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We investigate numerically a models of the static spherically symmetric boson-fermion stars in scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous…
The most popular methods for self-consistent simulation of fields interacting with charged species is using finite difference time domain (FDTD) methods together with Newton's laws of motion to evolve locations and velocities of particles.…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
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…
The chameleon scalar field is a matter-coupled dark energy candidate whose nonlinear self-interaction partially screens its fifth force at laboratory scales. Nevertheless, small-scale experiments such as the torsion pendulum can provide…
We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied $f(R)$ gravity models. High resolution simulations for such models are…
Chameleon scalar fields are dark energy candidates which suppress fifth forces in high density regions of the universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their…
We present and analyze a new space-time finite element method for the solution of neural field equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on…
The Fokker-Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Usually this equation…
We present a framework for embedding scalar-tensor models of screened modifed gravity such as chameleons, symmetrons and environmental dilatons into global supersymmetry. This achieved by secluding the dark sector from both the observable…
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical…
We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions…
We investigate the dynamics and the phase-space evolution for the scalar nonmetricity cosmology with a Chameleon mechanism. In particular, we consider a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry and within the…
In this paper, we consider a class of systems of nonlinear equations, which arise in discretized mixed formulations of problems in solid mechanics by $hp$-finite elements. We introduce a semismooth Newton solver for this specific class and…
In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and a Hessian recovery based linear (HRBL) FEM for second order elliptic equations in non-divergence form. The elliptic equation is casted into a…
We propose a simple and computationally fast method for performing N-body simulations for a large class of modified gravity theories with a screening mechanism such as chameleons, symmetrons and galileons. By combining the linear…
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…
The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several…