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 answer 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 quandary difficulties in 3 house Dimensions.- Adaptive element Block Methods.- Adaptive Computation of Compressible Fluid Flow.- On Numerical Experiments with critical distinction Operators on exact Piecewise Uniform Meshes for issues of Boundary Layers.- The field strategy for Elliptic Interface difficulties on in the community sophisticated Meshes.- Parallel regular Euler Calculations utilizing Multigrid tools and Adaptive abnormal Meshes.- An Object-Oriented procedure for Parallel Self Adaptive Mesh Refiement on Block based Grids.- A Posteriori blunders Estimates for the Cell-Vertex Finite quantity Method.- Mesh version through a Predictor-Corrector-Strategy within the Streamline Diffusion technique for Nonstationary Hyperbolic Systems.- at the V-Cycle of the totally Adaptive Multigrid Method.- Wavelets and Frequency Decomposition Multilevel tools.
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Additional resources for Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993
TSOL (total solution time) is for a 10-6 reduction in residual norm on level j after a nested iteration. Multigrid data: VI = V2 = 1, ""1 = 1 for mmgm, II = 1 for amgm with a point Jacobi smoother. Refinement was uniform up to level 4 (h = 1/32) except for cases w = 1 and P > 1 where refinement was uniform up to level 5. N is the number of unknowns after j adaption steps, EIT is the parallel efficiency in one multigrid iteration. 96 45 • The additive method has always better or equal (only one case) efficiencies than the multiplicative method.
J. , 83, 303-323 (1989).  M. C. RIVARA, Design and data structure of a fully adaptive multigrid finite element software, ACM Trans. on Math. Software, 10 (1984), pp. 242-264.  R. STEVENSON: On the robustness of multi-grid applied to anisotropic equations: Smoothing- and Approximation-Properties. Preprint Rijksuniversiteit Utrecht, Wiskunde, 1992.  - : New estimates of the contraction number of V-cycle multi-grid with applications to anisotropic equations. , Wittum, G. ) : Incomplete Decompositions, Algorithms, theory, and applications.
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, .