A generic interface for parallel and adaptive discretization schemes: abstraction principles and the Dune-Fem module
A generic interface for parallel and adaptive discretization schemes: abstraction principles and the Dune-Fem module
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DOI：
10.1007/s00607-010-0110-3
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发表时间：
2010-11
期刊：
影响因子：
3.7
通讯作者：
A. Dedner;R. Klöfkorn;M. Nolte;Mario Ohlberger
中科院分区：
文献类型：
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作者：
A. Dedner;R. Klöfkorn;M. Nolte;Mario Ohlberger
从一个抽象的数学概念的离散函数空间和运营商，我们推导出一个一般的抽象的一大类基于网格的离散计划的固定和非固定偏微分方程。特别强调的是局部自适应和动态负载平衡的并行化的概念。这些概念是基于相应的抽象定义的并行和层次的自适应网格在巴斯蒂安等人。（Computing 82（2-3）：103-119，2008）。基于抽象的框架，我们描述了一个有效的面向对象的实现通用接口的基于网格的离散化计划，实现在沙丘-Femlibrary（ http://dune.mathematik.uni-freiburg.de ).通过使用接口类，我们设法将功能与数据结构分开。效率是通过使用现代模板为基础的泛型编程技术，包括静态多态性，引擎的概念，和模板元编程。我们提出了几个基准问题和一些先进的应用程序的数值结果。
Starting from an abstract mathematical notion of discrete function spaces and operators, we derive a general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations. Special emphasis is put on concepts for local adaptivity and parallelization with dynamic load balancing. The concepts are based on a corresponding abstract definition of a parallel and hierarchical adaptive grid given in Bastian et al. (Computing 82(2–3):103–119, 2008). Based on the abstract framework, we describe an efficient object oriented implementation of a generic interface for grid-based discretization schemes that is realized in theDune-Femlibrary ( http://dune.mathematik.uni-freiburg.de ). By using interface classes we manage to separate functionality from data structures. Efficiency is obtained by using modern template based generic programming techniques, including static polymorphism, the engine concept, and template metaprogramming. We present numerical results for several benchmark problems and some advanced applications.