Two-dimensional Mesh Generation Research Articles

Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system

Through mathematical models, it is possible to turn a problem of the physical domain to the computational domain. In this context, the paper presents a two-dimensional mesh generator in generalized coordinates, which uses the parametric linear spline method and partial differential equations. The generator is automated and able to treat real complex domains and, consequently, more realistic problems. However, there is a possibility that lower quality elements may be introduced into the computational mesh. Thus, metrics are investigated that identify elements considered to be of lower quality. Experiments are carried out to verify the efficiency of the adopted metrics, considering meshes with single block, and multi-blocks. According to the experiments, the work allowed the detection of elements of lower quality, contributing to the realization of an adequate modeling of geometries

A self-learning finite element extraction system based on reinforcement learning

AbstractAutomatic generation of high-quality meshes is a base of CAD/CAE systems. The element extraction is a major mesh generation method for its capabilities to generate high-quality meshes around the domain boundary and to control local mesh densities. However, its widespread applications have been inhibited by the difficulties in generating satisfactory meshes in the interior of a domain or even in generating a complete mesh. The element extraction method's primary challenge is to define element extraction rules for achieving high-quality meshes in both the boundary and the interior of a geometric domain with complex shapes. This paper presents a self-learning element extraction system, FreeMesh-S, that can automatically acquire robust and high-quality element extraction rules. Two central components enable the FreeMesh-S: (1) three primitive structures of element extraction rules, which are constructed according to boundary patterns of any geometric boundary shapes; (2) a novel self-learning schema, which is used to automatically define and refine the relationships between the parameters included in the element extraction rules, by combining an Advantage Actor-Critic (A2C) reinforcement learning network and a Feedforward Neural Network (FNN). The A2C network learns the mesh generation process through random mesh element extraction actions using element quality as a reward signal and produces high-quality elements over time. The FNN takes the mesh generated from the A2C as samples to train itself for the fast generation of high-quality elements. FreeMesh-S is demonstrated by its application to two-dimensional quad mesh generation. The meshing performance of FreeMesh-S is compared with three existing popular approaches on ten pre-defined domain boundaries. The experimental results show that even with much less domain knowledge required to develop the algorithm, FreeMesh-S outperforms those three approaches in essential indices. FreeMesh-S significantly reduces the time and expertise needed to create high-quality mesh generation algorithms.

Two-dimensional non-uniform mesh generation for finite element models using MATLAB

This paper demonstrates non-uniform mesh generation scheme for two-dimensional domains. For many models in fluid dynamics like turbulent flow, channel flow there is large gradient in the small narrow portion, for example near the wall region. To solve this kind of problems the non-uniform meshing scheme near the wall region helps to capture the fine details of the region. Meshing is carried through MATLAB codes which generate triangular meshes for two dimensional domains. The MATLAB code is based on distmesh2d developed for linear straight sided triangular element by Persson and Gilbert Strang (2004). The proposed meshing scheme is based on nodal relation and subparametric point transformations extracted from parabolic arcs developed by Rathod.et.al (2008). In this work a higher order triangular meshing upto quartic order for two domains the holey pie slice and a circle inscribed in a square has been demonstrated. These in turn finds its application in flow problems, thermodynamics and aerospace engineering. Present meshing scheme provides an improved high quality meshes for these domains and produce accurate results of the nodal position, boundary nodes and element connectivity for the discretized domain. The obtained output is advantageous in executing finite element procedure with less computational efforts.

OceanMesh2D 1.0: MATLAB-based software for two-dimensional unstructured mesh generation in coastal ocean modeling

Abstract. OceanMesh2D is a set of MATLAB functions with preprocessing and post-processing utilities to generate two-dimensional (2-D) unstructured meshes for coastal ocean circulation models. Mesh resolution is controlled according to a variety of feature-driven geometric and topo-bathymetric functions. Mesh generation is achieved through a force balance algorithm to locate vertices and a number of topological improvement strategies aimed at improving the worst-case triangle quality. The placement of vertices along the mesh boundary is adapted automatically according to the mesh size function, eliminating the need for contour simplification algorithms. The software expresses the mesh design and generation process via an objected-oriented framework that facilitates efficient workflows that are flexible and automatic. This paper illustrates the various capabilities of the software and demonstrates its utility in realistic applications by producing high-quality, multiscale, unstructured meshes.

Application of variational mesh generation approach for selecting centers of radial basis functions collocation method

Abstract In this paper, a two-dimensional variational mesh generation method is applied to obtain adaptive centers for radial basis functions (RBFs). At first, a set of uniform centers is distributed in the domain, then mesh generation differential equations are used to move the centers to region with high gradients. An iterative algorithm is introduced to solve steady-state mesh generation differential equations with RBFs. Functions with steep variation in the domains are used to validate the adaptive centers generation method. In addition to the centers adaption process is applied to solve elliptic partial differential equations via RBFs collocation method. Numerical results of Helmholtz differential equation show a clear reduction in the error, when the adaptive centers are used for RBFs.

A distributed-memory parallel technique for two-dimensional mesh generation for arbitrary domains

This work describes a technique for generating two-dimensional triangular meshes using distributed memory parallel computers, based on a master/slaves model. This technique uses a coarse quadtree to decompose the domain and a serial advancing front technique to generate the mesh in each subdomain concurrently. In order to advance the front to a neighboring subdomain, each subdomain suffers a shift to a Cartesian direction, and the same advancing front approach is performed on the shifted subdomain. This shift-and-remesh procedure is repeatedly applied until no more mesh can be generated, shifting the subdomains to different directions each turn. A finer quadtree is also employed in this work to help estimate the processing load associated with each subdomain. This load estimation technique produces results that accurately represent the number of elements to be generated in each subdomain, leading to proper runtime prediction and to a well-balanced algorithm. The meshes generated with the parallel technique have the same quality as those generated serially, within acceptable limits. Although the presented approach is two-dimensional, the idea can be easily extended to three dimensions.

Algorithm, software, and hardware optimizations for Delaunay mesh generation on simultaneous multithreaded architectures

This article focuses on the optimization of PCDM, a parallel, two-dimensional (2D) Delaunay mesh generation application, and its interaction with parallel architectures based on simultaneous multithreading (SMT) processors. We first present the step-by-step effect of a series of optimizations on performance. These optimizations improve the performance of PCDM by up to a factor of six. They target issues that very often limit the performance of scientific computing codes. We then evaluate the interaction of PCDM with a real SMT-based SMP system, using both high-level metrics, such as execution time, and low-level information from hardware performance counters.

A computational methodology for automatic two-dimensional anisotropic mesh generation and adaptation

This paper describes a versatile computational program for automatic two-dimensional mesh generation and remeshing adaptation of triangular, quadrilateral and mixed meshes. The system is flexible to be incorporated into an adaptive global or local remeshing procedure and for generating both, iso and anisotropic meshes. The main contribution of this work is to extend well established procedures for the generation and adaptation of both, iso and anisotropic triangular meshes, such as local and global remeshing as well as boundary layer mesh generation, to deal with iso and anisotropic quadrilateral and mixed meshes. Several examples are presented to illustrate the quality of the meshes produced, and the flexibilities of the computational system.

BatTri: A two-dimensional bathymetry-based unstructured triangular grid generator for finite element circulation modeling

A brief summary of Delaunay unstructured triangular grid refinement algorithms, including the recent “off-centers” method, is provided and mesh generation requirements that are imperative to meet the criteria of the circulation modeling community are defined. A Matlab public-domain two-dimensional (2-D) mesh generation package (BatTri) based on these requirements is then presented and its efficiency shown through examples. BatTri consists of a graphical mesh editing interface and several bathymetry-based refinement algorithms, complemented by a set of diagnostic utilities to check and improve grid quality. The final output mesh node locations, node depths and element incidence list are obtained starting from only a basic set of bathymetric data. This simple but efficient setup allows fast interactive mesh customization and provides circulation modelers with problem-specific flexibility while satisfying the usual requirements on mesh size and element quality. A test of the “off-centers” method performed on 100 domains with randomly generated coastline and bathymetry shows an overall 25% reduction in the number of elements with only slight decrease in element quality. More importantly, this shows that BatTri is easily upgradeable to meet the future demands by the addition of new grid generation algorithms and Delaunay refinement schemes as they are made available.

Two-dimensional adaptive mesh generation algorithm and its application with higher-order compressible flow solver

A combined procedure for two-dimensional Delaunay mesh generation algorithm and an adaptive remeshing technique with higher-order compressible flow solver is presented. A pseudo-code procedure is described for the adaptive remeshing technique. The flux-difference splitting scheme with a modified multidimensional dissipation for high-speed compressible flow analysis on unstructured meshes is proposed. The scheme eliminates nonphysical flow solutions such as the spurious bump of the carbuncle phenomenon observed from the bow shock of the flow over a blunt body and the oscillation in the odd-even grid perturbation in a straight duct for the Quirk's odd-even decoupling test. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. The performance of the combined procedure is evaluated on unstructured triangular meshes by solving several steady-state and transient high-speed compressible flow problems.

MIXED ENTROPY FIX METHOD FOR ROE S FLUX-DIFFERENCE SPLITTING SCHEME WITH AUTOMATIC MESH ADAPTATION

A combined procedure for two-dimensional Delaunay mesh generation algorithm and an adaptive remeshing technique with higher-order compressible flow solver is presented. The flux-difference splitting scheme with a mixed entropy fix method is introduced for high-speed compressible flow analysis on unstructured meshes. The scheme eliminates unphysical flow solutions such as a spurious bump of the carbuncle phenomenon that occurs on the bow shock from flow over a blunt body, and the oscillation in the odd-even grid perturbation in a straight duct for the Quirk's odd-even decoupling test. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. The performance of the combined procedure is evaluated by solving several high-speed compressible flow problems on unstructured triangular meshes.

A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation

In this paper we study the problem of two-dimensional adaptive mesh generation using a variational approach and, specifically, the effect that the monitor function has on the resulting mesh behavior. The basic theoretical tools employed are Green's function for elliptic problems and the eigendecomposition of symmetric positive definite matrices. Based upon this study, a general strategy is suggested for how to choose the monitor function, and numerical results are presented for illustrative purposes.The three-dimensional case is also briefly discussed. It is noted that the strategy used here can be applied to other elliptic mesh generation techniques as well.

Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation

We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz--Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT solves all difficulties with crowding and global convergence, although these facts depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications in two-dimensional potential theory and mesh generation. We demonstrate CRDT on problems in long, thin regions in which no other known algorithm can perform comparably.

Meshing by successive superelement decomposition (MSD) — A new approach to quadrilateral mesh generation

An automatic two-dimensional mesh generation scheme based on superelement decomposition technique is presented. The proposed approximate skeletal method (ASM) uses shape interrogation techniques on simplified geometric representation of the shape boundary to generate non-intersecting, topologically simple and mappable superelements. A recursive mesh generation scheme, meshing by successive decomposition, is introduced which uses edge-based hierarchical data structures to successively create parent-child edge relations and possible transitions based on the nodal spacing on these edges. Individual edge segments are obtained by transfinite mapping techniques. The use of a structured background grid is suggested to ensure full control of the mesh in case of transitions and grading. Finally, application to plane adaptive FEA problems demonstrates that the proposed mesh generator (MSD) results in good mesh grading and convergence characteristics.

Two-Dimensional Automatic Mesh Generation Optimizing Memory Size and Computing Time for the Finite Element Analysis of High Voltage Insulators

The Finite Element Method (FEM) is commonly used for the solution of electrical and magnetic field problems due to some of its advantages. However, preparation of the input data is an important difficulty for the method. In this study, in order to compute the potential and electrical field distribution for high voltage (HV) insulators by the FEM an algorithm has been developed to get the input data for the solution region automatically. The algorithm can generate elements, and nodes, and determine the properties of material such as dielectric constant, conductivity, etc. by the limited initial information. In addition, the generated data is rearranged to minimize the bandwidth of the coefficient matrix. Thus the memory size to be used and the computing time required are minimized.

A two-dimensional mesh generator with boundary conditions generation

A two-dimensional mesh generator with automatically generated boundary conditions which is an improved version of a variable order mesh generator program by Liu and Chen [ Comput. Struct. 29, 1033–1053, (1988)], is presented. The improvements include the ability to generate a series of points or face constraints and loads on the boundary generated nodes or element sides from original superelement information. A FORTRAN programme is given to generate quadrilateral mesh and various boundary conditions for an axisymmetric problem.

MSHGEN — a FORTRAN program on automatic two-dimensional and three-dimensional triangular mesh generation

A computer program on automatic generation of three-node or six-node triangular finite element mesh based on isoparametric mapping functions is presented. The program is written in FORTRAN-77 and implemented on an IBM-AT compatible personal computer. Given the boundaries of the surface of the structure, this program discretises the internal space into regular grids of user defined density and produce nodal coordinates and nodal connectivity with optional bandwidth/ profile reduction for efficient finite element analysis. Listing of the main part of the FORTRAN codings are included.

A two-dimensional adaptive mesh generation method

Abstract An automatic two-dimensional adaptive mesh generation method is persented. The method is designed so that a small portion of the mesh can be modified without disturbing a large number of adjacent mesh points. The method can be used with or without boundary-fitted coordinate generation procedures. On the generated mesh a differential equation can be discretized by using classical difference formulas designed for uniform meshes as well as the difference formulas developed in this work. Both cases are illustrated by applying the method to the Hiemenz flow for which the exact solution of the Navier-Stokes equation is known [1] and to a two-dimensional viscous internal flow model problem.

A two-dimensional automatic mesh generator for finite element analysis for random composites

In this paper a two-dimensional automatic mesh generation technique has been proposed for composites, in which the second phase consisting of particulates or unidirectional fibers are randomly dispersed in the matrix. The discretization is based on Dirichlet tessellation of the composite domain to yield an aggregate of convex polygons. These polygons, called Voronoi polygons or Dirichlet cells, will serve as the elements in the finite element analysis of a composite structure. Effects of arbitrary domain boundaries, shapes and sizes of the inclusions have been incorporated in the mesh generator.

A two-dimensional adaptive mesh generation method.: Irfan Altas and John W. Stephenson, University of Saskatchewan, Saskatoon, Saskatchewan, CANADA

A two-dimensional adaptive mesh generation method.: Irfan Altas and John W. Stephenson, University of Saskatchewan, Saskatoon, Saskatchewan, CANADA