Tomasz Jurczyk

Metric 3d surface mesh generation using delaunay criteria

This paper presents a technique of incorporating anisotropic metric into the Delaunay triangulation algorithm for unstructured mesh generation on 3D parametric surfaces. Both empty circumcircle and inner angles criteria of Delaunay retriangulation can be successfully used with the developed method of coordinate transformation with little adjustments. We investigate the efficiency of mesh generation process for different criteria and the quality of obtained meshes.

Anisotropic Volume Mesh Generation Controlled by Adaptive Metric Space

This article describes automated procedure of construction of unstructured volume meshes. The meshes are constructed using a modified algorithm of Delaunay incremental insertion working in Riemannian metric space. During the meshing process the metric describes the desired size, shape and direction of elements in the domain being discretized, which allows creating graded and anisotropic meshes. The metric is stored in a discrete form, in a specially designed structure called control space. The form of the control space directly influences the quality of the created mesh, as well as the efficiency of the actual meshing process.

Domain Decomposition Techniques for Parallel Generation of Tetrahedral Meshes

We present solutions for dealing with the problem of parallel generation of unstructured meshes for 3D domains. The selected approach is based on a geometric decomposition of the domain where the input data is given in the form of a surface mesh. The difference between the two presented decomposition techniques lies in the step where the actual partitioning takes place. In the first method the partitioning is obtained using solely the surface mesh while in the latter one a coarse tetrahedral mesh is used. After the decomposition and creation of an interface mesh (which is a surface mesh in both approaches) the final volume meshes are generated independently for each subdomain. The interface mesh and the subdomain meshes are constructed using a Riemannian metric combined with a control space structure which allows to generate meshes with varied density and anisotropy [1].

Organization of the Mesh Structure

The subject of this article concerns some aspects of the generation of 3D surface meshes, widely used in many scientific applications. This work contains a description of data structure used in the developed mesh generator and issues related to the management of this structure. The proper organization of this structure coupled with the appropriately selected algorithms, allow to achieve the satisfactory efficiency of the mesh generation process.

MULTI-FRONTAL SOLVER FOR SIMULATIONS OF LINEAR ELASTICITY COUPLED WITH ACOUSTICS

This paper describes the concurrent multi-frontal direct solver algorithm for a multi-physicsFinite Element Method (FEM). The multi-physics FEM utilizes different element sizes aswell as polynomial orders of approximation over element edges, faces, and interiors (elementnodes). The solver is based on the concept of a node, and management of unknowns isrealized at the level of nodes. The solver is tested on a challenging multi-physis problem:acoustics coupled with linear elasticity over a 3D ball shape domain.

Complex Modelling Platform based on Digital Material Representation

Proposition of innovative software platform dedicated to modelling of metallurgical processes is presented in the paper. Developed approach is based on the idea of material representation in the form of digital data sets describing various material properties in different length scales. The platform is equipped with additional software modules dedicated to support data gathering, microstructure image analysis, mesh generation and performance of multiscale simulations. The latter module, based on Cellular Automata — Finite Element (CAFE) method, contains two algorithms related to modelling of microstructural phenomena occuring in material during deformation under varying conditions i.e. micro shear and shear bands analysis and recrystallization modelling. The complex approach described in this paper allows not only knowledge based prediction of detailed material properties after thermomechanical metallurgical processes but it also gives possibility to modell entire life cycle of considered material. Thus, it facilitates the investigation of properties of final products and their development by strong quality improvement. Moreover, the platform allows to limit costs of manufacturing by reduction of many expensive industrial trials and their replacement by pure virtual research. Some of the results obtained from application of selected software modules are presented in the paper.

Parallel 3D Mesh Generation using Geometry Decomposition

The paper refers to the problem of parallel generation of 3D meshes for complex objects. Simulation of processes using finite element method (FEM) consists essentially of two phases: generation of finite element mesh and solving the appropriate set of algebraic equations. The parallel solving of such problems has been often reduced to sequential generation of a mesh and than decomposing of this mesh. The latter operation was usually performed sequentially as well. In such approach the only part being parallelized is the solver. In the recent years much attention has been directed to the task of parallelization of the mesh generation process. The need for considering this problem results mainly from the fact that the simulations are currently being run on meshes with very large number of elements. In such cases the sequential generation of meshes poses significant problems regarding both the amount of the required memory and the discretization time.In this work there is described the decomposition strategy...

Domain Decomposition Coupled with Delaunay Mesh Generation

This paper presents a domain decomposition method for finite element meshes created using the Delaunay criterion. The decomposition is performed at the intermediate stage of the generation process and is successively refined as the number of nodes in the mesh increases. The efficiency of the algorithm and the quality of the partitioning is evaluated for different partition heuristics and various finite element meshes.

An Empirical Comparison of Decomposition Algorithms for Complex Finite Element Meshes

This paper presents comparison of the efficiency of several most commonly used simple decomposition methods as applied to various finite element meshes. The tested meshes are characterized by complex boundary shape, large number of gaps, non-uniform size of elements, or anisotropy. Algorithms are evaluated in terms of both computational cost and quality of decomposition. The quality of results is estimated by means of several coefficients describing different aspects of the decomposition.

Tree Structures for Adaptive Control Space in 3D Meshing

The article presents a comparison of several octree- and kd-tree-based structures used for the construction of control space in the process of anisotropic mesh generation and adaptation. The adaptive control space utilized by the authors supervises the construction of meshes by providing the required metric information regarding the desired shape and size of elements of the mesh at each point of the modeled domain. Comparative tests of these auxiliary structures were carried out based on different versions of the tree structures with respect to computational and memory complexity as well as the quality of the generated mesh. Analysis of the results shows that kd-trees (not present in the meshing literature in this role) offer good performance and may become a reasonable alternative to octree structures.