Fast and Exact (Poisson) Solvers on Symmetric Geometries

In computer graphics, numerous geometry processing applications reduce to the solution of a Poisson equation. When considering geometries with symmetry, a natural question to consider is whether and how the symmetry can be leveraged to derive an efficient solver for the underlying system of linear e...

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Bibliographic Details
Published inComputer graphics forum Vol. 34; no. 5; pp. 153 - 165
Main Author Kazhdan, M.
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.08.2015
Subjects
Analysis
and systems-Fluid Simulation
Blocking
Boundaries
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
I.3.5 [Computer Graphics]: Geometric algorithms
I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems—Fluid Simulation
Image processing systems
languages
Linear operators
Mathematical models
Poisson distribution
Poisson equation
Solvers
Studies
Symmetry
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Summary:In computer graphics, numerous geometry processing applications reduce to the solution of a Poisson equation. When considering geometries with symmetry, a natural question to consider is whether and how the symmetry can be leveraged to derive an efficient solver for the underlying system of linear equations. In this work we provide a simple representation‐theoretic analysis that demonstrates how symmetries of the geometry translate into block diagonalization of the linear operators and we show how this results in efficient linear solvers for surfaces of revolution with and without angular boundaries.
Bibliography:ark:/67375/WNG-KPSZL2N1-9
ArticleID:CGF12704
istex:40F2BB4F272B83ED17664EE9AC13B30A9878D86B
SourceType-Scholarly Journals-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12704