Adaptive Methods — Algorithms, Theory and Applications: by A. Auge, G. Lube, D. Weiß (auth.), Wolfgang Hackbusch,

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 predicament difficulties in 3 area Dimensions.- Adaptive aspect Block Methods.- Adaptive Computation of Compressible Fluid Flow.- On Numerical Experiments with vital distinction Operators on certain Piecewise Uniform Meshes for issues of Boundary Layers.- The field procedure for Elliptic Interface difficulties on in the community 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 strategy for Nonstationary Hyperbolic Systems.- at the V-Cycle of the totally Adaptive Multigrid Method.- Wavelets and Frequency Decomposition Multilevel tools.

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Galerkin/Least-Squares-FEM and Anisotropic Mesh Refinement. - Adaptive Multigrid equipment: The UG proposal. - 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.

Extra resources for Adaptive Methods — Algorithms, Theory and Applications: Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993

Sample text

Up to now some theory is contained in [28],[29] and the new papers by Stevenson [22], [23] for uniformly refined grids. This theory shows that the basic requirement that the smoother is an exact solver in the limit case is not sufficient to obtain robustness. Additionally it must be guaranteed that the spectrum of the smoother is contained in [-19,1] for 0 ~ 19 < 1. This can be achieved by modification (d. [28]. [23]). , is the kernel of a robust multigrid method and makes up the main problem when applying this concept to unstructured grids.

Table 6: Iteration times in seconds for a (2,2, V) multiplicative multigrid cycle with Block-Jacobi smoother with 2 steps symmetric GaufJ-Seidel as inner solver. The residual in the level 0 equation has been reduced by 10- 4 . 9 seconds (22% increase) when going from one to 16 processors with problem size also increased by a factor of 16. Table 7 shows a computation of 50 timesteps on level 2 with various processor numbers from 2 to 20. 1 times faster than on two processors for a fixed problem size.

MULDER: A New Multigrid Approach to Convection Problems. J. , 83, 303-323 (1989). [21] 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. [22] R. STEVENSON: On the robustness of multi-grid applied to anisotropic equations: Smoothing- and Approximation-Properties. Preprint Rijksuniversiteit Utrecht, Wiskunde, 1992. [23] - : New estimates of the contraction number of V-cycle multi-grid with applications to anisotropic equations.

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