Hexahedral Mesh Untangling

We investigate a well-motivated mesh untangling objective function whose optimization automatically produces non-inverted elements when possible. Examples show the procedure is highly effective on simplicial meshes and on non-simplicial (e.g., hexahedral) meshes constructed via mapping or sweeping algorithms. The current whisker-weaving (WW) algorithm in CUBIT usually produces hexahedral meshes that are unsuitable for analyses due to inverted elements. The majority of these meshes cannot be untangled using the new objective function. The most likely source of the difficulty is poor mesh topology

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Hexahedral-dominant meshing

This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh.It follows a three-steps pipeline similar to the one proposed by Carrier-Baudoin et al.:(1) generate a frame field; (2) generate a pointset P that is mostly organized on a regulargrid locally aligned with the frame field; and (3) generate thehexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P.For step (1), we use a state of the art algorithm to generate a smooth frame field. For step (2), weintroduce an extension of Periodic Global Parameterization to the volumetric case. As compared withother global parameterization methods (such as CubeCover), our method relaxes some global constraintsand avoids creating degenerate elements, at the expense of introducing some singularities that aremeshed using non-hexahedral elements. For step (3), we build on the formalism introduced byMeshkat and Talmor, fill-in a gap in their proof and provide a complete enumeration of all thepossible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh.The method is evaluated and compared with the state of the art on adatabase of examples with various mesh complexities, varying fromacademic examples to real industrial cases. Compared with the methodof Carrier-Baudoin et al., the method results in better scoresfor classical quality criteria of hexahedral-dominant meshes(hexahedral proportion, scaled Jacobian, etc.). The methodalso shows better robustness than CubeCover and its derivativeswhen applied to complicated industrial models

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

The Biomechanics of Pregnancy: Simulating Pregnancy Mechanics, Evaluating Preterm Delivery Interventions, and Measuring in-vivo Mechanical Properties

Preterm birth is a public health problem affecting almost 15 million newborns each year, with almost one million cases annually being fatal. Despite many decades of research, identifying high-risk pregnancies remains difficult. Even with the therapies currently available to clinicians, 95% of preterm births are seemingly intractable. We see a great opportunity for engineers to collaborate with clinicians to help reduce the adverse health impact of this phenomenon. This work is a multi-faceted contribution to the study of the biomechanical problem of preterm birth. We portray the successful, full-term, pregnancy as a delicate balance of organ geometry, tissue deformation behavior, and the physical interaction between the uterus, cervix, and fetal membranes. The cervix is our focus, as its preterm ripening and dilation are the final pathway to premature delivery. We consider a selection of geometric and material factors, studying their impact on the loading that occurs in the cervix. We also study the mechanical implications of the use of a cervical pessary on the mechanical environment of pregnancy. Our mechanical analyses use a custom parameterized model of the pregnant anatomy, coupled with Finite Element Analysis techniques, to allow for rapid model development. In addition, we present a push towards the in-vivo measurement of cervical material properties by way of a phantom study using modern MRI techniques

Physically Based Forehead Modelling and Animation including Wrinkles

There has been a vast amount of research on the production of realistic facial models and animations, which is one of the most challenging areas of computer graphics. Recently, there has been an increased interest in the use of physically based approaches for facial animation, whereby the effects of muscle contractions are propagated through facial soft-tissue models to automatically deform them in a more realistic and anatomically accurate manner. Presented in this thesis is a fully physically based approach for efficiently producing realistic-looking animations of facial movement, including animation of expressive wrinkles, focussing on the forehead. This is done by modelling more physics-based behaviour than current computer graphics approaches. The presented research has two major components. The first is a novel model creation process to automatically create animatable non-conforming hexahedral finite element (FE) simulation models of facial soft tissue from any surface mesh that contains hole-free volumes. The generated multi-layered voxel-based models are immediately ready for simulation, with skin layers and element material properties, muscle properties, and boundary conditions being automatically computed. The second major component is an advanced optimised GPU-based process to simulate and visualise these models over time using the total Lagrangian explicit dynamic (TLED) formulation of the FE method. An anatomical muscle contraction model computes active and transversely isotropic passive muscle stresses, while advanced boundary conditions enable the sliding effect between the superficial and deep soft-tissue layers to be simulated. Soft-tissue models and animations with varying complexity are presented, from a simple soft-tissue-block model with uniform layers of skin and muscle, to a complex forehead model. These demonstrate the flexibility of the animation approach to produce detailed animations of realistic gross- and fine-scale soft-tissue movement, including wrinkles, with different muscle structures and material parameters, for example, to animate different-aged skin. Owing to the detail and accuracy of the models and simulations, the animation approach could also be used for applications outside of computer graphics, such as surgical applications. Furthermore, the animation approach can be used to animate any multi-layered soft body (not just soft tissue)

Meshing methods and adaptive algorithms in two and three dimensions for solving closed electromagnetic problems by means of the finite element method

[SPA] La primera parte de esta tesis, desarrollada en los capítulos 1, 2, 3 y 4, está dedicada al diseño de nuevos métodos de mallado bidimensional, superficial y volumétrico que sigan estas premisas. Aunque esos métodos han sido desarrollados en el contexto del análisis de guiado de ondas y el diseño de cavidades resonantes de microondas, su aplicación puede abarcar cualquier campo de la física, pues la fase de discretización del MEF presenta una clara independencia del problema tratado. La segunda parte de esta tesis, presentada en el capítulo 5, está dedicada al estudio de este tipo de métodos. En ella se describen los distintos indicadores de error y estrategias de refinamiento h desarrolladas, y se presentan y analizan los resultados obtenidos con ellos en distintas estructuras de guiado de ondas.[ENG] In its first part, the dissertation develops a multiblock methodology of surface and volumetric mesh generation from the discretization of the problem boundary, in order to apply the finite element method. Different structured and unstructured meshing techniques in 2D (interpolation and generalized fast advancing front), 3D surface and volumetric (advancing front) domains are presented. Moreover, some a posteriori techniques for improvement of quality mesh are described. The second part of this dissertation deals with adaptive meshing within an adaptive finite element method. This technique is an iterative variant of the finite element method where, in a first step, an initial mesh with few and low order elements is generated, the corresponding algebraic problem is solved and the error in the solution is estimated in order to add degrees of freedom in those regions of the domain with the biggest error estimation. This process is repeated until an ending condition is reached. The two basic stages in this method are the error indication and the mesh enrichment. In this dissertation, within the analysis of waveguiding structures, three kinds of error indicator have been developed: (1) Error indicators based on the residual of the vector wave equation and the boundary conditions at the edges of each element. (2) Error indicators based on the comparison of the solution curl with a smoothed or recovered curl, obtained from the solution curl. (3) Error indicators based on the flux (electric or magnetic) continuity through the inner edges in the mesh. In addition, an overview on refinement techniques is presented, and the h-refinement employed in this work is in depth described. Results obtained with the different error indicators and refinement strategies are discussed and compared with the classical, non-adaptive finite element method.Universidad Politécnica de ValenciaPrograma de doctorado de Telecomunicació