Robust Multi-Grid Methods by Wolfgang Hackbusch
In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec- tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.-
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New Developments in Computational Fluid Dynamics
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Active Flow Control II
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New Results in Numerical and Experimental Fluid Mechanics V
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New Results in Numerical and Experimental Fluid Mechanics VI
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Numerical Flow Simulation I
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Summary of Flow Modulation and Fluid-Structure Interaction Findings
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Turbulence and Interactions
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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
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New Results in Numerical and Experimental Fluid Mechanics VII
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Nature-Inspired Fluid Mechanics
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Imaging Measurement Methods for Flow Analysis
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Fundamental Medical and Engineering Investigations on Protective Artificial Respiration
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Numerical Techniques in Continuum Mechanics
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Active Flow and Combustion Control 2021
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Adaptive Finite Element Solution Algorithm for the Euler Equations
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Progress in Hybrid RANS-LES Modelling
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Computational Science and High Performance Computing IV
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Efficient Solutions of Elliptic Systems
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Computational Flight Testing
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Noise and Vibration Mitigation for Rail Transportation Systems
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Numerical Simulation of Compressible Navier-Stokes Flows
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Computational Fluid Dynamics on Parallel Systems
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Supercomputers and Their Performance in Computational Fluid Dynamics
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Vectorization of Computer Programs with Applications to Computational Fluid Dynamics
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Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects
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Multiblock Grid Generation
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Numerical Simulation of Oscillatory Convection in Low-Pr Fluids
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Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications
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New Results in Numerical and Experimental Fluid Mechanics X
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Wolfgang Hackbusch is a Professor in the Scientific Computing department at Max Planck Institute for Mathematics in the Sciences. His research areas include numerical treatment of partial differential equations, numerical treatment of integral equations, and hierarchical matrices.
| SKU | Unavailable |
| ISBN 13 | 9783528080976 |
| ISBN 10 | 3528080973 |
| Title | Robust Multi-Grid Methods |
| Author | Wolfgang Hackbusch |
| Series | Notes On Numerical Fluid Mechanics And Multidisciplinary Design |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Friedrich Vieweg & Sohn Verlagsgesellschaft mbH |
| Year published | 1989-01-01 |
| Number of pages | 244 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |