Related papers: Solving nonlinear Klein-Gordon equations on unboun…
Development of particle in cell methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better…
The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the…
We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet…
These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular,…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We extend the chameleon models by considering Scalar-Fluid theories where the coupling between matter and the scalar field can be represented by a quadratic effective potential with density-dependent minimum and mass. In this context, we…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only first order differential equations. It is…
Chameleon fields may modify gravity on cluster scales while recovering general relativity locally. This article reviews signatures of chameleon modifications in the nonlinear cosmological structure, comparing different techniques to model…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
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…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
We present a formalism to study screening mechanisms in modified theories of gravity via perturbative methods in different cosmological scenarios. We consider Einstein frame posed theories that are recast as Jordan frame theories, where a…
We consider $f(R)$ modified gravity theory incorporating the chameleon mechanism to address galactic dynamics. By employing the metric formalism and utilizing a conformal transformation, we simplify the field equations and describe the…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…