English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
 
 
DownloadE-Mail
  Constructing Reference Metrics on Multicube Representations of Arbitrary Manifolds

Lindblom, L., Taylor, N. W., & Rinne, O. (2016). Constructing Reference Metrics on Multicube Representations of Arbitrary Manifolds. Journal of Computational Physics, 313, 31-56. doi:10.1016/j.jcp.2016.02.029.

Item is

Files

show Files
hide Files
:
1411.6785.pdf (Preprint), 706KB
Name:
1411.6785.pdf
Description:
File downloaded from arXiv at 2015-01-07 13:20
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
:
JCP313_31.pdf (Publisher version), 2MB
 
File Permalink:
-
Name:
JCP313_31.pdf
Description:
-
OA-Status:
Visibility:
Restricted (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), MPGR; )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show

Creators

show
hide
 Creators:
Lindblom, Lee, Author
Taylor, Nicholas W., Author
Rinne, Oliver1, Author           
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

Content

show
hide
Free keywords: Physics, Computational Physics, physics.comp-ph,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
 Abstract: Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics automatically on multicube representations of manifolds with arbitrary topologies. The method is tested here by constructing reference metrics for compact, orientable two-dimensional manifolds with genera between zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity numerically to the level of truncation error (which converges toward zero as the numerical resolution is increased). These reference metrics can be made smoother and more uniform by evolving them with Ricci flow. This smoothing procedure is tested on the two-dimensional reference metrics constructed here. These smoothing evolutions (using volume-normalized Ricci flow with DeTurck gauge fixing) are all shown to produce reference metrics with constant scalar curvatures (at the level of numerical truncation error).

Details

show
hide
Language(s):
 Dates: 2014-11-252015-01-022016
 Publication Status: Issued
 Pages: 37 pages, 16 figures
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1411.6785
DOI: 10.1016/j.jcp.2016.02.029
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Computational Physics
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 313 Sequence Number: - Start / End Page: 31 - 56 Identifier: -