Parallel adaptive mesh generation and decomposition

An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e. meshes, grids) is the so calledgeometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balancedsubdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem. For this reason several fast heuristics have been proposed. In this paper we explore a decomposition approach which is part of a parallel adaptive finite element mesh procedure. The proposed integrated approach consists of five steps. It starts with a coarse background mesh that isoptimally decomposed by applying well known heuristics. Then, the initial mesh is refined in each subdomain after linking the new boundaries introduced by its decomposition. Finally, the decomposition of the new refined mesh is improved so that it satisfies the objectives and conditions of the mesh decomposition problem. Extensive experimentation indicates the effectiveness and efficiency of the proposed parallel mesh and decomposition approach.     

Hexahedral mesh generation constraints

For finite element analyses within highly elastic and plastic structural domains, hexahedral meshes have historically offered some benefits over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability. However, hexahedral finite element mesh generation continues to be difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer than current tetrahedral mesh generators to complete. Thus, developing a better understanding of the underlying constraints that make hexahedral meshing difficult could result in dramatic reductions in the amount of time necessary to prepare a hexahedral finite element model for analysis. In this paper, we present a survey of constraints associated with hexahedral meshes (i.e., the conditions that must be satisfied to produce a hexahedral mesh). In presenting our formulation of these constraints, we will utilize the dual of a hexahedral mesh. We also discuss how incorporation of these constraints into existing hexahedral mesh generation algorithms could be utilized to extend the class of geometries to which these algorithms apply. We also describe a list of open problems in hexahedral mesh generation and give some context for future efforts in addressing these problems.     

Compositional design of isochronous systems

The synchronous modeling paradigm provides strong correctness guarantees for embedded system design while requiring minimal environmental assumptions. In most related frameworks, global execution correctness is achieved by ensuring the insensitivity of (logical) time in the program from (real) time in the environment. This property, called endochrony or patience, can be statically checked, making it fast to ensure design correctness. Unfortunately, it is not preserved by composition, which makes it difficult to exploit with component-based design concepts in mind. Compositionality can be achieved by weakening this objective, but at the cost of an exhaustive state-space exploration. This raises a trade-off between performance and precision. Our aim is to balance it by proposing a formal design methodology that adheres to a weakened global design objective: the non-blocking composition of weakly endochronous processes, while preserving local design objectives for synchronous modules. This yields an effective and cost-efficient approach to compositional synchronous modeling.     

Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm

This paper describes mesh correction techniques necessary for meshing an arbitrary volume with a completely hexahedral mesh. Specifically, it describes seams and wedges, mechanisms that overcome major hurdles encountered in the preliminary work on the plastering algorithm. The plastering algorithm iteratively projects layers of elements inward from a quadrilateral discretization of the volume's bounding faces. Seams and wedges resolve incompatibilities in the mesh and in the progressing boundary, thus ensuring the correct formation of a hexahedral mesh from the plastering algorithm.     

High-quality 2D mesh generation without obtuse and small angles

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles.     

A quantitative assessment of approaches to mesh generation for surgical simulation

In surgical simulation, it is common practice to use tetrahedral meshes as models for anatomy. These meshes are versatile, and can be used with a number of different physically based modelling schemes. A variety of mesh generators are available that can automatically create tetrahedral meshes from segmented anatomical volumes. Each mesh generation scheme offers its own set of unique attributes. However, few are readily available. When choosing a mesh generator for simulation, it is critical for it to output good-quality, patient-specific meshes that provide a good approximation of the shape or volume to be modelled. To keep computation time within the bounds required for real-time interaction, there is also a limit imposed on the number of elements in the mesh generated. To the authors knowledge, there has been little work directly assessing the suitability of mesh generators for surgical simulation. This paper seeks to address this issue by assessing the use of six mesh generators in a surgical simulation scenario, and examining how they affect simulation precision. This paper aims to perform these comparisons against high-resolution reference meshes, where we examine the precision of meshes from the same mesh generator at different levels of complexity.

Using sequential NETGEN as a component for a parallel mesh generator

A parallel tetrahedral mesh generator is developed using the existing sequential NETGEN mesh generator. Mesh generation algorithms developed decompose the geometry into multiple sub-geometries sequentially on a master node and then mesh each sub-geometry in parallel on multiple processors. Two methods are implemented. The first decomposes the geometry and produces conforming surface sub-meshes from which volume meshes can be generated in parallel. A second refinement based method also makes use of the CAD geometry information. A scalable mesh migration algorithm that utilizes “owner updates” rule is implemented. Results show that using the refinement based method, a mesh with a billion elements can be generated in about a minute.     

Octree-based automatic mesh generation for non-manifold domains

Automatic mesh generation within the context of non-manifold geometric models is far from a commercial reality. While manifold objects are the most commonly encountered domains in many applications, other applications such as those requiring multiple material models and mixedmodel representations (combination of 1-D, 2-D and 3-D domains) fall beyond the realm of the existing automatic meshing procedures as they require a non-conventional modeling enviroment, namely the non-manifold topology (NMT) based environment. This paper focuses on automatic mesh generation issues in the context of two such applications: (i) finite element modeling for multiple material models and (ii) geometric abstractions requiring a mixed-model representation. Specifically, the paper describes a geometry utility system, built around an NMT data structure and geometry-based meshing algorithms that ensure the validity of the mesh for non-manifold domains.GE Consulting Services.     

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.     

Limits of formal methods

Formal methods can help to increase the correctness and trustworthiness of the software developed. However, they do not solve all the problems of software development. This paper analyses some limitations of formal methods.     

Anisotropic quadrilateral mesh generation: An indirect approach

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and higher element quality. The aim is to generate meshes with less elements which fit some anisotropy criterion to satisfy numerical accuracy while reducing processing times remarkably. The generation of high quality volume meshes using an advancing front algorithm relies heavily on a well designed surface mesh. For this reason this paper presents a new technique for the generation of high quality surface meshes containing a significantly reduced number of elements. This is achieved by creating quadrilateral meshes that include anisotropic elements along a source of anisotropy.     

Applying abstraction and formal specification in numerical software design

Numerical software development tends to struggle with an increasing complexity. This is, on the one hand, due to the integration of numerical models, and on the other hand, due to change of hardware. Parallel computers seem to fulfill the need for more and more computer resources, but they are more complex to program.

The article shows how abstraction is used to combat complexity. It motivates that separating a specification, “what,” its realisation, “how,” and its implementation, “when, where,” is of vital importance in software development. The main point is that development steps and levels of abstraction are identified, such that the obtained software has a clear and natural structure.

Development steps can be cast into a formal, i.e., mathematical framework, which leads to rigourous software development. This way of development leads to accurate and unambiguous recording of development steps, which simplifies maintenance, extension and porting of software. Portability is especially important in the field of parallel computing where no universal parallel computer model exists.     

形式方法与面向对象方法的结合探讨

文中讨论了形式方法和面向对象方法各自的优缺点，结合作者设计的面向对象形式规格说明语言ＯＯＺＳ，介绍了将这两种方法结合起来的三种途径，并对这三种途径进行分析，评价和对比，最后提出了今后的研究方向。     

Socio-technical systems: From design methods to systems engineering

It is widely acknowledged that adopting a socio-technical approach to system development leads to systems that are more acceptable to end users and deliver better value to stakeholders. Despite this, such approaches are not widely practised. We analyse the reasons for this, highlighting some of the problems with the better known socio-technical design methods. Based on this analysis we propose a new pragmatic framework for socio-technical systems engineering (STSE) which builds on the (largely independent) research of groups investigating work design, information systems, computer-supported cooperative work, and cognitive systems engineering. STSE bridges the traditional gap between organisational change and system development using two main types of activity: sensitisation and awareness; and constructive engagement. From the framework, we identify an initial set of interdisciplinary research problems that address how to apply socio-technical approaches in a cost-effective way, and how to facilitate the integration of STSE with existing systems and software engineering approaches.     

A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints

This paper presents a new automated method of quadrilateral meshes with random line constraints which have not been fully considered in previous models. The authors developed a new looping scheme and a direct quadrilateral forming algorithm based on advanced front techniques. This generator overcomes the limitations of previous studies such as line constraint, unmeshed hole and mesh refinement. A qualitative test reveals that our algorithm is reliable and suitable at the field needed for very accurate results. The developed direct method to handle line-typed features automatically makes the multiple discretizations without any user interaction and modification.     

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvement of meshes in a broad range of applications.     

Alternating Schwarz methods for partial differential equation-based mesh generation

To solve boundary value problems with moving fronts or sharp variations, moving mesh methods can be used to achieve reasonable solution resolution with a fixed, moderate number of mesh points. Such meshes are obtained by solving a nonlinear elliptic differential equation in the steady case, and a nonlinear parabolic equation in the time-dependent case. To reduce the potential overhead of adaptive partial differential equation-(PDE) based mesh generation, we consider solving the mesh PDE by various alternating Schwarz domain decomposition methods. Convergence results are established for alternating iterations with classical and optimal transmission conditions on an arbitrary number of subdomains. An analysis of a colouring algorithm is given which allows the subdomains to be grouped for parallel computation. A first result is provided for the generation of time-dependent meshes by an alternating Schwarz algorithm on an arbitrary number of subdomains. The paper concludes with numerical experiments illustrating the relative contraction rates of the iterations discussed.     

A comparison of two optimization methods for mesh quality improvement

We compare inexact Newton and block 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.

On local modularity and interpolation in entailment systems

We generalise and clarify connections between variants of modularity (preservation of faithfulness) and interpolation by localising them to a diagram in an entailment system. The variants of modularity arise naturally from the idea of building specifications in steps. We establish, by an algebraic approach, connections between these variants and (the existence of) versions of interpolating specifications. We also extend these correspondences to specification and interpolating families, and clarify the role of pushout diagrams in this context.     

Shape optimization of quad mesh elements

We study the problem of optimizing the face elements of a quad mesh surface, that is, re-sampling a given quad mesh to make it possess, as much as possible, face elements of some desired aspect ratio and size. Unlike previous quad mesh optimization/improvement methods based on local operations on a small group of elements, we adopt a global approach that does not introduce extra singularities and therefore preserves the original quad structure of the input mesh. Starting from a collection of quad patches extracted from an input quad mesh, two global operations, i.e. re-sampling and re-distribution, are performed to optimize the number and spacings of grid lines in each patch. Both operations are formulated as simple optimization problems with linear constraints.