Mesh quality

Objective: Human body finite element models (FE-HBMs) are available in standard occupant or pedestrian postures. There is a need to have FE-HBMs in the same posture as a crash victim or to be configured in varying postures. Developing FE models for all possible positions is not practically viable. The current work aims at obtaining a posture-specific human lower extremity model by reconfiguring an existing one. Methodology: A graphics-based technique was developed to reposition the lower extremity of an FE-HBM by specifying the flexion–extension angle. Elements of the model were segregated into rigid (bones) and deformable components (soft tissues). The bones were rotated about the flexion–extension axis followed by rotation about the longitudinal axis to capture the twisting of the tibia. The desired knee joint movement was thus achieved. Geometric heuristics were then used to reposition the skin. A mapping defined over the space between bones and the skin was used to regenerate the soft tissues. Mesh smoothing was then done to augment mesh quality. Results: The developed method permits control over the kinematics of the joint and maintains the initial mesh quality of the model. For some critical areas (in the joint vicinity) where element distortion is large, mesh smoothing is done to improve mesh quality. Conclusions: A method to reposition the knee joint of a human body FE model was developed. Repositions of a model from 9 degrees of flexion to 90 degrees of flexion in just a few seconds without subjective interventions was demonstrated. Because the mesh quality of the repositioned model was maintained to a predefined level (typically to the level of a well-made model in the initial configuration), the model was suitable for subsequent simulations.

Finite element (FE) analysis is a valuable tool in musculoskeletal research. The demands associated with mesh development, however, often prove daunting. In an effort to facilitate anatomic FE model development we have developed an open source software toolkit (IA-FEMesh). IA-FEMesh employs a multiblock meshing scheme aimed at hexahedral mesh generation. An emphasis has been placed on making the tools interactive, in an effort to create a user friendly environment. The goal is to provide an efficient and reliable method for model development, visualization, and mesh quality evaluation. While these tools have been developed, initially, in the context of skeletal structures they can be applied to countless applications.

The various manufacturers of digitization systems speak of the effectiveness and accuracy of their tools under optimal conditions, but actual experimentation with simple or complex objects and different materials yields results that on occasions refute the effectiveness of those systems. In order to help choose a digitization system on the basis of its accuracy and the quality of the distribution of points and triangular meshes, in the field of reverse engineering, we compared five digitization techniques (three versions of the laser scanner, a fringe projection version and an X-ray version): (1) an ordered point cloud obtained with a laser incorporated in a CMM, (2) a disordered point cloud obtained with a manual laser the position of which is determined with a Krypton Camera, (3) an Exascan manual laser with targets, (4) an ordered point cloud obtained by high precision Computerized Tomography (CT) and an Atos fringe projection scanner with targets. Each of the three calibrated pieces (a sphere, a cylinder and a gauge block) was measured five times by the five digitization systems to confirm the accuracy of the measurement. A comparison was also made of the meshes generated by the five software packages (Focus-Inspection, Metris, VxScan, Mimics and Atos) of the five digitization systems for the three calibrated pieces and two more complex pieces (a bone and an automobile window winder pulley) to determine meshing quality. Finally, all the pieces were meshed by triangulation in the Catia V5 DSE (Digitized Shape Editor) module in order to test the quality of the points distribution.

We compare inexact Newton and coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

The main aim of this paper is the development of a refinement procedure able to operate in the context of the constrained natural element method (C-NEM). The C-NEM was proposed by the authors in a former work [Yvonnet J, Ryckelynck D, Lorong P, Chinesta F. A new extension of the natural element method for non-convex and discontinuous domains: the constrained natural element method (C-NEM). Int J Numer Methods Eng 2004;60:1451-1474] and its main meshless features, that allow to describe large domain changes as well as to handle fixed or moving discontinuities, were analyzed in [Yvonnet J, Chinesta F, Lorong P, Rynckelynck D. The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces. Int J Thermal Sci 2005;44:559-569; Yvonnet J, Lorong P, Ryckelynck D, Chinesta F. Simulating dynamic thermo-elastoplasticity in large transformations with adaptive refinement in the natural element method: application to shear banding. Int J Forming Process 2005;8:347-363]. Sometimes, in order to improve the interpolation accuracy for describing boundary layers or an anisotropic behavior, new nodes must be added, removed or repositioned. The interpolation in the vast majority of meshless techniques is free of mesh quality requirement. Thus, introduction, elimination or repositioning of nodes is a trivial task, because no geometrical restrictions exist. In this way, nodes can be added without geometrical checks in the regions where the solution must be improved (identified by using an appropriate error indicator). For this purpose, in this paper an a posteriori error indicator will be proposed and tested in some linear elastostatic problems benchmarks involving different levels of difficulty (stress concentration, solution singularities, . . .) all of them with a known exact solution. The computational implementation of this error indicator is very simple, and when it is used in tandem with an efficient refinement procedure, which makes use of the meshless features of the C-NEM, provides an accurate adaptation procedure, specially appropriate in the C-NEM framework.

This paper presents on-going finite element modeling efforts of friction stir spot welding (FSSW) process by an explicit finite element code. Adaptive meshing and advection schemes, which makes it possible to maintain mesh quality under large deformations, is utilized to simulate the material flow and temperature distribution in FSSW process. The predicted overall deformation shape of the weld joint resembles that experimentally observed. Temperature and stress graphs in the radial direction as well as temperature-deformation distribution plots are presented. However, refinements of several modeling aspects are needed for more realistic prediction of the FSSW process.

We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two

This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, multi-scale volumetric synthetic electron density maps are constructed from parsed atomic location data of biomolecules in the PDB, using Gaussian isotropic kernels. An appropriate parameter selection is made for constructing an error bounded implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the molecular surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flows are used to improve the mesh quality. Some of our generated meshes have been successfully used in finite element simulations.

Many physical phenomena in science and engineering can be modeled by partial differential equations and solved by means of the finite element method. Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. The 'mesh quality' is a key-point for the accuracy of the numerical simulation. One can show that this quality is related to the shape and the size of the mesh elements. In the case where the element sizes are not specified in advance, a quality mesh is a regular mesh (whose elements are almost equilateral). This problem is a particular case of a more general mesh generation problem whose purpose is to construct meshes conforming to a prespecified isotropic size field associated with the computational domain. Such meshes can be seen as 'unit meshes' (whose elements are of unit size) in an appropriate non-Euclidean metric. In this case, a quality mesh of the domain is a unit mesh as regular as possible. In this paper, we are concerned with the generation of such a mesh and we propose a method to achieve this goal. First, the boundary of the domain is meshed using an indirect scheme via parametric domains and then the mesh of the three-dimensional (3D) domain is generated. In both cases, an empty mesh is first constructed, then enriched by field points, and finally optimized. The field points are defined following an algebraic or an advancing-front approach and are connected using a generalized Delaunay type method. To show the overall meshing process, we give an example of a 3D domain encountered in a classical computational fluid dynamics problem. q

Airborne LiDAR (Light Detection And Ranging) combines cost efficiency, high degree of automation, high point density of typically 1-10 points per m 2 and height accuracy of better than ±15 cm. For all these reasons LiDAR is particularly suitable for deriving precise Digital Terrain Models (DTM) as geometric basis for hydrodynamic-numerical 5 (HN) simulations. The application of LiDAR for river flow modelling requires a series of preprocessing steps. Terrain points have to be filtered and merged with river bed data, e.g. from echo sounding. Then, a smooth Digital Terrain Model of the Watercourse (DTM-W) needs to be derived, preferably considering the random measurement error during surface interpolation. In a subsequent step, a hydraulic computation mesh has 10 to be constructed. Hydraulic simulation software is often restricted to a limited number of nodes and elements, thus, data reduction and data conditioning of the high resolution LiDAR DTM-W becomes necessary. We will present a DTM thinning approach based on adaptive TIN refinement which allows a very effective compression of the point data (more than 95% in flood plains and up to 90% in steep areas) while preserving 15 the most relevant topographic features (height tolerance ±20 cm). Traditional hydraulic mesh generators focus primarily on physical aspects of the computation grid like aspect ratio, expansion ratio and angle criterion. They often neglect the detailed shape of the topography as provided by LiDAR data. In contrast, our approach considers both the high geometric resolution of the LiDAR data and additional mesh quality parameters.

High-quality surface extraction is a crucial prerequisite for high-quality flow simulation and analysis in cerebral aneurysms. In this paper we present a two-step approach that first efficiently extracts a smooth surface from segmented aneurysms by means of MPU Implicits and then further improves the mesh quality to generate high-quality surfaces as input for the numerical simulation of blood flow in cerebral aneurysms. The presented work is an important step towards methods to assess growth, rupture risk, and therapeutic alternatives in the treatment of cerebral aneurysms.

We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an area-based smoothing technique. Area-based smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some

This paper describes an algorithm for generating unstructured triangulations for arbitrarily shaped two- dimensional regions. The algorithm works for regions without cracks, as well as for regions with one or multiple cracks. The algorithm incorporates aspects of well-known meshing procedures and includes some original steps. It includes an advancing front technique, which uses an quadtree procedure to develop local guidelines

High-quality surface extraction is a crucial prerequisite for high-quality flow simulation and analysis in cerebral aneurysms. In this paper we present a two-step approach that first efficiently extracts a smooth surface from segmented aneurysms by means of MPU Implicits and then further improves the mesh quality to generate high-quality surfaces as input for the numerical simulation of blood flow in cerebral aneurysms. The presented work is an important step towards methods to assess growth, rupture risk, and therapeutic alternatives in the treatment of cerebral aneurysms.

This article addresses the quality of service provisioning issues in the wireless mesh backbone for broadband wireless access. Differentiated services over the wireless mesh backbone is investigated in the avenues of QoS routing and MAC mechanisms. Challenges and open issues are identified, along with potential solutions and possible research directions.

A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.

This paper presents a novel Scalar-field based Free-Form Deformation (SFFD) technique founded upon general flow constraints and implicit functions. In contrast to the traditional lattice-based FFD driven by parametric geometry and spline theory, we employ scalar fields as embedding spaces instead. Upon the deformation of the scalar field, the vertices will move accordingly, which result in freeform deformations of the embedded object. The scalar field construction, sketching, and manipulation are both natural and intuitive. By tightly coupling self-adaptive subdivision and mesh optimization with SFFD, versatile multi-resolution free-form deformations can be achieved because our algorithm can adaptively refine and improve the model on the fly to improve the mesh quality. We can also enforce various constraints on embedded models, which enable our technique to preserve the shape features and facilitate more sophisticated design. Our system demonstrates that SFFD is very powerful and intuitive for shape modeling. It significantly enhances traditional FFD techniques and facilitates a larger number of shape deformations.

The various manufacturers of digitization systems speak of the effectiveness and accuracy of their tools under optimal conditions, but actual experimentation with simple or complex objects and different materials yields results that on occasions refute the effectiveness of those systems. In order to help choose a digitization system on the basis of its accuracy and the quality of the distribution of points and triangular meshes, in the field of reverse engineering, we compared five digitization techniques (three versions of the laser scanner, a fringe projection version and an X-ray version): (1) an ordered point cloud obtained with a laser incorporated in a CMM, (2) a disordered point cloud obtained with a manual laser the position of which is determined with a Krypton Camera, (3) an Exascan manual laser with targets, (4) an ordered point cloud obtained by high precision Computerized Tomography (CT) and an Atos fringe projection scanner with targets. Each of the three calibrated pieces (a sphere, a cylinder and a gauge block) was measured five times by the five digitization systems to confirm the accuracy of the measurement. A comparison was also made of the meshes generated by the five software packages (Focus-Inspection, Metris, VxScan, Mimics and Atos) of the five digitization systems for the three calibrated pieces and two more complex pieces (a bone and an automobile window winder pulley) to determine meshing quality. Finally, all the pieces were meshed by triangulation in the Catia V5 DSE (Digitized Shape Editor) module in order to test the quality of the points distribution.

1 Brigham Young UniversityP rovo,U TU .S.A. [email protected] 2 Brigham Young UniversityP rovo,U TU .S.A. [email protected] 3 Brigham Young UniversityP rovo,U TU .S.A. [email protected] 4 M. B. Stephenson &A ssociates, Provo,U TU .S.A. [email protected]

This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A top-down octree subdivision coupled with a dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with boundary feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing quality meshes for finite element calculations.

This paper presents ongoing finite element modeling efforts of friction stir spot welding (FSSW) process by an explicit finite element code. Adaptive meshing and advection schemes, which makes it possible to maintain mesh quality under large deformations, is utilized to simulate the material flow and temperature distribution in FSSW process. The predicted overall deformation shape of the weld joint resembles that experimentally observed. Temperature and stress graphs in the radial direction as well as temperature-deformation distribution plots are presented. However, refinements of several modeling aspects are needed for more realistic prediction of the FSSW process.

This paper describes an approach to construct unstructured tetrahedral and hexahedral meshes for a domain with multiple materials. In earlier works, we developed an octreebased isocontouring method to construct unstructured 3D meshes for a single-material domain. Based on this methodology, we introduce the notion of material change edge and use it to identify the interface between two or several materials. We then mesh each material region with conforming boundaries. Two kinds of surfaces, the boundary surface and the interface between two different material regions, are distinguished and meshed. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for hexahedral mesh construction. Finally the edge-contraction and smoothing method is used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set is defined automatically as the boundary of each material region. Several application results in different research fields are shown.

CFD analysis of heat and mass flow due to natural convection in partitioned enclosures has recently been the focus of many CFD researchers. In some cases, it was reported in the literature that different CFD solutions (due to different numerical stability characteristics) were obtained for different mesh quality, time step, and discretization order. The objective of this paper is to investigate the feasibility of using neural networks (NNs) as a means lending support to the authenticity of steady-state CFD solutions for such ill-posed problems through inter-model comparisons. Attention is focused on using NNs trained on a database generated by numerically-stable CFD analysis to predict flow variables for the aforementioned ill-posed cases, thereby giving confidence in steady-state CFD results for these cases. Three types of NNs were evaluated and parametric studies were performed to optimize network designs for best predictions of the flow variables. A validated CFD code was used to generate a database that covered the range of Rayleigh number Ra from 10 4 to 4.7 • 10 6. The CFD analysis was used to calculate the normalized temperature h and stream function w throughout a partitioned enclosure. The results of the CFD were used to train and test the neural networks. The robustness of the trained NNs was tested by applying them to a number of ''production'' data sets that the networks have never ''seen'' before. The trained NNs were used to verify CFD solutions in cases of higher Ra ranges for which CFD simulations produce different solutions for different discretization schemes. The results showed that it is possible to design and train certain architectures of NNs to accurately predict h and w distribution within the enclosure, and hence impart confidence in the legitimacy of CFD solutions for new cases.

In this paper, we present a novel method, based on an implementation of quasi-statistical modeling, for improving hexahedral solid mesh. A method for improving meshes by producing elements with a Gaussian (normal) distribution of the mesh quality parameter values is discussed. The main intention is to attain a fairly smooth change from one mesh element to another without creating a significant difference between the shapes of neighboring elements. As regards the initial distribution of the mesh quality parameter values, we assume that after improvement the distribution varies from a rather random distribution to a smoother one, such as a normal distribution. The preliminary choice of the desirable distribution affects the new parameter values modeled by the formula presented here. Our proposed method can be used in a pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.

We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various ...

This paper presents a novel Scalar-field based Free-Form Deformation (SFFD) technique founded upon general flow constraints and implicit functions. In contrast to the traditional lattice-based FFD driven by parametric geometry and spline theory, we employ scalar fields as embedding spaces instead. Upon the deformation of the scalar field, the vertices will move accordingly, which result in freeform deformations of the embedded object. The scalar field construction, sketching, and manipulation are both natural and intuitive. By tightly coupling self-adaptive subdivision and mesh optimization with SFFD, versatile multi-resolution free-form deformations can be achieved because our algorithm can adaptively refine and improve the model on the fly to improve the mesh quality. We can also enforce various constraints on embedded models, which enable our technique to preserve the shape features and facilitate more sophisticated design. Our system demonstrates that SFFD is very powerful and intuitive for shape modeling. It significantly enhances traditional FFD techniques and facilitates a larger number of shape deformations.

The opening and closing behavior of the valve is a delicate interaction between blood flow and geometrical and stiffness properties of the heart valve leaflets and aortic root. Numerical analysis of the opening and closing behavior is complicated by the three-dimensional finite motion of the very flexible leaflets in a compliant system of fluid and structure. Fluid-structure interaction models of the heart valve have been developed before, e.g. see Peskin & McQueen (1) and Horsten (2). However, none of these models was able to analyse the physiological condition in which the valve functions because of numerical artefacts. The Fictitious Domain/Arbitrary Lagrange-Euler method is introduced, which allows numerical modeling of valves under physiological conditions. Methods In modeling fluid-structure interaction, the fluid domain is most conveniently described with respect to an Eulerian reference frame while a Lagrangian formulation is more appropriate for the structure domain. Howeve...

The generation of triangulations on p-order parametric surfaces is a fundamental first step to numerical solutions for multidomain problems involving complex geometries such as those encountered in biological fluid dynamics and other applications. In this study we develop a novel, computationally efficient method for generating triangulations in computational space, which, under parametric mapping, are of high geometric quality. Computational efficiency is maintained over parametric orders (p) through approximating the parametric surface by a grid of simplified vector functions. Unlike other length metric approximations, a maximum bound on the error introduced to the calculation of lengths by this approximation is defined to ensure the fidelity of the transformation. This technique is applied to three parametric functions which demonstrate its robustness in handling high mesh distortions, singularities, and high order surfaces. Further, three complex high-order biological finite element meshes are triangulated. High mesh quality and a linear relationship between triangle generation and CPU time is observed for each of these meshes.

Progressive mesh streaming enables users to view 3D meshes over the network with increasing level of details, by sending coarse version of the meshes initially, followed by a series of refinements. To optimally increase the rendered mesh quality, refinements should be sent in descending order of their visual contributions based on the user's viewpoint. A common approach is to let the sender decide this sending order, but the computational cost of making this decision prohibits such sender-driven approach from scaling to large number of clients. To improve scalability, we propose a receiver-driven protocol, in which the receiver decides the sending order and explicitly requests the refinements, while the sender simply sends the data requested. The sending order is computed at the receiver by estimating the visibility and visual contributions of the refinements, even before receiving them, with the help of GPU. Experiments show that our protocol reduces the CPU cost of the sender by 24% and the outgoing traffic of the sender by 40%.

A procedure is presented to improve the quality of surface meshes while maintain- ing the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local para- metric spaces such that the vertices remain on the original discrete surface. The movement of the mesh vertices is driven by a non-linear

We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various ...

Many physical phenomena in science and engineering can be modeled by partial differential equations and solved by means of the finite element method. Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. The 'mesh quality' is a key-point for the accuracy of the numerical simulation. One can show that this quality is related to the shape and the size of the mesh elements. In the case where the element sizes are not specified in advance, a quality mesh is a regular mesh (whose elements are almost equilateral). This problem is a particular case of a more general mesh generation problem whose purpose is to construct meshes conforming to a prespecified isotropic size field associated with the computational domain. Such meshes can be seen as 'unit meshes' (whose elements are of unit size) in an appropriate non-Euclidean metric. In this case, a quality mesh of the domain is a unit mesh as regular as possible. In this paper, we are concerned with the generation of such a mesh and we propose a method to achieve this goal. First, the boundary of the domain is meshed using an indirect scheme via parametric domains and then the mesh of the three-dimensional (3D) domain is generated. In both cases, an empty mesh is first constructed, then enriched by field points, and finally optimized. The field points are defined following an algebraic or an advancing-front approach and are connected using a generalized Delaunay type method. To show the overall meshing process, we give an example of a 3D domain encountered in a classical computational fluid dynamics problem. q

Discrete fracture network simulations are computationally intensive and usually time-consuming to construct and configure. This paper presents a case study with techniques for building a 3D finite element model of an inhomogeneous fracture network for modelling flow and tracer transport, combining deterministic and stochastic information on fracture aperture distributions. The complex intersected fractures represent a challenge for geometrical model design, mesh quality requirements and property allocations. For the integrated and holistic modelling approach, including the application of numerical and analytical simulation techniques, new object-oriented concepts in software engineering are implemented to ensure a resourceful and practicable software environment.

Whisker Weaving is an advancing front algorithm for all-hexahedral mesh generation. It uses global information derived from grouping the mesh dual into surfaces, the STC, to construct the connectivity of the mesh, then positions the nodes afterwards. Currently we are able to reliably generate hexahedral meshes for complicated geometries and surface meshes. However, the surface mesh must be modified locally. Also, in large, highlyunstructured meshes, there are usually isolated regions where hex quality is poor. Reliability has been achieved by using new, provable curve-contraction algorithms to sequence the advancing front process. We have also demonstrated that sheet moving can remove certain types of invalid connectivity.

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to nite element methods is used to understand the basis of present-day geometrical mesh quality indicators. A survey of more recent work in the development of nite element methods reveals work on anisotropic meshing algorithms and on providing good error estimates that reveal the relationship between the error and both the mesh and the solution gradients. The realities of solving complex three dimensional problems is that such indicators are presently not available for many problems of interest. A simple tetrahedral mesh quality measure using both geometrical and solution information will be described. Some of the issues in mesh quality for unstructured tetrahedral meshes will be illustrated by means of a simple example.

An automatic mesh generator is described based on a Let-It-Grow neural network, Starting from a rough mesh of triangles with a small number of nodes, the neural algorithm increases the number of nodes llntil a user-selected value is reached. The node growth is driven by a predefined probability density function. Several modifications to the original Let-It-Grow algorithm were made in oirder to save the boundary of the domain and to take the mesh quality into account.

In this paper, we present a novel method, based on an implementation of quasi-statistical modeling, for improving hexahedral solid mesh. A method for improving meshes by producing elements with a Gaussian (normal) distribution of the mesh quality parameter values is discussed. The main intention is to attain a fairly smooth change from one mesh element to another without creating a significant difference between the shapes of neighboring elements. As regards the initial distribution of the mesh quality parameter values, we assume that after improvement the distribution varies from a rather random distribution to a smoother one, such as a normal distribution. The preliminary choice of the desirable distribution affects the new parameter values modeled by the formula presented here. Our proposed method can be used in a pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.

In this paper, we present a new technique called Trapezium Drawing to improve surface mesh quality while maintaining the essential surface characteristics. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our approach allows keeping new mesh close to the surface approximated by the initial mesh. All operations are performed directly on the surface. As a result our technique is robust and runs at interactive speeds. It can be applied to triangular and quadrilateral meshes iteratively. Various quantitative measures are presented to demonstrate the effectiveness of proposed technique.