A two-dimensional infinite element for Maxwell's equations

Cecot, Witold; Demkowicz, Leszek; Rachowicz, Waldemar

doi:10.1016/s0045-7825(99)00290-x

Cited by 21 publications

(10 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A mathematically precise variational formulation of infinite elements has only recently been proposed [15].…”

Section: Earlier Infinite Element Methods Workmentioning

confidence: 99%

A formulation of a multi-wave elastodynamic infinite element

Kazakov¹

2007

WIT Transactions on Modelling and Simulation, Vol 46

View full text Add to dashboard Cite

In this paper, a formulation of a multi-wave elastodynamic four and eight node infinite element is proposed. Such a kind of element is appropriate for multi-wave soil-structure interaction problems. The formulation follows the standard infinite element formulation steps which are the same as for the Finite element method after mapping the infinite element domain to a finite element domain. It is shown that if only one wave function is used (only one frequency) the proposed multi-wave elastodynamic infinite element is reduced to a singlewave elastodynamic infinite element.The mapping and the Lagrange isoparametric shape functions for a 2D axisymmetric four and eight node multi-wave elastodynamic quadrilateral infinite element are also given. The basic aspects of the continuity along the finite/infinite element (artificial boundary) line are discussed in brief. In this type of model such a line marks the boundary between the near and the far field of the model.The formulation is appropriate for wave propagation problems only.

show abstract

“…A mathematically precise variational formulation of infinite elements has only recently been proposed [15].…”

Section: Earlier Infinite Element Methods Workmentioning

confidence: 99%

A formulation of a multi-wave elastodynamic infinite element

Kazakov¹

2007

WIT Transactions on Modelling and Simulation, Vol 46

View full text Add to dashboard Cite

show abstract

“…Detailed construction principles of the space splitting (22), as well as a concrete set of appropriate basis functions for tetrahedral elements can be found in [65]. Its generalisation to other element types can be found in [78].…”

Section: Tangential-continuous Hp-finite Elements and Explicit Kernelmentioning

confidence: 99%

“…Several variants of these basis functions have been proposed including, Webb and Forghani [76], Webb [73], Demkowicz et al [27,59], Ainsworth and Coyle [1,2], Bossavit [20] and Schöberl and Zaglmayr [65]. In the context of computational electromagnetism, these elements have been applied to a range of applications including eigenvalue computation [35,3,23] and electromagnetic scat-tering [28,26,22,52,46,51,49,50,53] where evidence of accurate solutions and exponential convergence, for the correct combination of h and p refinements, has been demonstrated.…”

Section: Introductionmentioning

confidence: 99%

hp-Finite element simulation of three-dimensional eddy current problems on multiply connected domains

Ledger

Zaglmayr

2010

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

This work considers the accurate and efficient finite element simulation of threedimensional eddy current problems. We review the application of H and A based formulations for multiply connected domains for the cases where the conductor has a handle and/or a hole. We focus on an hierarchical hp-finite element discretization of the A based formulation that is gauged by regularization. Based on an explicit kernel splitting of the underlying hp-finite element basis, we present a novel preconditioning technique for eddy current problems. We demonstrate its validity on multiply connected domains and include a series of numerical examples to show the effectiveness of the proposed approach.

show abstract

“…We follow the philosophy of our previous implementations [3], and choose a simpler way, based on treating the infinite elements as an (implicit) form of an Absorbing Boundary Condition (ABC). Instead of setting up a permanent data structure, we generate a temporary data every time, the problem on the FE/IE mesh is solved.…”

Section: Data Structure Interface With Frontal Solvermentioning

confidence: 99%