Paper Info
Title
The multilevel finite element method for adaptive mesh optimization and visualization of volume data
Abstract
Multilevel representations and mesh reduction techniques have been used for accelerating the processing and the rendering of large datasets representing scalar or vector valued functions de fined on complex 2 or 3 dimensional meshes. We present a method based on finite element approximations which combines these two ap - proaches in a new and unique way that is conceptually simple and theoretically sound. The main idea is to consider mesh reduction as an approximation problem in appropriate finite element sp aces. Starting with a very coarse triangulation of the functional domain a hierarchy of highly non-uniform tetrahedral (or triangul ar in 2D) meshes is generated adaptively by local refinement. This pro cess is driven by controlling the local error of the piecewise lin ear finite element approximation of the function on each mesh element. A reliable and efficient computation of the global approximat ion er- ror combined with a multilevel preconditioned conjugate gradient solver are the key components of the implementation. In order to analyze the properties and advantages of the adaptively generated tetrahedral meshes we implemented two volume visualization algo- rithms: an iso-surface extractor and a ray-caster. Both alg orithms, while conceptually simple, show significant speedups over c onven- tional methods delivering comparable rendering quality fr om adap- tively compressed datasets.
Year
DOI
Venue
1997
10.1145/266989.267107
IEEE Visualization 2003
Keywords
Field
DocType
adaptive mesh optimization,multilevel finite element method,volume data,3 dimensional,data visualisation,finite element method,piecewise linear,finite element,value function,mesh generation,vector valued functions,approximation error,function approximation,speedup,ray tracing,conjugate gradient
Polygon mesh,Function approximation,Computer science,Volume mesh,Theoretical computer science,Finite element method,Triangulation (social science),Rendering (computer graphics),Approximation error,Mesh generation
Conference
ISBN
Citations 
PageRank 
1-58113-011-2
54
3.27
References 
Authors
22
3
Name
Order
Citations
PageRank
Roberto Grosso112415.72
Christoph Lürig2808.09
Thomas Ertl34417401.52