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The determination of liquid phase equilibria plays an important role in chemical process simulation. This work presents a generalization of an approach called the convex envelope method (CEM), which constructs all liquid phase equilibria…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
For the calculation of complex neutral/ionized gas phase chemical equilibria, we present a semi-analytical versatile and efficient computer program, called FastChem. The applied method is based on the solution of a system of coupled…
Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo…
Parallel tempering Monte Carlo simulations have been applied to a variety of systems presenting rugged free-energy landscapes. Despite this, its efficiency depends strongly on the temperature set. With this query in mind, we present a…
This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…
We introduce the harmonic virtual element method (harmonic VEM), a modification of the virtual element method (VEM) for the approximation of the 2D Laplace equation using polygonal meshes. The main difference between the harmonic VEM and…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…
If a finite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during finite element…
equilibrium-c (eqc) is a program for computing the composition of gas mixtures in chemical equilibrium. In typical usage, the program is given a known thermodynamic state, such as fixed temperature and pressure, as well as an initial…
In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that…
We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or…
The state of the art in electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) has advanced significantly in the last few years. These have included understanding function spaces that must be used to represent sources and fields…
Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a…
A flexible treatment for gas- and aerosol-phase chemical processes has been developed for models of diverse scale, from box models up to global models. At the core of this novel framework is an "abstracted aerosol representation" that…