Related papers: Technologies for supporting high-order geodesic me…
Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
We propose to study the behavior of complicated numerical solutions to Einstein's equations for generic cosmologies by following the geodesic motion of a swarm of test particles. As an example, we consider a cylinder of test particles…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
In this article, we present new computational realizations of principal geodesic analysis for the unit sphere $S^2$ and the special orthogonal group $SO(3)$. In particular, we address the construction of long-time smooth lifts across…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
Solutions to the field equations of the Nonsymmetric Gravitational Theory with $g_[i0] = 0$ are obtained for the homogeneous, plane-symmetric, time-dependent case, both in vacuum and in the presence of a perfect fluid. Cosmological…
It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal…
We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…
We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
LLM pre-training efficacy increasingly depends on data composition rather than sheer volume. Yet, optimal mixing is hindered by categorization flaws: human taxonomies suffer from ontological misalignment, and Euclidean clustering fails to…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
It has been shown that the Cauchy problem for geodesics in the space of K\"ahler metrics with a fixed cohomology class on a compact complex manifold $M$ can be effectively reduced to the problem of finding the flow of a related hamiltonian…
We investigate the three-dimensional structure of the pulsar magnetosphere through time-dependent numerical simulations of a magnetic dipole that is set in rotation. We developed our own Eulerian finite difference time domain numerical…
Astrophysical accretion discs that carry a significant mass compared with their central object are subject to the effect of self-gravity. In the context of circumstellar discs, this can, for instance, cause fragmentation of the disc gas,…
The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution employing the gravitational decoupling by means of Minimal…
Higher dimensional solutions are obtained for a homogeneous, spatially isotropic cosmological model in Wesson theory of gravitation. Some cosmological parameter are also calculated for this model.