530 research outputs found
An Axisymmetric Gravitational Collapse Code
We present a new numerical code designed to solve the Einstein field
equations for axisymmetric spacetimes. The long term goal of this project is to
construct a code that will be capable of studying many problems of interest in
axisymmetry, including gravitational collapse, critical phenomena,
investigations of cosmic censorship, and head-on black hole collisions. Our
objective here is to detail the (2+1)+1 formalism we use to arrive at the
corresponding system of equations and the numerical methods we use to solve
them. We are able to obtain stable evolution, despite the singular nature of
the coordinate system on the axis, by enforcing appropriate regularity
conditions on all variables and by adding numerical dissipation to hyperbolic
equations.Comment: 19 pages, 9 figure
Simulating streamer discharges in 3D with the parallel adaptive Afivo framework
We present an open-source plasma fluid code for 2D, cylindrical and 3D
simulations of streamer discharges, based on the Afivo framework that features
adaptive mesh refinement, geometric multigrid methods for Poisson's equation,
and OpenMP parallelism. We describe the numerical implementation of a fluid
model of the drift-diffusion-reaction type, combined with the local field
approximation. Then we demonstrate its functionality with 3D simulations of
long positive streamers in nitrogen in undervolted gaps, using three examples.
The first example shows how a stochastic background density affects streamer
propagation and branching. The second one focuses on the interaction of a
streamer with preionized regions, and the third one investigates the
interaction between two streamers. The simulations run on up to grid
cells within less than a day. Without mesh refinement, they would require
grid cells
Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
We present a modification to the Berger and Oliger adaptive mesh refinement
algorithm designed to solve systems of coupled, non-linear, hyperbolic and
elliptic partial differential equations. Such systems typically arise during
constrained evolution of the field equations of general relativity. The novel
aspect of this algorithm is a technique of "extrapolation and delayed solution"
used to deal with the non-local nature of the solution of the elliptic
equations, driven by dynamical sources, within the usual Berger and Oliger
time-stepping framework. We show empirical results demonstrating the
effectiveness of this technique in axisymmetric gravitational collapse
simulations. We also describe several other details of the code, including
truncation error estimation using a self-shadow hierarchy, and the
refinement-boundary interpolation operators that are used to help suppress
spurious high-frequency solution components ("noise").Comment: 31 pages, 15 figures; replaced with published versio
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
Solution of an industrially relevant coupled magneto–mechanical problem set on an axisymmetric domain
Eddy currents are generated when low frequency magnetic fields interact with conducting components and this, in turn, generates Lorentz forces, which can cause these metallic components to deform and vibrate. An important application of this magneto–mechanical coupling is in coil design for magnetic resonance imaging scanners, where such vibrations can have unwanted effects such as ghosting of images, reduction of the life span of devices and discomfort for the patient. This work is aimed at developing an accurate computational tool for better understanding these deformations by considering a benchmark problem proposed by Siemens plc (Kruip, personal communication, 2013) on an idealised axisymmetric geometry. We present a new fixed point algorithm and develop new weak variational statements, which use a stress tensor approach for force calculation and permit discretisation using H1 conforming hp-version finite elements. Numerical results are included, which show the importance of high order finite elements for predicting the eddy currents and the associated coupling in the resonance region
Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
The Landau collision integral is an accurate model for the small-angle
dominated Coulomb collisions in fusion plasmas. We investigate a high order
accurate, fully conservative, finite element discretization of the nonlinear
multi-species Landau integral with adaptive mesh refinement using the PETSc
library (www.mcs.anl.gov/petsc). We develop algorithms and techniques to
efficiently utilize emerging architectures with an approach that minimizes
memory usage and movement and is suitable for vector processing. The Landau
collision integral is vectorized with Intel AVX-512 intrinsics and the solver
sustains as much as 22% of the theoretical peak flop rate of the Second
Generation Intel Xeon Phi, Knights Landing, processor
Aeronautical engineering: A continuing bibliography with indexes (supplement 218)
This bibliography lists 469 reports, articles, and other documents introduced into the NASA scientific and technical information system in September, 1987
- …