Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of Three-Dimensional Conservation Laws

1999 ◽  
pp. 113-134 ◽  
Author(s):  
J. E. Flaherty ◽  
R. M. Loy ◽  
M. S. Shephard ◽  
M. L. Simone ◽  
B. K. Szymanski ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Data Structures ◽  
Three Dimensional ◽  
Local Refinement ◽  
Parallel Solution ◽  
Refinement Method

scholarly journals Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws

1997 ◽  
Vol 47 (2) ◽  
pp. 139-152 ◽  
Author(s):  
J.E. Flaherty ◽  
R.M. Loy ◽  
M.S. Shephard ◽  
B.K. Szymanski ◽  
J.D. Teresco ◽  
...  
Keyword(s):  
Load Balancing ◽  
Conservation Laws ◽  
Three Dimensional ◽  
Local Refinement ◽  
Parallel Solution ◽  
Adaptive Local Refinement

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

scholarly journals The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fubiao Lin ◽  
Junying Cao ◽  
Zhixin Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Local Defect ◽  
Local Refinement ◽  
Element Discretization ◽  
One Dimensional ◽  
Correction Technique ◽  
Polar Coordinate ◽  
Multiscale Finite Element

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

scholarly journals Mechanochemical synthesis of bismuth ferrite

2013 ◽  
Vol 49 (1) ◽  
pp. 27-31 ◽  
Author(s):  
Z. Marinkovic-Stanojevica ◽  
L. Mancic ◽  
T. Sreckovic ◽  
B. Stojanovic
Keyword(s):  
Milling Time ◽  
Structure Refinement ◽  
Bismuth Ferrite ◽  
Renewable Energy Sources ◽  
Microstructural Analysis ◽  
Three Dimensional ◽  
Conventional Solid State Reaction ◽  
Refinement Method ◽  
Crystallite Sizes ◽  
Size And Morphology

A powder mixture of Bi2O3 and Fe2O3 was mechanically treated in a planetary ball mill in an air from 30 to 720 minutes. It was shown that the mechanochemical formation of BiFeO3 (BFO) phase was initiated after 60 min and its amount increased gradually with increasing milling time. A detailed XRPD structural analysis is realized by Rietveld?s structure refinement method. The resulting lattice parameters, relative phase abundances, crystallite sizes and crystal lattice microstrains were determined as a function of milling time. Microstructural analysis showed a little difference in morphology of obtained powders. The primary particles, irregular in shape and smaller than 400 nm are observed clearly, although they have assembled together to form agglomerates with varying size and morphology. Dense BFO ceramics were prepared by conventional solid-state reaction at the temperature of 810?C for 1h followed immediately by quenching process. [Projekat Ministarstva nauke Republike Srbije, br. III45007: Zero- to Three-Dimensional Nanostructures for Application in Electronics and Renewable Energy Sources: Synthesis, Characterization and Processing

Three-dimensional grayscale-free topology optimization using a level-set based r-refinement method

2017 ◽  
Vol 112 (10) ◽  
pp. 1402-1438 ◽  
Author(s):  
Shintaro Yamasaki ◽  
Seiichiro Yamanaka ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Three Dimensional ◽  
Refinement Method
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