Title: Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing (Advances in Numerical Mathematics)
Publisher: Teubner 2003-01-01
Publication Date: 2003
Language: English
ISBN 10: 3519004518
ISBN 13: 9783519004516
Binding: Paperback
Condition: New

About this title

Synopsis

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.

About the Author

Prof. Dr. Gerhard Zumbusch, Universit�t Jena

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