The multilevel finite element method for adaptive mesh optimization and visualization of volume data
R. Grosso, Christoph Lürig, Thomas Ertl · 1997
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 defined on complex 2 or 3 dimensional meshes. We present a method based on finite elements and hierarchical bases which combines these two approaches in a new and unique way that is conceptually simple and theoretically sound. Starting with a very coarse triangulation of the functional domain a hierarchy of highly non-uniform tetrahedral (or triangular in 2D) meshes is generated adaptively by local refinement. This process is driven by controlling the local error of the piecewise linear finite element approximation of the function (in the least-squares sense) on each mesh element. A reliable and efficient a posteriori estimate of the global approximation error combined with a preconditioned conjugate gradient solver are the key components of the implementation. Many areas where the proposed method can ...