A characterization of mapping unstructured grids onto structured grids and using multigrid as a preconditioner

1997 ◽  
Vol 37 (3) ◽  
pp. 661-677 ◽  
Author(s):  
C. C. Douglas ◽  
S. Malhotra ◽  
M. H. Schultz
Keyword(s):  
Unstructured Grids ◽  
Structured Grids

HIGH-PERFORMANCE PARALLEL VISUALIZATION LIBRARY FOR VARIOUS SIMULATION ENVIRONMENTS

2008 ◽  
Vol 05 (02) ◽  
pp. 273-287
Author(s):  
LI CHEN ◽  
HIROSHI OKUDA
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Unstructured Grids ◽  
Structured Grids ◽  
The Earth ◽  
Parallel Frameworks ◽  
Parallel Visualization ◽  
Simulation Environments

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.

scholarly journals Numerical methods for black box software

2019 ◽  
pp. 147-169
Author(s):  
С.И. Мартыненко
Keyword(s):  
Mathematical Modeling ◽  
Numerical Methods ◽  
Unstructured Grids ◽  
Numerical Algorithms ◽  
Black Box ◽  
Optimal Complexity ◽  
Structured Grids ◽  
Accurate Definition ◽  
Definition Of ◽  
Robust Multigrid

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.

Potentialities of the Robust Multigrid Technique

2010 ◽  
Vol 10 (1) ◽  
pp. 87-94 ◽  
Author(s):  
S.I. Martynenko
Keyword(s):  
Load Balance ◽  
Unstructured Grids ◽  
Multigrid Methods ◽  
Structured Grids ◽  
Minimum Speed ◽  
Speed Up ◽  
Coarse Grids ◽  
Robust Multigrid ◽  
Geometric Nature

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.

An Improved Methodology for Gridding Fractured Reservoirs for Simulation

2021 ◽  
Author(s):  
Sheldon Gorell ◽  
Jim Browning ◽  
Justin Andrews
Keyword(s):  
Reservoir Simulation ◽  
Unstructured Grids ◽  
Fractured Reservoirs ◽  
Simulation Models ◽  
Horizontal Wells ◽  
Design Parameters ◽  
Structured Grids ◽  
Fractured Horizontal Wells ◽  
The Impact ◽  
Base Grid

Abstract A significant amount of research for gridding of complex reservoirs, including models with fractures, has focused on use of unstructured grids. While models with unstructured grids can be extremely flexible, they can also be expensive, both in configuring, computationally, and visual display. Even with this focus on unstructured grids, most reservoir simulation models are still built on structured grids. Current methods for creating reservoir simulation models with structured grids often involve defining a base grid upfront and then "somehow" inserting one or more Features of Interest (FOI's) into the model. Applied to fractured horizontal wells with many stages it can be extremely difficult to accurately align wells and completions within a pre-existing simulation grid. This work describes and demonstrates a methodology to resolve such issues. This approach changes the order of model design and creation steps. This paper describes the process where FOI's are identified, a base grid is designed around the FOI's, then local grid refinements (LGR's) are defined as desired. Applied to a horizontal well with fractures, the well and completion locations are defined before the detailed grid definition is created. This process is illustrated for generalized FOI's, and then applied to fractured horizontal wells. Formulas for creation of models for wells with evenly space homogeneous completions are presented. Numerical testing and analyses are presented that show the impact of the gridding parameters and various design parameters on performance of reservoir simulations.

Unconstrained Voronoi Grids for Densely Spaced Complex Wells in Full-Field Reservoir Simulation

SPE Journal ◽  
2014 ◽  
Vol 19 (05) ◽  
pp. 803-815 ◽  
Author(s):  
L.S.K.. S.K. Fung ◽  
X.Y.. Y. Ding ◽  
A.H.. H. Dogru
Keyword(s):  
Finite Volume ◽  
Reservoir Simulation ◽  
Unstructured Grid ◽  
Unstructured Grids ◽  
Field Scale ◽  
Full Field ◽  
Structured Grids ◽  
Grid Simulation ◽  
Local Grid ◽  
Complex Well

Summary Accurate representation of near-well flow is an important subject matter in reservoir simulation. In today's field-scale reservoir simulation, cell-centered structured grids remain the predominant practice. Typically, well-inflow performance of the perforated cells is connected to the finite-volume solution by means of well indices that may not be well-defined when the wellbore intersects the finite-volume cells in a complex trajectory. Fine gridding is also required to resolve the flow dynamics in the near-well regions. Strong grid-orientation sensitivities can also contribute to the numerical errors and may require significant local grid refinement to alleviate. There are ongoing resesarch-and-development (R&D) efforts on applying unstructured grids to better represent the near-well flow in reservoir simulation, but their applications are mainly in single-well study or sector modeling with a few wells. Some of the reasons cited for this include (1) the lack of an effective, easy-to-use full-field complex well-gridding tool; (2) the lack of supporting unstructured workflow for full-cycle reservoir simulation; (3) the cost of unstructured-grid simulation; and (4) the availability of post-analysis and visualization tools for unstructured-grid simulation. The paper describes a novel method to automatically generate unstructured grids that conform to complex well paths in field-scale simulation. The method uses a multilevel approach to place cells optimally within the solution domain on the basis of the “regions of interests.” The wellbore geometry is honored by means of the construction of a near-well grid that is complemented with multilevel quad-tree (Fig. 1) refinements to achieve the desired resolution in grid transition zones. The method includes an algorithm to remove small cells and pinching cells on the basis of local grid quality measures and cell prioritization to honor well paths. The gridding process forms a component of a production-level reservoir-simulation workflow. The use of unstructured grid results in computational savings by placing cells where the resolution is needed. An in-house massively parallel simulator is used to run the unstructured-grid models. Simulation examples for full-field applications with hundreds of complex wells by use of both structured grids and unstructured grids will be used to compare results, accuracy, and performance of the gridding method for reservoir simulation.

Application of Unstructured Finite Volume Method in Structural Static Mechanics

2013 ◽  
Vol 572 ◽  
pp. 273-276
Author(s):  
Wei Dong Chen ◽  
Yan Chun Yu ◽  
Xian De Wu ◽  
Jian Cao Li ◽  
Ping Jia ◽  
...  
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Irregular Boundary ◽  
Structured Grids ◽  
Basic Equations ◽  
Volume Method ◽  
Unstructured Finite Volume Method

Unstructured finite volume method applied in structural static mechanics has been discussed to direct at the difficulty of dealing with irregular boundary, unstructured triangle elements have been used in computational domain, the basic equations of unstructured finite volume method applied in structural static mechanics has been deduced. Comparing the unstructured grids with the structured grids, the former has obvious advantage on dealing with irregular boundary by theoretical analysis. According to examples analysis, the comparison of numeric results with analytic solutions and FEM solutions showed the effectiveness of the unstructured finite volume method.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

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