A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization

机译：稀疏网格PDE解算器；离散化，适应性，软件设计和并行化

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Sparse grids are an efficient approxiamtion method for functions, especially in higher dimensions d >= 3. Compared to regular, uniform grids of a mesh parameter h, which contain h~(-d) points in d dimensions, sparse grids require only h~(-1)|log h|~(d-1) points due to a truncated, tensor-product multi-scale basis representation. The purpose of this paper is to survey some activities for the solution of partial differential equations with method based sparse grids. Furthermore some aspects of sparse grids are discussed such as adaptive grid refinement, parallel computing, a space-time discretization scheme and the structure of a code to implement these methods.

机译：稀疏网格是一种有效的函数逼近方法，尤其是在d> = 3的更高维度上。与网格参数为h的规则均匀网格相比，稀疏网格仅需要h〜，而网格参数h包含d个维度中的h〜（-d）个点。（-1）| log h |〜（d-1）点归因于截断的张量积多尺度基础表示。本文旨在研究基于稀疏网格的偏微分方程解的一些活动。此外，还讨论了稀疏网格的某些方面，例如自适应网格细化，并行计算，时空离散方案以及实现这些方法的代码结构。

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来源
《International Workshop on Modern Software Tools for Scientific Computing in Oslo, Norway, September 14-16, 1998》|1998年|p.133-177|共45页
会议地点 Oslo(NO)
作者
Gerhard W. Zumbusch;
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正文语种 eng
中图分类自动化技术、计算机技术;
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A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization

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