Related papers: Geophysical-astrophysical spectral-element adaptiv…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…
Adaptive mesh refinement (AMR) is a classical technique about local refinement in space where needed, thus effectively reducing computational costs for HPC-based physics simulations. Although AMR has been used for many years, little…
This paper presents the development of a well-balanced gas-kinetic scheme (GKS) with space-time adaptive mesh refinement (STAMR) for the shallow water equations (SWE). While well-balanced GKS have been established on Cartesian and…
This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…
We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh Refinement code), which has adopted a novel approach to improve the performance of adaptive mesh refinement (AMR) astrophysical simulations by a large factor with the…
The multi-resolution method, e.g., the Adaptive Particle Refinement (APR) method, has been developed to increase the local particle resolution and therefore the solution quality within a pre-defined refinement zone instead of using a…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
Implementation details and test cases of a newly developed hydrodynamic code, AMRA, are presented. The numerical scheme exploits the adaptive mesh refinement technique coupled to modern high-resolution schemes which are suitable for…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use…
In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
We present and test a general-purpose code, called PPASPH, for evolving self-gravitating fluids in astrophysics, both with and without a collisionless component. In PPASPH, hydrodynamical properties are computed by using the SPH (Smoothed…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…