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Results Obtained with a Semi-lagrangian Mass-Integrating Transport Algorithm by Using the GME Grid
(2008)
The defect of mass by actual schemes within the GME has motivated the implementation of a conservative semi-Lagrangian scheme on an icosahedral mesh. This scheme for the GME-mesh is unique. The properties are demonstrated by applying the new algorithm to typical test cases as they can be derived from the shallow water test suite. The results using coarse grids show: this scheme is extremely attractive for a climate version of the GME. Even for periods longer than those as specified in the SWE test suite, a defect of mass in the range of accuracy of the machine is obtained. The relative error results show that the order of accuracy of the proposed algorithm is two.
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.
This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the details of the subject.
