Parallel Multilevel Methods

1. Front Matter

   Pages 1-9

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2. Introduction

   • Gerhard Zumbusch

   Pages 11-18

3. Multilevel Iterative Solvers

   • Gerhard Zumbusch

   Pages 19-58

4. Adaptively Refined Meshes

   • Gerhard Zumbusch

   Pages 59-89

5. Space-Filling Curves

   • Gerhard Zumbusch

   Pages 90-143

6. Adaptive Parallel Multilevel Methods

   • Gerhard Zumbusch

   Pages 144-168

7. Numerical Applications

   • Gerhard Zumbusch

   Pages 169-193

8. Concluding Remarks and Outlook

   • Gerhard Zumbusch

   Pages 194-196

9. Back Matter

   Pages 197-216

   PDF

Numerical simulation promises new insight in science and engineering. In ad­ dition to the traditional ways to perform research in science, that is laboratory experiments and theoretical work, a third way is being established: numerical simulation. It is based on both mathematical models and experiments con­ ducted on a computer. The discipline of scientific computing combines all aspects of numerical simulation. The typical approach in scientific computing includes modelling, numerics and simulation, see Figure l. Quite a lot of phenomena in science and engineering can be modelled by partial differential equations (PDEs). In order to produce accurate results, complex models and high resolution simulations are needed. While it is easy to increase the precision of a simulation, the computational cost of doing so is often prohibitive. Highly efficient simulation methods are needed to overcome this problem. This includes three building blocks for computational efficiency, discretisation, solver and computer. Adaptive mesh refinement, high order and sparse grid methods lead to discretisations of partial differential equations with a low number of degrees of freedom. Multilevel iterative solvers decrease the amount of work per degree of freedom for the solution of discretised equation systems. Massively parallel computers increase the computational power available for a single simulation.

• Adaptive Parallel Multilevel Methods
• Adaptively Refined Grids
• Multilevel Iterative Solver
• Numerical Applications
• Space-Filling Curves
• differential equation

• TU München, Deutschland

  Gerhard Zumbusch

• Konrad-Zuse-Zentrum für Informationstechnik Berlin, Deutschland

  Gerhard Zumbusch

• FU Berlin, Deutschland

  Gerhard Zumbusch

• SINTEF Anvendt Matematikk Oslo, Norway

  Gerhard Zumbusch

• Universität Bonn, Deutschland

  Gerhard Zumbusch

• Wissenschaftliches Rechnen/Numerische Mathematik, Friedrich-Schiller-Universität Jena, Deutschland

  Gerhard Zumbusch

• Instituts für Angewandte Mathematik, Deutschland

  Gerhard Zumbusch

Prof. Dr. Gerhard Zumbusch, Universität Jena

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