A Two-Dimensional Self-Adaptive Finite Element Method for the Analysis of Open Region Problems in Electromagnetics (original) (raw)
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IEEE Transactions on Magnetics, 2000
A two-dimensional self-adaptive finite element method (FEM) for the analysis of open region problems in electromagnetics is described. The method incorporates an iterative procedure for solving open region problems. More precisely, solution of the open problem is achieved by solving a low number of closed domain problems with the same matrix, so the computational cost for the second and subsequent problems is very small. Thus, the particularities due to the open nature of the problem are hidden and, among other advantages, self-adaptive strategies developed for conventional closed domains and, specifically, of type, can be used without modifications. The -FEM discretization is made in terms of quadrangles/triangles of variable order of approximation supporting anisotropy and hanging nodes. The adaptive strategy is fully automatic and is based on minimizing the interpolation error (by using the projection of the error from a fine grid) delivering exponential convergence rates for the energy error, even in the presence of singularities.
Anhp-adaptive finite element method for scattering problems in computational electromagnetics
International Journal for Numerical Methods in Engineering, 2005
An hp-adaptive finite element (FE) approach is presented for a reliable, efficient and accurate solution of 3D electromagnetic scattering problems. The radiation condition in the far field is satisfied automatically by approximation with infinite elements (IE). Near optimal discretizations that can effectively resolve local rapid variations in the scattered field are sought adaptively by mesh refinements blended with graded polynomial enrichments. The p-enrichments need not be spatially isotropic. The discretization error can be controlled by a self-adaptive process, which is driven by implicit or explicit a posteriori error estimates. The error may be estimated in the energy norm or in a quantity of interest. A radar cross section (RCS) related linear functional is used in the latter case. Adaptively constructed solutions are compared to pure uniform p approximations. Numerical, highly accurate, and fairly converged solutions for a number of generic problems are given and compared to previously published results. Copyright © 2004 John Wiley & Sons, Ltd.
A goal-oriented hp-adaptive finite element method with electromagnetic applications
2004
We describe the development and application of a finite element (FE) self-adaptive hp goal-oriented algorithm for elliptic problems. The algorithm delivers (without any user interaction) a sequence of optimal hp-grids. This sequence of grids minimizes the error of a prescribed quantity of interest with respect to the problem size. The refinement strategy is an extension of a fully automatic, energy-norm based, hp-adaptive algorithm.
International Journal for Numerical Methods in Engineering, 2006
We describe the development and application of a finite element (FE) self-adaptive hp goal-oriented algorithm for elliptic problems. The algorithm delivers (without any user interaction) a sequence of optimal hp-grids. This sequence of grids minimizes the error of a prescribed quantity of interest with respect to the problem size. The refinement strategy is an extension of a fully automatic, energy-norm based, hp-adaptive algorithm.
International Journal for Numerical Methods in Engineering, 2003
This paper is a continuation of Reference [26] (Cecot, Demkowicz and Rachowicz, Computer Methods in Applied Mechanics and Engineering 2000; 188: 625–643) and describes an implementation of the infinite element for three-dimensional, time harmonic Maxwell's equations, proposed in Reference [15] (Demkowicz and Pal, Computer Methods in Applied Mechanics and Engineering 1998; 164: 77–94). The element is compatible with the hp finite element discretizations for Maxwell's equations in bounded domains reported in References [16–18] (Computer Methods in Applied Mechanics and Engineering 1998; 152: 103–124, 1999; 169: 331–344, 2000; 187: 307–337). Copyright © 2003 John Wiley & Sons, Ltd.
Progress In Electromagnetics Research, 2012
In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an userprescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity.
IEEE Transactions on Magnetics, 2010
Solving scattering problems using the finite element method (FEM) introduces two sources of error: from the discretization and from the truncation boundary. Here both errors are addressed in an iterative, balanced way. For the discretization error, -adaption is used. An a posteriori error indicator automatically determines which elements should be increased in order to reduce and equi-distribute the discretization error. For the boundary error, an iterative absorbing boundary condition is applied. The overall scheme starts with low order polynomials and a first order absorbing boundary condition and progressively improves the quality of the solution by a combination of -adaption and updating the boundary condition, so that both the discretization and the boundary errors are similar at each stage. Results are presented to show the reduction of computation time when -adaption is used as opposed to an earlier approach of uniformly increasing the element orders.
Self-adaptive algorithms based on h-refinement applied to finite element method
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.
A Brief History of Finite Element Method and Its Applications to Computational Electromagnetics
The Applied Computational Electromagnetics Society Journal (ACES)
The development of the finite element method is traced, from its deepest roots, reaching back to the birth of calculus of variations in the 17th century, to its earliest steps, in parallel with the advent of computers, up to its applications in electromagnetics and its flourishing as one of the most versatile numerical methods in the field. A survey on papers published on finite elements, and on ACES Journal in particular, is also included.