Potentialities of the Robust Multigrid Technique

2010 ◽  
Vol 10 (1) ◽  
pp. 87-94 ◽  
Author(s):  
S.I. Martynenko

AbstractThe present paper discusses the parallelization of the robust multigrid technique (RMT) and the possible way of applying this to unstructured grids. As opposed to the classical multigrid methods, the RMT is a trivial method of parallelization on coarse grids independent of the smoothing iterations. Estimates of the minimum speed-up and parallelism efficiency are given. An almost perfect load balance is demonstrated in a 3D illustrative test. To overcome the geometric nature of the technique, the RMT is used as a preconditioner in solving PDEs on unstructured grids. The procedure of auxiliary structured grids generation is considered in details.

Author(s):  
С.И. Мартыненко

Сформулированы требования к вычислительным алгоритмам для перспективного программного обеспечения, устроенного по принципу "черного ящика" и предназначенного для математического моделирования в механике сплошных сред. Выполнен анализ прикладных свойств классических многосеточных методов и универсальной многосеточной технологии в рамках проблемы "универсальность-эффективность-параллелизм". Показано, что близкая к оптимальной трудоемкость при минимуме проблемно-зависимых компонентов и высокая эффективность параллелизма достижимы при использовании универсальной многосеточной технологии на глобально структурированных сетках. Применение неструктурированных сеток потребует определения двух проблемно-зависимых компонентов (межсеточных операторов), которые значительно влияют на трудоемкость алгоритма. A number of requirements are formulated to the numerical algorithms for black box software intended for mathematical modeling in continuum mechanics. An analysis of applied properties of the classical multigrid methods and robust multigrid technique in the framework of "robustness-efficiency-parallelism" problem is performed. It is shown that a close-to-optimal complexity with the least number of problem-dependent components and high parallel efficiency can be achieved with the robust multigrid technique on globally structured grids. Application of unstructured grids requires the accurate definition of two problem-dependent components (intergrid operators) that strongly affect on the complexity of an algorithm.


Author(s):  
Wen Wang ◽  
Chao Yan ◽  
Sheng Wang ◽  
Yu Huang ◽  
Wu Yuan

An efficient, robust and fully automatic grid assembly method on multi-block cell-centered structured grids for massively parallel computation is proposed in this paper. Compared with the traditional serial algorithm, the new approach eliminates the complex irregular boundaries created during the grid partition and avoids the large load imbalance caused by the large variation of grid-block overlapping. The main task of the overlapping grid assembly is to categorize all grid points into field points, fringe points and hole points. As to the main processes of the overlapping grid assembly, for hole cutting, an improved hole map method is applied to accurately identify the hole points located on the wall boundary with less memory cost. For donor search which is the most complex process on account of the irregular distribution of the partitioned multi-block structured grids in a parallel computation environment, the Alternating Digital Tree (ADT) is utilized to find out the potential donor cells quickly for query points. Besides, to achieve better overlapping quality, the wall distance criterion is implemented for overlapping optimization. In addition, two load balance algorithms are designed to solve the imbalance problem of overlapping grid assembly. Two test cases are applied to test the new overlapping grid assembly algorithm and the results show that the new overlapping grid assembly algorithm can deal with large-scale simulation of vehicles. The comparison of total time and speed-up among three algorithms manifests that the initial load balance algorithm using query point number as load criterion is not reliable while the improved load balance algorithm achieves good speed-up and least runtime. Meanwhile, the maximum proportion the improved load balance algorithm takes in one physical unsteady step in wing-pylon-store separation test case is less than 6.1%.


2012 ◽  
Vol 236-237 ◽  
pp. 1049-1053
Author(s):  
Zong Zhe Li ◽  
Zheng Hua Wang ◽  
Lu Yao ◽  
Wei Cao

An automatic agglomeration methodology to generate coarse grids for 3D flow solutions on anisotropic unstructured grids has been introduced in this paper. The algorithm combines isotropic octree based coarsening and anisotropic directional agglomeration to yield a desired coarsening ratio and high quality of coarse grids, which developed for cell-centered multigrid applications. This coarsening strategy developed is presented on an unstructured grid over 3D ONERA M6 wing. It is shown that the present method provides suitable coarsening ratio and well defined aspect ratio cells at all coarse grid levels.


2012 ◽  
Vol 241-244 ◽  
pp. 2957-2961
Author(s):  
Zong Zhe Li ◽  
Zheng Hua Wang ◽  
Wei Cao ◽  
Lu Yao

A robust aspect ratio based agglomeration algorithm to generate high quality coarse grids for unstructured grid is proposed in this paper. The algorithm focuses on multigrid techniques for the numerical solution of Euler equations, which conform to cell-centered finite volume scheme, combines isotropic vertex-based agglomeration to yield large increases in convergence rates. Aspect ratio is used as fusing weight to capture the degree of cell convexity and give an indication of cell quality, agglomerating isotropic cells sharing a common vertex. Consequently, we conduct agglomeration multigrid method to solve Euler equations on 2D isotropic unstructured grid, and compare the results with MGridGen


2008 ◽  
Vol 05 (02) ◽  
pp. 273-287
Author(s):  
LI CHEN ◽  
HIROSHI OKUDA

This paper describes a parallel visualization library for large-scale datasets developed in the HPC-MW project. Three parallel frameworks are provided in the library to satisfy different requirements of applications. Meanwhile, it is applicable for a variety of mesh types covering particles, structured grids and unstructured grids. Many techniques have been employed to improve the quality of the visualization. High speedup performance has been achieved by some hardware-oriented optimization strategies on different platforms, from PC clusters to the Earth Simulator. Good results have been obtained on some typical parallel platforms, thus demonstrating the feasibility and effectiveness of our library.


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