Parallel partitioning tool GridSpiderPar for large mesh decomposition

Задача рациональной декомпозиции расчетных сеток возникает при численном моделировании на высокопроизводительных вычислительных системах проблем механики сплошных сред, импульсной энергетики, электродинамики и др. Число процессоров, на котором будет считаться вычислительная задача, как правило, заранее не известно. В этой связи имеет смысл предварительно однократно разбить сетку на большое число микродоменов, а затем формировать из них домены. Методы разбиения графов параллельных пакетов ParMETIS, Jostle, PT-Scotch и Zoltan основываются на иерархических алгоритмах, недостатком которых является образование несвязных доменов. Другим недостатком указанных пакетов является получение сильно несбалансированных разбиений. Разработан пакет программ GridSpiderPar для параллельной декомпозиции больших сеток. Проведены вычислительные эксперименты по сравнению различных разбиений на микродомены, разбиений графов микродоменов на домены, а также разбиений сразу на домены нескольких сеток ($10^8$ вершин, $10^9$ элементов), полученных методами созданного комплекса программ GridSpiderPar и пакетов ParMETIS, Zoltan и PT-Scotch. Качество разбиений проверялось по дисбалансу числа вершин в доменах, числу несвязных доменов и числу разрезанных ребер, а также по эффективности параллельного счета задач газовой динамики при распределении сеток по ядрам в соответствии с различными разбиениями. Полученные результаты выявили преимущества разработанных алгоритмов. The problem of load balancing arises in parallel mesh-based numerical solution of problems of continuum mechanics, energetics, electrodynamics etc. on high-performance computing systems. The number of processors to run a computational problem is often unknown. It makes sense, therefore, to partition a mesh into a great number of microdomains which then are used to create subdomains. Graph partitioning methods implemented in state-of-the-art parallel partitioning tools ParMETIS, Jostle, PT-Scotch and Zoltan are based on multilevel algorithms. That approach has a shortcoming of forming unconnected subdomains. Another shortcoming of present graph partitioning methods is generation of strongly imbalanced partitions. The program package for parallel large mesh decomposition GridSpiderPar was developed. We compared different partitions into microdomains, microdomain graph partitions and partitions into subdomains of several meshes (10^8 vertices, 10^9 elements) obtained by means of the partitioning tool GridSpiderPar and the packages ParMETIS, Zoltan and PT-Scotch. Balance of the partitions, edge-cut and number of unconnected subdomains in different partitions were compared as well as the computational performance of gas-dynamic problem simulations run on different partitions. The obtained results demonstrate advantages of the proposed algorithms.

A Novel Adaptive Match Scheme for Parallel Mesh-Decomposition in OpenFOAM

A parallel multilevel k-way partitioning algorithm is used in OpenFOAM to perform parallel mesh-decomposition. Before the parallel decomposition procedure, mesh has to be pre-decomposed by the Simple method in OpenFOAM. Match-computation for the algorithms parallel coarsening phase is based on a kind of global match scheme which introduces large amount of communication overhead. However, the domains of the mesh generated by Simple maintain good locality and continuity, which makes it unnecessary to adopt global match scheme in the parallel coarsening phase. In this paper, a novel adaptive match scheme AMS is brought forward for the parallel multilevel k-way partitioning algorithm. An adaptive critical x is calculated firstly according to the scale of the mesh and the parallel degree. For the first x stages of the coarsening phase, a local match scheme is adopted in which vertexes are only allowed to match with their adjacent unmatched vertexes with heaviest edge-weight on their local processors. For the rest stages, the traditional global match scheme is introduced and match of two vertexes on different processors is allowed. AMS can efficiently reduce the communication overhead introduced by simply adopting global match scheme. The experiment is performed on mesh of LinearPTT application on Tianhe-1A. The results show that the parallel multilevel k-way paritioning algorithm based on AMS has a better performance than that based on traditional global match scheme.

FAST MESH INTERPOLATION AND MESH DECOMPOSITION WITH APPLICATIONS

A new approach for constructing a smooth subdivision surface to interpolate the vertices of an arbitrary mesh is presented. The construction process does require setting up neither any linear systems, nor any matrix computation, but is simply done by iteratively moving vertices of the given mesh locally until control mesh of the required interpolating surface is reached. The new interpolation method has the simplicity of a local method in effectively dealing with meshes of a large number of vertices. It also has the capability of a global method in faithfully resembling the shape of a given mesh. Furthermore, the new method is fast and does not require a fairing step in the construction process because the iterative process converges to a unique solution at an exponential rate. Another important result of this work is, with the new iterative process, each mesh (surface) can be decomposed into a sum of simpler meshes (surfaces) which carry high-and low-frequency information of the given model. This mesh decomposition scheme provides us with new approaches to some classic applications in computer graphics such as texture mapping, denoising/smoothing/sharpening, and morphing. These new approaches are demonstrated in this paper and test results are included.