the amplitude and phase information of the scattered electric field from random rough surfaces, which can be directly compared to ellipsometric…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
The practically unlimited high-dimensional composition space of high-entropy materials (HEMs) has emerged as an exciting platform for functional materials design and discovery. However, the identification of stable and synthesizable HEMs…