Related papers: Adaptive mesh and geodesically sliced Schwarzschil…
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
Spherically symmetric spacetimes admit the so-called Kodama vector, which provides a locally conserved current and a preferred time even for dynamical spacetime without any time translation symmetry. A charge associated with this conserved…
Causal differencing has shown to be one of the promising and successful approaches towards excising curvature singularities from numerical simulations of black hole spacetimes. So far it has only been actively implemented in the ADM and…
The 3+1 (ADM) formulation of General Relativity is used in, for example, canonical quantum gravity and numerical relativity. Here we present a 3+1 decomposition of the minimal Standard-Model Extension gravity Lagrangian. By choosing the…
Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
This preliminary report proposes integrating the Maxwell equations in Minkowski spacetime using coordinates where the spacelike surfaces are hyperboloids asymptotic to null cones at spatial infinity. The space coordinates are chosen so that…
This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal surfaces with the requirement that time runs equally fast at both spatial ends of the…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
Among the coordinates used to construct a conformal compactification of the Schwarzschild spacetime, none of them simultaneously extend smoothly both through an event horizon and beyond null infinity.To construct such coordinates, instead…
In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
An analysis of conformal geodesics in the Schwarzschild-de Sitter and Schwarzschild-anti de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh…