Analysis of linear difference schemes in the sparse grid combination technique
نویسندگان
چکیده
منابع مشابه
Analysis of Linear Difference Schemes in the Sparse Grid Combination Technique
Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a d-dimensional cube, the number of grid points is N = O(h−1| log h|d−1) with a mesh size parameter h. The so-called combination technique, based on hierarchical decomposition, facilitates the numerical solution of partial differential equations on these grids. Key to the convergence analysis are specific mu...
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The coming large fusion experiment ITER will heavily benefit from numerical simulations. One model for simulating the hot plasmas occurring in such a device are the gyrokinetic equations, which can resolve the micro-turbulence in the plasma. Due to their moderately high dimensionality they could profit from using sparse grids. Since the highly efficient and paral-lelized simulation code GENE is...
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The sparse grid combination technique provides a framework to solve high dimensional numerical problems with standard solvers. Hierarchization is preprocessing step facilitating the communication needed for the combination technique. The derived hierarchization algorithm outperforms the baseline by up to 30x and achieves close to 5% of peak performance. It also shows stable performance for the ...
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Parallel implementation of the sparse grid combination technique in high dimensions presents many complexity challenges. We enumerate these challenges, classifying them respectively as computational, algorithmic, and software complexity. We discuss strategies for overcoming the individual complexity barriers. We describe our architecture for a software framework that will allow its users to bui...
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2012
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drs004