Adaptive refinement strategies in three dimensions

IEEE Transactions on Magnetics, 2000

This paper describes the performance of a novel adaptive mesh refinement AMR procedure. The AMR procedure proposed here is based on h-version mesh refinement strategy. The novelty of the current approach is the new refinement index derived from an error functional that is based upon the parameters for the multiport microwave devices. Moreover, the index consists of, from the physical insights of the error functional, two terms: the contributions from residual charges and residual currents. The performance of this novel procedure for various numerical examples, in terms of accuracy in parameters, are compared with the theoretical rate of convergence. The conclusion drawn from these examples is that the newly proposed mesh refinement index is very effective and accurate in locating regions for refinement. Consequently, it results in a very efficient h-version adaptive mesh refinement procedure. Index Terms-h-version adaptive mesh refinement, a posteriori error estimate, multiport microwave components, three-dimensional vector finite elements.

IEEE Transactions on Magnetics, 1989

ABSTRACT

Indian Journal of Engineering and Materials Sciences, 1999

Among the acce pt ab le numerical methods. Finite Element Analysis stands as the most acceptable one for problems characterised by partial differential equations. However. in accuracy in Finite Element An alysis is• unavoidable since a co ntinuum with infinite degrees of freedo m is modelled into finite degrees of freed o m. In addition to the mesh generation tas k being tedious and e rror prone. the accuracy and cost of the analysis de pe nd directly o n size. shape and number of d e ments in the mes h. The procedure of refining the mesh automatic ally based on the error estimate and distribution of the e rror is known as "adap ti ve" mesh refineme nt. A si mplified method called " Divide and Conquer" rule based on "Fuzzy Logic" is used to refi ne th e mes h by using Ir, p and Irp versions. Aut o matic mes h generato r develo ped in thi s paper based on Fuzzy log ic is able to develop well shaped elements. The program for automati c mes h gene ration and subsequent mesh re linement is developed in "C' language and the analys is is carried o ut usi ng " ANSYS " I package. Automatic mesh ge ne ratio n i~ app li cd to problems suc h as dam, square pl ate with a ho le. thi ck sphe rical press ure vessel and a co rbel and e rror less than 5 % is ac hi eved in most of th e cases.

33rd Structures, Structural Dynamics and Materials Conference, 1992

A simple algoritlinl for adaptive and automatic h refinement of t,hree dimensional tetrahedral finite element meshes is presented. The algorithm is based on an aposteriori error indicator that is calculated by the finite element solver. The elrment subdivision algorithm is robust and rccilrsive. Smooth transition between large and small c~l(~lnents is achieved without significant degradation of the aspect rat,io of t,he elements in the n~e s h. An cxaniplr is presented to illustrate the utility of the approach.

Computers & Structures, 1989

A valuable approach for the automatic generation of effective finite element meshes is presented. The approach comprises, firstly, an initial mesh construction and, secondly, an h-version of adaptive refinement based on an error analysis. For the initial mesh construction, a robust triangulation scheme for 20 analysis and tetrahedronixation scheme for 30 analysis am used, in which the elements are generated from the outside boundaries. For the adaptive Winement process, an error indicator is used with a relaxation factor to obtain efficient solutions. The initial mesh construction schemes have been implemented for 2D and 30 analyses whereas the self-adaptive mesh improvement procedure. has only been implemented for 20 analysis. Example solutions are given to demonstrate the solution procedures. IdlialMMll constntcdoo Coauntot dats fib fat ADINA-IN

Finite element analysts and designers need to feel confident in the results of their analyses before sending a product to prototype or production. Mesh discretization can greatly influence the desired results. In this paper we present framework for adaptive mesh refinement to obtain FEA results with a desired accuracy. The process involves adaptively refining the mesh based on solution error norms until the result desired converges to certain accuracy. The adaptive refinement/meshing process must be fully automatic and very robust. We present an exhaustive method to create a fully automatic and integrated process that takes advantage of many of the mesh refinement and mesh optimization algorithms found in literature. The results of the process provide the user with the desired accuracy in the smallest number of iterations possible.

IEEE Transactions on Magnetics, 1998

A local error estimation and adaptive meshing method developed by some of the authors for finite element analysis of 2D electrostatic and magnetostatic problems is now extended to 3D problems. The problems are formulated in terms of scalar potentials and discretized on a tetrahedral mesh using linear shape functions. Local error is estimated by approximately solving an independent differential problem in each tetrahedral element. The elements selected for refinement are subdivided by adding nodes inside the element, or along an edge, depending on their geometrical quality factor. Index terms-Error analysis, finite element methods, magnetostatics, electrostatic analysis. aforementioned error estimation procedure with an hrefinement technique. Similar approaches can be found in [ 5 ] and [61, but are restricted to electrostatic problems involving only one dielectric material. In the authors' knowledge, adaptive meshing has never been applied to a 3D magnetostatic formulation in term of scalar potentials.

2005 IEEE Antennas and Propagation Society International Symposium, 2005

Two error indicators of the solution of an electromagnetic problem by Finite Element Method (FEM) and two local refinement algorithms for tetrahedral meshes are developed and combined to build up different self-adaptive (h-refinement) algorithms. 2"d order curl-conforming N6delec tetrahedral elements are used. The performance of the different methods is checked and compared by means of the electromagnetic analysis of resonant cavities.

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.

IEEE Transactions on Magnetics, 1990

In this paper a comparative evaluation of performance of adaptive meshing algorithms with different error estimators is presented. The performance of a selected set of algorithms, based on an element-by-element h-refinement technique, are assessed in some test cases in comparison with analytical results, in a uniform environment. Finally, the features of various possible refinement indicators, adaption convergence criteria and error estimation parameters a r e presented and discussed.