Automatic Mesh Generation for 3D Objects. February 1996

Computing and Visualization in Science, 2006

This work deals with all aspects of the numerical simulation of nonlinear time-periodic eddy current problems, ranging from the description of the nonlinearity to an efficient solution procedure. Due to the periodicity of the solution, we suggest a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Linearization is done by a Newton iteration, where the preconditioning of the linearized problems is a special issue: Since the matrices are non-symmetric, we need a special adaptation of a multigrid preconditioner to our problem. Eddy current problems comprise another difficulty that complicates the numerical simulation, namely the formation of extremely thin boundary layers. This challenge is handled by means of adaptive mesh refinement.

Computational Methods in Applied Sciences, 2008

Computers & Mathematics with Applications, 1979

A method for automatic generation of triangnlar finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p. such that: minm>c T m(T) vp, p=l,Z,... p(T) and h(T) being respectively the dieter of the inscribed circle and the largest edge of a generated triangle T.

Springer tracts in mechanical engineering, 2018

The quality of a mesh is crucially important if FEM solutions are to be deemed acceptable. Too coarse a mesh will lead to inaccurate FEM solutions. The finer the mesh, the better the convergence of the numerical solution. However, finer meshes tend to be expensive in terms of computing resources. The experienced user of FEM would have, over time, developed the skills required for creating just the right mesh for a given problem. Becoming proficient users of FEA, with the ability to create representative meshes of the idealized physical problem will serve as a motivation for this chapter. This chapter presents fundamentals of finite element meshes by defining nodes and elements, and the different types of elements. The chapter also describes the principle behind meshing algorithms in commercial FEM solvers. This chapter concludes by presenting reflections on quality of meshes and the type of meshes needed for different type of practical problems. It is expected that at the end of this chapter, readers should have developed a holistic understanding of the effects of meshes to the FEM process.

International Journal for Numerical Methods in Engineering, 2006

This paper gives an explicit geometric interpretation of finite element formulations of the eddy-current problem. The paper shows, step-by-step how the eddy-current problem can be implemented in a finite element kind of software system exploiting familiar geometric ideas such as lengths of edges, areas of faces, volumes of tetrahedra, and the mutual interconnections between the simplices of a mesh. The approach is a specific case of the so-called geometric techniques.

Computers & Structures, 1988

Some recent efforts on the development of methods to ensun the robustness of automatic thracdimensional mesh generation techniques arc discuss& The topic arcas considered arc mesh entity classification, finite octrcc cell triangulation, and coarse mesh generation by element removal.

1991

This paper deals with key aspects of the coupling of automatic mesh generation with adaptive analysis and shape optimisation of planar and surface structures. Adaptive analysis requires the design of nearly optimal meshes with varying element sizes to achieve a prescribed accuracy. In any shape optimisation process as the region to be discretised changes continuously and sometimes dreustically, mesh generation should ideally take place without intervention by the analyst and without any excessive distortion of elements. To carry out these processes in a fully automatic and efficient manner a highly robust, versatile and flexible mesh generator is required. A brief introduction to the features of one such automatic mesh generator, based on the advancing front method, is described. Several examples are presented exploiting the potential of this mesh generator for adaptive analysis and shape optimisation. The integration of the rnesh generator with these procedures is discussed as well as some issues which required special attention.

This paper describes an adaptive mesh refinement algorithm for improving the accuracy in the solution of electromagnetic problems in transmission lines. A residual error indicator is used for detecting the refinement zones, and two h-refinement techniques for triangular meshes (the longest edge bisection and the regular split) are applied for increasing the degrees of freedom in the mesh. This procedure has been applied in several structures and the results show that the adaptive meshing allows obtaining accurate solution with a small amount of unknowns.

IET Science, Measurement & Technology, 2008

Manifolds offer a generalisation to the modelling procedure, where the domain of an electromagnetic boundary value problem is a subset of a particular coordinate system. First of all, instead of identifying the points of the domain with coordinates, manifolds implement the principle that coordinates are not canonical. Second, in manifolds the coordinates are deliberately not bound by the distances between the points of the domain they represent. Finally, a manifold does not need to be coverable by a single coordinate system, but by several. These basic properties of manifolds make it possible to choose a coordinate system or systems that alleviate mesh generation problems caused by limited accuracy of floating point numbers. The authors propose three practical mesh generation-friendly problem representations.