Related papers: Using FEMLAB for Gravitational problems: numerical…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
We experience some challenges in general gravitational theory owing to Einstein to explain late time acceleration of universe. To address this issue, geometric components of gravity have been modified in quite a few occasions to have a more…
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
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…
We construct exact solutions representing a Friedmann-Lema\^itre-Robsertson-Walker (FLRW) universe in a generalized hybrid metric-Palatini theory. By writing the gravitational action in a scalar-tensor representation, the new solutions are…
A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current…
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…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…
A nonlocal gravity model (2.1) was introduced and considered recently [49], and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark…
This work is focused on the theory of Gravitoelectromagnetism (GEM). In the first part of this work we present a brief review of gravitoelectromagnetism, we locate and discuss all the problems which appear in this approach. We also try to…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…
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…
Previous studies of the response of the Moon to gravitational waves have been carried out using analytical or semi-analytical models assuming ideal lunar structures. Such models are advantageous for their high-speed calculation but fail to…