.png){kind=icon}
返回
Solving the Einstein constraint equations on multi-block triangulations using finite element methods
.png){kind=icon}
OA
AI
DOI：10.1088/0264-9381/26/14/145007.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor.. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.
Keyword:
MEAN-CURVATURE SOLUTIONS
NUMERICAL RELATIVITY
SUPERCONVERGENCE
IMPLEMENTATION
GRADIENT
REFINEMENT
STABILITY
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.7
论文数:
1.3W
被引数:
3.0W
机构
引用论文
分享收藏Synthesis and Characterization of Konjac Glucomannan/Carrageenan/Nano-silica Films for the Preservation of Postharvest White Mushrooms.png)
PolymersOAAI
PolymersIF0
OAAI分享收藏
查看更多内容