Improvement of Unstructured Quadrilateral Mesh Quality for Multigrid Analysis

2008 ◽  
Vol 33-37 ◽  
pp. 833-838
Author(s):  
Yoshitaka Wada ◽  
Takuji Hayashi ◽  
Masanori Kikuchi ◽  
Fei Xu
Keyword(s):  
Mesh Quality ◽  
Iterative Solver ◽  
Initial Shape ◽  
Multigrid Solver ◽  
Adaptive Analysis ◽  
Initial Mesh ◽  
Mesh Improvement ◽  
Improvement Method ◽  
Effective Analysis ◽  
Mesh Coarsening

Due to more complex and severe design restrictions, more effective and faster finite element analyses are demanded. There are several ways to compute FE analysis efficiently: parallel computing, fast iterative or direct solvers, adaptive analysis and so on. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with difference resolutions and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to be applied to an initial mesh, and better convergence is achieved by the improved initial mesh.

scholarly journals An efficient method to improve the quality of tetrahedron mesh with MFRC

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuzheng Ma ◽  
Monan Wang
Keyword(s):  
Quality Improvement ◽  
Large Scale ◽  
Tetrahedral Mesh ◽  
Limited Area ◽  
Target Area ◽  
Mesh Quality ◽  
Edge Removal ◽  
Mesh Improvement ◽  
Improvement Method ◽  
Vertex Insertion

AbstractIn this paper, we proposed a novel operation to reconstruction tetrahedrons within a certain region, which we call MFRC (Multi-face reconstruction). During the existing tetrahedral mesh improvement methods, the flip operation is one of the very important components. However, due to the limited area affected by the flip, the improvement of the mesh quality by the flip operation is also very limited. The proposed MFRC algorithm solves this problem. MFRC can reconstruct the local mesh in a larger range and can find the optimal tetrahedron division in the target area within acceptable time complexity. Therefore, based on the MFRC algorithm, we combined other operations including smoothing, edge removal, face removal, and vertex insertion/deletion to develop an effective mesh quality improvement method. Numerical experiments of dozens of meshes show that the algorithm can effectively improve the low-quality elements in the tetrahedral mesh, and can effectively reduce the running time, which has important significance for the quality improvement of large-scale mesh.

Improving the Condition Number of Finite Element Stiffness Matrices via Inverted Elements

2011 ◽  
Author(s):  
Josh Danczyk ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Condition Number ◽  
Poor Quality ◽  
Iterative Solvers ◽  
Mesh Quality ◽  
Mathematical Properties ◽  
Stiffness Matrices ◽  
Mesh Improvement

In the finite element method, poor quality elements typically increase the condition number of the underlying stiffness matrix, thereby potentially: (1) degrading the computed solution, and (2) slowing the convergence of iterative solvers. Current mesh improvement strategies rely on node movement and edge-flipping to alleviate these problems. However, these methods cannot guarantee a lower-bound on mesh quality, especially in 3-D. In this paper we propose the concept, and use, of inverted elements to improve mesh quality and condition number. Inverted elements are standard finite elements, but with negative Jacobian. After establishing the mathematical properties of these elements we show how they can be used to dramatically improve the quality of a mesh through the use of an ‘element cover’. Further, we show that a lower-bound on the mesh quality can be easily achieved, as supported by numerical experiments and case-studies.

scholarly journals A Novel Mesh Quality Improvement Method for Boundary Elements

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hou-lin Liu ◽  
Cui Dai ◽  
Liang Dong ◽  
Ming-gao Tan
Keyword(s):  
Topology Optimization ◽  
Weight Coefficient ◽  
Mesh Quality ◽  
Practical Application ◽  
New Approach ◽  
Discrete Surfaces ◽  
Improvement Method ◽  
Quality Improvement Method ◽  
Better Than

In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

scholarly journals Hexahedral Mesh Quality Improvement with Geometric Constraints

2021 ◽  
Author(s):  
wei peng ◽  
Xinguang Wu ◽  
Yidong Bao ◽  
Chaoyang Zhang ◽  
Weixi Ji
Keyword(s):  
Quality Improvement ◽  
Geometric Constraints ◽  
Mesh Quality ◽  
Quality Improvements ◽  
Hexahedral Mesh ◽  
Different Types ◽  
Hexahedral Meshes ◽  
Improvement Method ◽  
Quality Improvement Method

Abstract Hexahedral mesh is of great value in the analysis of mechanical structure, and the mesh quality has an important impact on the efficiency and accuracy of the analysis. This paper presents a quality improvement method for hexahedral meshes, which consists of node classification, geometric constraints based single hexahedron regularization and local hexahedral mesh stitching. The nodes are divided into different types and the corresponding geometric constraints are established in single hexahedron regularization to keep the geometric shapes of original mesh. In contrast to the global optimization strategies, we perform the hexahedral mesh stitching operation within a few local regions surrounding elements with undesired quality, which can effectively improve the quality of the mesh with less consuming time. A number of mesh quality improvements for hexahedral meshes generated by a variety of methods are introduced to demonstrate the effectiveness of our method.

Subsmoothing: An Optimized Smoothing Method

1993 ◽  
Author(s):  
Ron S. Gutfinger ◽  
Raj Abraham
Keyword(s):  
Iterative Process ◽  
Smoothing Algorithm ◽  
Mesh Quality ◽  
Mesh Generator ◽  
Cpu Time ◽  
Initial Mesh ◽  
Time Savings ◽  
Laplacian Smoothing ◽  
Automatic Mesh ◽  
Number Of Iterations

Abstract Usually, a mesh created by an automatic mesh generator is of low quality. In order to improve the mesh quality, a smoothing algorithm is applied on the mesh. The result is a mesh ready for analysis. The smoothing is a CPU intensive iterative process. In some cases, smoothing may take longer than the initial mesh creation. In this work an optimized smoothing algorithm is presented. While iterating, the algorithm recognizes nodes that are sufficiently smoothed, and ignores them in subsequent iterations. Progressively, a smaller and smaller subset of nodes is smoothed. The result is less CPU time spent per iteration, and some decrease in the total number of iterations. This method, called subsmoothing, is applied on Laplacian smoothing of shell meshes. Examples show 30% CPU time savings and little change in mesh quality (¼%).

SINK INSERTION FOR MESH IMPROVEMENT

2002 ◽  
Vol 13 (02) ◽  
pp. 223-242 ◽  
Author(s):  
HERBERT EDELSBRUNNER ◽  
DAMRONG GUOY
Keyword(s):  
New Technique ◽  
Mesh Quality ◽  
Insertion Technique ◽  
Delaunay Triangulations ◽  
Running Time ◽  
Mesh Improvement ◽  
Numerical Robustness ◽  
A New Technique

We propose sink insertion as a new technique to improve the mesh quality of Delaunay triangulations. We compare it with the conventional circumcenter insertion technique under three scheduling regimes: incremental, in blocks, and in parallel. Justification for sink insertion is given in terms of mesh quality, numerical robustness, running time, and ease of parallelization.

Tensile Failure of 55-Nitinol Wire

1975 ◽  
Vol 33 ◽  
pp. 46-47
Author(s):  
F. I. Grace
Keyword(s):  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Stoichiometric Composition ◽  
Tensile Failure ◽  
Initial State ◽  
Initial Shape ◽  
Nitinol Wire ◽  
Cscl Type ◽  
Shear Transformation

An interest in NiTi alloys with near stoichiometric composition (55 NiTi) has intensified since they were found to exhibit a unique mechanical shape memory effect at the Naval Ordnance Laboratory some twelve years ago (thus refered to as NITINOL alloys). Since then, the microstructural mechanisms associated with the shape memory effect have been investigated and several interesting engineering applications have appeared.The shape memory effect implies that the alloy deformed from an initial shape will spontaneously return to that initial state upon heating. This behavior is reported to be related to a diffusionless shear transformation which takes place between similar but slightly different CsCl type structures.

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