These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid results was provided for a third time. Multigrid methods no longer have problems being accepted by numerical analysts and users of numerical methods; on the contrary, they have been further developed in such a successful way that they have penetrated a variety of new fields of application. The high number of 154 participants from 18 countries and 76 presented papers show the need to continue the series of the European Multigrid Conferences. The papers of this volume give a survey on the current Multigrid situation; in particular, they correspond to those fields where new developments can be observed. For example, se� veral papers study the appropriate treatment of time dependent problems. Improvements can also be noticed in the Multigrid approach for semiconductor equations. The field of parallel Multigrid variants, having been started at the second European Multigrid Conference, is now at the centre of interest.

Contenuti:

Invited Papers.- Multigrid Methods for Steady Euler- and Navier-Stokes Equations Based on Polynomial Flux-Difference Splitting.- Recent Developments for the PSMG Multiscale Method.- An adaptive multigrid approach for the solution of the 2D semiconductor equations.- Multiscale Monte Carlo Algorithms in Statistical Mechanics and Quantum Field Theory.- Two Fast Solvers Based on the Multi-Level Splitting of Finite Element Spaces.- Multigrid Methods for Turbulent Flow Problems.- A survey of Fourier smoothing analysis results.- Contributed Papers.- Multilevel Methods for Fast Solution of N-Body and Hybrid Systems.- Parabolic Multigrid Revisited.- Time-Parallel Multigrid Solution of the Navier-Stokes Equations.- Solution of 3-D Problems using Overlapping Grids and Multi-Grid Methods.- A Multigrid Method for the Solution of a Convection — Diffusion Equation with Rapidly Varying Coefficients.- Parallel Multigrid Solution of 2D and 3D Anisotropic Elliptic Equations: Standard and Nonstandard Smoothing.- Parallel Multigrid Methods on Sparse Grids.- Analysis of multigrid methods for general systems of PDE.- On the convergence of the nonlinear multigrid algorithm for potential operators.- A Multigrid Algorithm with Time-Dependent, Locally Refined Grids for Solving the Nonlinear Diffusion Equation on a Nonrectangular Geometry.- Multigrid Methods for Hyperbolic Equations.- Low-Diffusion Rotated Upwind Schemes, Multigrid and Defect Correction for Steady, Multi-Dimensional Euler Flows.- Multigrid Convergence Acceleration for Complex Flow Including Turbulence.- Time Accurate Multigrid Solutions of the Navier-Stokes Equations.- Mesh-Adaptive Solution of the Navier-Stokes Equations.- A two-grid analysis of the combination of mixed finite elements and Vanka-type relaxation.- Multigrid Applied to Mixed Finite Element Schemes for Current Continuity Equations.- Adaptive Higher Order Multigrid Methods.- Shape from Shading using Parallel Multigrid Relaxation.- Cell-centered Multigrid Methods in Porous Media Flow.- Multigrid Waveform Relaxation for Solving Parabolic Partial Differential Equations.

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