By A. Auge, G. Lube, D. Weiß (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)
Galerkin/Least-Squares-FEM and Anisotropic Mesh Refinement.- Adaptive Multigrid tools: The UG Concept.- Finite quantity equipment with neighborhood Mesh Alignment in 2-D.- a brand new set of rules for Multi-Dimensional Adaptive Numerical Quadrature.- Adaptive resolution of One-Dimensional Scalar Conservation legislation with Convex Flux.- Adaptive, Block-Structured Multigrid on neighborhood reminiscence Machines.- Biorthogonal Wavelets and Multigrid.- Adaptive Multilevel-Methods for challenge difficulties in 3 area Dimensions.- Adaptive aspect Block Methods.- Adaptive Computation of Compressible Fluid Flow.- On Numerical Experiments with vital distinction Operators on detailed Piecewise Uniform Meshes for issues of Boundary Layers.- The field approach for Elliptic Interface difficulties on in the neighborhood sophisticated Meshes.- Parallel regular Euler Calculations utilizing Multigrid tools and Adaptive abnormal Meshes.- An Object-Oriented method for Parallel Self Adaptive Mesh Refiement on Block based Grids.- A Posteriori blunders Estimates for the Cell-Vertex Finite quantity Method.- Mesh variation through a Predictor-Corrector-Strategy within the Streamline Diffusion technique for Nonstationary Hyperbolic Systems.- at the V-Cycle of the absolutely Adaptive Multigrid Method.- Wavelets and Frequency Decomposition Multilevel tools.
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Extra info for Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993
This is possible with O(n) work count. 3 Semi-coarsening Another strategy to obtain a robust multi-grid method is the so-called semi-coarsening approach (cf. ). The basic idea is to improve the coarse grid correction instead of the smoother. Starting with a fine and structured grid, coarsening is performed only in those co-ordinate directions, in which the scale of the equation is already resolved. g. ). 3 Such a sequence of coarse grids yields a rob'ust m'ulti-grid method for the anisotropic model problem (9) without using a special smoother, since the coar'se grzd resolves the scale in the direction where the smoother does not work.
We have used this scheme in combination with local mesh refinement and local mesh alignment. After describing the algorithm and the Kornhuber-Roitzsch alignment we shall show some results for numerical experiments concerning the system (1). a) Fluctuation-distribution scheme for linear scalar conservation laws We shall use a notation which is slightly different from that one used in section 2. Let us assume that a regular triangulation T is given. The nodes of T are denoted by Pj, j = 1, ... ,N.
Now way down anisotropic ref in ement (b) good approximation II •ffijj EE isotropic ref i nement good app rox i mati on anisotrop i c refinement bad approx. Figure 2: Illustration of semi-coarsening (a) and anisotropic refinement (b). 4 Anisotropic Refinement Instead of starting with a fine grid and constructing the grid hierarchy by coarsening we start with a coarse grid and refine that anisotropically in order to resolve the scale successively. g. by the "blue refinement strategy" due to Kornhuber, .
Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993 by A. Auge, G. Lube, D. Weiß (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)