Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves

M. Bader; S. Schraufstetter; C. A. Vigh; J. Behrens

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Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves

机译：使用Sierpinski曲线的内存高效自适应网格生成和多网格算法的实现

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We will present an approach to numerical simulation on recursively structured adaptive discretisation grids. The respective grid generation process is based on recursive bisection of triangles along marked edges. The resulting refinement tree is sequentialised according to a Sierpinski space-filling curve, which leads to both minimal memory requirements and inherently cache-efficient processing schemes. The locality properties induced by the space-filling curve are even retained throughout adaptive refinement of the grid. We demonstrate the efficiency of the approach by implementing a multilevel-preconditioned conjugate gradient solver for a simple, yet adaptive, test problem: solving Poisson's equation on a re-entrant corner problem.

机译：我们将介绍一种在递归结构自适应离散化网格上进行数值模拟的方法。相应的网格生成过程基于沿着标记边缘的三角形递归二等分。生成的细化树根据Sierpinski空间填充曲线进行顺序排列，这导致最小的内存需求和固有的高效缓存处理方案。由空间填充曲线引起的局部性甚至在整个网格的自适应细化中都得以保留。我们通过对一个简单但自适应的测试问题实施多级预处理共轭梯度求解器来证明该方法的有效性：在重入角问题上求解泊松方程。

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来源
《International Journal of Computational Science and Engineering》 |2008年第1期|共10页
作者
M. Bader; S. Schraufstetter; C. A. Vigh; J. Behrens;
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正文语种 eng
中图分类计算技术、计算机技术;
关键词
Adaptive grid generation; Space-filling curves; Cache efficiency; Simulation;

机译：自适应网格生成;空间填充曲线;缓存效率;仿真;

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1. Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves [J] . M. Bader, S. Schraufstetter, C. A. Vigh, International Journal of Computational Science and Engineering . 2008,第1期

机译：使用Sierpinski曲线的内存高效自适应网格生成和多网格算法的实现
2. Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation [J] . HuaJi, Fue-SangLien, EugeneYee International Scholarly Research Notices . 2012,第Supplementa1期

机译：泊松方程有效解的并行自适应网格细化与加法多重网格相结合
3. Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver [J] . Ainsworth Mark, Glusa Christian Computer Methods in Applied Mechanics and Engineering . 2017,第deca1期

机译：分数拉普拉斯算子的自适应有限元方法的方面：先验和后验误差估计，有效实现和多网格求解器
4. An adaptive, memory-efficient and fast algorithm for Huffman decoding and its implementation [C] . Hoang-Anh Pham, Van-Hieu Bui, Anh-Vu Dinh-Duc 2nd international conference on interaction sciences : Information technology, culture and human 2009 . 2009

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5. A scalable parallel multigrid solver for three dimensional adaptive mesh structural analysis. [D] . Crane, Nathan Karl. 2002

机译：可扩展的并行多网格求解器，用于三维自适应网格结构分析。
6. Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm [O] . Chin F. Ng, Hermann B. Frieboes -1

机译：完全自适应非线性全多重网格算法模拟多物种间质癌的生长
7. Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves [O] . Bader M., Schraufstetter S., Vigh C. A., 2008

机译：内存有效的自适应网格生成和使用sierpinski曲线实现多重网格算法
8. Final Report for 'Non-Conforming Finite Elements; Mesh Generation, Adaptivity and Related Algebraic Multigrid and Domain Decomposition Methods in Massively Parallel Computing Environment [R] . Lazarov, R., Pasciak, J., Jones, J. 2002

机译：'不合格有限元的最终报告;大规模并行计算环境中的网格生成，适应性及相关代数多重网格和域分解方法

Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves

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