Edge-based Finite Element Research Articles

A review and comparative study of upwind biased schemes for compressible flow computation. Part II: 1-D higher-order schemes

Higher-order upwind biased procedures for solving the equations of 1-D compressible unsteady flow are surveyed. Approaches based upon the use of either switched artificial viscosity, flux-limiting or slopelimiting are considered and described within a unified framework. The approaches are implemented within the context of an edge-based finite element solution algorithm, which represents the basis for a future multi-dimensional extension on general grids. The performance of the different approaches is illustrated by application to the solution of the shock tube problem in different flow regimes.

Fast multigrid solution method for nested edge-based finite element meshes

In this paper a fast multigrid solution method for edge-based finite element magnetostatic field computation with nested meshes is introduced and its efficiency is investigated. Special prolongation and restriction matrices were constructed according to the nature of the edge based field approximation. The comparison of the computation speed between the multigrid method and the ICCG method is also presented, showing that the multigrid method is very promising as a fast solution method for large system of equations.

Inverse Problem Analyses with Noised Signals in Eddy Current Testing.

This paper demonstrates crack reconstruction from the relative signals, which overlap with noises in eddy current testing. A method for the reconstruction from the signals, a kind of inverse problem, has been developed with fast signal predictions and the steepest descent algorithm. The signal predictions use a pre-computed unflawed database approach based on edge-based finite elements and the reciprocity theorem.This approach makes it possible that the problem domain of an electromagnetic field is reduced to a small region where a crack/cracks possibly exist.In the inspection of steam generator tubes in nuclear power plants, this test detects deposits on the surfaces of thetubes and structures to fix the tubes such as support sheets or plates, and rigs, as well as defects.The signals from the structures are thought to be noises when finding out the defects.Crack profile identification is given from the crack signals with residual noises, which remain after multi-frequency processing of the signals disturbed by the presence of copper/magnetic deposits and support plantes.

Multigrid solutions of the Euler and Navier-Stokes equations on unstructured grids

A computationally efficient multigrid algorithm for upwind edge-based finite element schemes is developed for the solution of the two-dimensional Euler and Navier–Stokes equations on unstructured triangular grids. The basic smoother is based upon a Galerkin approximation employing an edge-based formulation with the explicit addition of an upwind-type local extremum diminishing (LED) method. An explicit time stepping method is used to advance the solution towards the steady state. Fully unstructured grids are employed to increase the flexibility of the proposed algorithm. A full approximation storage (FAS) algorithm is used as the basic multigrid acceleration procedure. Copyright © 1999 John Wiley & Sons, Ltd.

Turbulent flow computations on 3D unstructured grids

An edge-based finite element method is presented for the simulation of compressible turbulent flows on unstructured tetrahedral grids. A two equation k– ω turbulence model is employed and the standard Galerkin approach is used for spatial discretisation. Stabilisation of the resulting procedure is achieved by the addition of an appropriate diffusion. An explicit multistage time-stepping scheme is used to advance the solution in time to steady state. The performance of the algorithm is demonstrated for the simulation of a high Reynolds number transonic separated flow over a wing.

Full-wave solutions to the propagation characteristics of buried microstrip lines by VFEM and ABCs

The propagation factors of buried microstrip lines are considered. The associated eigenvalue problems are solved by the edge-based vectorial finite element method (VFEM). To improve the higher-order VFEM solutions, the problem infinite domain is truncated by second-order absorbing boundary conditions (ABCs). This reduces the number of unknowns and, consequently, the numerical effort. Owing to the many advantages of both the edge-based VFEM and the second-order ABCs, this full-wave method is implemented by a general computer program for solving unbounded domain problems involving complex geometries and inhomogeneous media. The examples presented show the validity of this technique. © 1998 John Wiley & Sons, Ltd.

Two-dimensional singular vector elements for finite-element analysis

The finite-element method (FEM) exhibits a reduced convergence rate when used for the analysis of geometries containing sharp edges where the electromagnetic field is singular. The convergence of the method can be-improved by introducing singular elements that model analytically predicted singular behavior. A number of authors have developed singular elements that are compatible with the scalar FEM. In this paper, we propose a new singular element that is compatible with edge-based vector finite elements and can cope with any order of singularity while preserving the sparsity of the FEM equations. Edge-based singular elements more correctly model singular fields and thus require fewer unknowns, while avoiding the introduction of spurious modes in the numerical solution. Numerical results verify that the convergence of the FEM is significantly improved.

Implementation and Derivation of Conformal Absorbing Boundary Conditions for the Vector Wave Equation

A rigorous implementation, in an edge-based finite element formulation, of a second-order absorbing boundary condition (ABC) is presented for the solution of the 3-D scattering problem when the boundary S terminating the mesh is conformal to the object. Numerical experiments performed on a cone-sphere and a cylinder with hemispherical caps are presented that justify the use of this ABC. A high-order ABC is derived in the locally planar approximation, and its performances are evaluated for the analytical case of the sphere, which serves to address a number of important issues pertaining, e.g., to the accuracy with which the creeping waves are taken into account when an ABC is utilized.

TREE-COTREE DECOMPOSITIONS FOR FIRST-ORDER COMPLETE TANGENTIAL VECTOR FINITE ELEMENTS

Edge-based finite elements have important applications in modelling both quasi-static and high-frequency electromagnetic problems. Recent work has demonstrated that formulations that exploit the graph structure of the edge-based finite element mesh may be extended to higher-order elements. This paper presents the details of how such an extension to a first-order complete finite element is accomplished and illustrates its application in two-dimensional magnetostatics. © 1997 by John Wiley & Sons, Ltd.

Higher-order vector finite elements for tetrahedral cells

Edge-based vector finite elements are widely used for two-dimensional (2-D) and three-dimensional (3-D) electromagnetic modeling. This paper seeks to extend these low-order elements to higher orders to improve the accuracy of numerical solutions. These elements have relaxed normal-component continuity to prohibit spurious modes, and also satisfy Nedelec's constraints to eliminate unnecessary degrees of freedom while remaining entirely local in character. Element matrix derivations are given for the first two vector finite element sets. Also, results of the application of these basis functions to cavity resonators demonstrate the superiority of the higher-order elements.

Analysis of magneto-thermal coupled problem involving moving eddy-current conductors

In this paper, 3-D finite element analysis of a magneto-thermal coupled problem with moving conductors is presented. For improved accuracy and due to the different character of the approximated unknown variables, two appropriate solution spaces are considered: a vectorial space using first-order, edge-based finite elements for analysis of the vectorial characteristics of the magnetic field and eddy-current distributions; and a scalar space using first-order nodal finite elements for the non-linear analysis of thermal field distribution. Separate 3-D mesh divisions are developed for accurate eddy-current and thermal field analysis. Time-dependent thermal field distribution is obtained using the Crank-Nicolson recurrence formula, and a moving conductor with eddy-current flow is considered using appropriate step division for the nature of the coupling process. The mathematical background, analyzed models and obtained results compared with measured results are presented.

A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements

An advanced A-V method employing edge-based finite elements for the vector potential A and nodal shape functions for the scalar potential V is proposed. Both gauged and ungauged formulations are considered. The novel scheme is particularly well suited for efficient iterative solvers such as the preconditioned conjugate gradient method, since it leads to significantly faster numerical convergence rates than pure edge element schemes. In contrast to nodal finite element implementations, spurious solutions do not occur and the inherent singularities of the electromagnetic fields in the vicinity of perfectly conducting edges and corners are handled correctly. Several numerical examples are presented to verify the suggested approach.

Edge-Based Finite Element Analysis of Singly-and Doubly-Periodic Scatterers Using Absorging and Periodic Boundary Conditions

ABSTRACT This paper presents a simple but accurate Finite Element Method (FEM) technique which is based on hexahedral parallelepiped finite elements and Whitney's edge basis functions. The technique is useful for the analysis of scattering from 1-D, 2-D, or from isolated 3-D scatterers. Numerical results are presented for a variety of such scatterers to show the usefulness of the method. The results also point to the need for the use of improved absorbing boundary conditions (ABCs) as well as of higher order basis functions when more accurate results are required. The emphasis in the proposed method is on its simplicity and versatility.

Parallel computation of 3D electromagnetic scattering using finite elements and conformal ABCs

An edge-based finite element formulation with conformal absorbing boundary conditions (ABCs) is presented for scattering by composite three dimensional structures having boundaries satisfying impedance and/or transition conditions. The methodology with its O(N) storage requirement is amenable to large-scale parallelization. Tests have been carried out on a massively parallel architecture with impressive speedups. >

Analysis of induction skull melting furnace by edge finite element method excited from voltage source

To optimize the production of high-efficiency induction skull melting furnace, we analyzed magnetic flux density, eddy current and electromagnetic force distributions using the 3D edge-based finite element method excited from a voltage source. Changing the number of copper rods and, therefore, the distance between them, we analyzed both the intensity and direction of the electromagnetic forces and the amount of power consumed by the molten alloy and the rods. In this paper, we present our analysis method, the obtained results and conclusions. >

Finite element method solutions of field distributions in large cavities

AbstractTo make possible the application of the three‐dimensional finite element method to electrically large problems, it is combined with the analytical solutions of arbitrary large cavity with aperture. In this paper, detailed analysis for this hybrid method is presented. The element matrices necessary for coupling the finite element method to analytical solutions are given. The proposed hybrid method significantly reduces the number of unknown since only the inhomogeneity needs to be discretized. Thus computer memory and storage demands are reduced. In addition. This hybrid method employs the edge element which is not expected to produce spurious solutions. Also, the formulation presented in this paper preserves the sparsity of the finite element matrix, and does not require any matrix inversion. This new hybrid method is used to compute the field distributions in various partially filled rectangular enclosure. The results match well with the pure edgebased finite element method and analytical solutions.

Edge-based finite element scheme for the Euler equations

We describe the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm

Edge-based finite elements and vector ABCs applied to 3-D scattering

An edge-based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust finite element solution for three-dimensional scattering

An edge-based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer.

Computation of cavity resonances using edge-based finite elements

The eigenvalues of a cavity resonator are computed using edge-based elements, and it is shown that these elements offer significant improvements in accuracy, in addition to being suitable for modeling arbitrarily shaped inhomogeneous regions. A performance comparison between the edge-based tetrahedra and rectangular brick elements is also carried out. >