Related papers: Solving nonlinear Klein-Gordon equations on unboun…
We study $f(R)$ gravity models in the language of scalar-tensor theories. The correspondence between $f(R)$ gravity and scalar-tensor theories is revisited since $f(R)$ gravity is a subclass of Brans-Dicke models, with a vanishing coupling…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
We apply the Noether symmetries to constrain the unknown functions of chameleon gravity in the cosmological scenario of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker space-time with an ideal gas. For this gravitational model…
This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
This work deals with chameleon field cosmology (a scalar field nonminimally coupled to cold dark matter) in the background of flat Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. Both classical and quantum cosmology have been…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
We investigate the validity of screening mechanism of the fifth force for chameleon field in highly inhomogeneous density profile. For simplicity, we consider a static and spherically symmetric system which is composed of concentric…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…
Following work by Khoury and Weltman, we introduce a scalar field phi, the chameleon, which is conformally coupled to matter. That is, matter experiences a metric which is a conformal transform (parametrized by phi) of the Einstein metric.…
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace-Beltrami problem posed on an $n$-dimensional…
The modified Lane-Emden equation for stellar hydrostatic equilibrium in f(R)-gravity is numerically solved by using an iterative procedure. Such an integro-differential equation can be obtained in the weak field limit approximation of…
We present a Virtual Element Method (VEM) for the solution of Dirichlet problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with essential boundary conditions. Within the VEM the nonlinear coefficient is evaluated with…
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field, which is produced by a slow moving matter source. The analysis is based on the Klein-Gordon…
New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of…
The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently…