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A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…
This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…
Screened scalars are ubiquitous in many dark-sector models. They give rise to non-trivial fifth forces whilst evading experimental constraints through density-dependent screening mechanisms. We propose equipping a 10\,m-scale long-baseline…
We study a model of scalar quantum field theory in which space-time is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get…
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navier-Stokes problem and in the von K\'{a}rm\'{a}n equations.…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
This paper is devoted to investigate the recently proposed modified Gauss-Bonnet $f(\mathcal{G},T)$ gravity, with $\mathcal{G}$, the Gauss-Bonnet term, coupled with ${T}$, the trace of energy-momentum tensor. We have used the Noether…
The chameleon mechanism enables a long range fifth force to be screened in dense environments when non-trivial self interactions of the field cause its mass to increase with the local density. To date, chameleon fifth forces have mainly…
In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the…
In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
We study constraints on f(R) dark energy models from solar system experiments combined with experiments on the violation of equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high…
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence)…
Following a comprehensive analysis of the historical literature, we model the geometry of the Stern$\unicode{x2013}$Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the…
This article is dedicated to the use the MICROSCOPE mission's data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE's instrument intrinsic to…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…