Related papers: The new discontinuous Galerkin methods based numer…
We present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of…
We implement a high-order numerical scheme for the entropy-based moment closure, the so-called M$_N$ model, for linear kinetic equations in slab geometry. A discontinuous Galerkin (DG) scheme in space along with a strong-stability…
We introduce a neural approach to dynamical modeling of galaxies that replaces traditional imaging-based deprojections with a differentiable mapping. Specifically, we train a neural network to translate Nuker profile parameters into…
Testing general relativity in the non-linear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity (GR) requires numerical inspiral, merger,…
We describe and analyse a space-time Trefftz discontinuous Galerkin method for the wave equation. The method is defined for unstructured meshes whose internal faces need not be aligned to the space-time axes. We show that the scheme is…
Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture…
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…
Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future…
One of the most promising sources of gravitational radiation is coalescence of binary neutron stars or black holes. In order to study gravitational radiation at the merging phase of coalescing binary neutron stars which is called the last…
We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…
The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…
An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of transient problems…
In astrophysics, the two main methods traditionally in use for solving the Euler equations of ideal fluid dynamics are smoothed particle hydrodynamics and finite volume discretization on a stationary mesh. However, the goal to efficiently…
High order accurate and explicit time-stable solvers are well suited for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfaces and nonlinear boundary and interface conditions,…
The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…
Approximate approach based on the Galerkin method is suggested for the investigation of equilibrium stellar models, a relativistic collapse problem and black hole formation. Some results of its simplified version - energetic method- are…
We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
A numerical method is formulated for the solution of the advective Cahn-Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…