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Article
Publication date: 1 March 2000

P. Alotto and I. Perugia

An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation…

237

Abstract

An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation minimises the residual of the constitutive equation, and exactly imposes Maxwell’s equations with Lagrange multipliers. Finite elements satisfying the physical continuity properties for both the magnetic and the magnetic induction fields are used in the numerical approximation. The possibility of decoupling the formulation in two separate sets of equations is discussed. A preconditioned iterative method to solve the final algebraic linear system is presented. Finally, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 October 1998

P. Di Barba, I. Perugia and A. Savini

A mixed formulation of two‐dimensional magnetostatic problems, where both B and H are unknowns, is considered. The solution is obtained by minimizing the residual of the…

199

Abstract

A mixed formulation of two‐dimensional magnetostatic problems, where both B and H are unknowns, is considered. The solution is obtained by minimizing the residual of the constitutive law, imposing Maxwell’s equations as constraints by means of Lagrange multipliers. When a finite element discretization involving face and edge elements is applied, we have to solve a linear system whose algebraic treatment presents some difficulties. In the paper, the attention is focused on the computational aspects of the proposed methodology with special emphasis on the choice of algebraic solvers and of possible preconditioning techniques. A case study, concerning the field analysis of a magnetic screen, is presented and discussed.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 17 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 June 2001

P. Alotto, A. Bertoni, I. Perugia and D. Scho¨tzau

The capability of discontinuous finite element methods of handling non‐matching grids is exploited in the simulation of rotating electrical machines. During time stepping, the…

518

Abstract

The capability of discontinuous finite element methods of handling non‐matching grids is exploited in the simulation of rotating electrical machines. During time stepping, the relative movement of two meshes, consistent with two different regions of the electrical device (rotor and stator), results in the generation of so‐called hanging nodes on the slip surface. A discretisation of the problem in the air‐gap region between rotor and stator, which relies entirely on finite element methods, is presented here. A discontinuous Galerkin method is applied in a small region containing the slip surface, and a conforming method is used in the remaining part.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 June 2000

K. Wiak

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines;…

925

Abstract

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 March 1967

William Ready

EVERYBODY AGREES that shared cataloguing is a good thing, but until recently nobody has done very much about it. I remember my first encounter with it was the regional catalogue…

13

Abstract

EVERYBODY AGREES that shared cataloguing is a good thing, but until recently nobody has done very much about it. I remember my first encounter with it was the regional catalogue for the libraries of South Wales set up in Cardiff in the 1930s under W. O. Padfield, but there was always something rather arcane about it, to me at any rate who was kept shelving books whenever they could find me.

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Library Review, vol. 21 no. 3
Type: Research Article
ISSN: 0024-2535

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Article
Publication date: 25 May 2021

Miaomiao Yang, Xinkun Du and Yongbin Ge

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only…

199

Abstract

Purpose

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

Design/methodology/approach

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

Findings

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Research limitations/implications

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

Practical implications

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

Originality/value

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

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Article
Publication date: 3 May 2013

Liang Li, Stéphane Lanteri and Ronan Perrussel

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional…

283

Abstract

Purpose

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.

Design/methodology/approach

The proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.

Findings

The approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L2 norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.

Originality/value

The work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 March 2002

Paolo Fernandes and Mirco Raffetto

From a theoretical point of view the question of spurious modes has been regarded as a closed problem. However, in this paper we show that even a precise definition of…

306

Abstract

From a theoretical point of view the question of spurious modes has been regarded as a closed problem. However, in this paper we show that even a precise definition of spurious‐free approximation was lacking. Hence, a sound definition of spurious‐free finite element method is given and a set of necessary and sufficient conditions ensuring that a finite element method is spurious‐free in the defined sense is stated. A critical comparison between the proposed theory and the currently accepted one is then carried out and existing counterexamples to the latter are pointed out. Comparison with an older theory leads to another set of necessary and sufficient conditions providing a better grasp of the key feature a finite element space must have to rule out spurious modes. The impact of the proposed theory is stressed, showing that Nedelec's tetrahedral edge elements of all orders provide spurious‐free approximations in all conditions of practical interest. Finally, it is shown, for the first time to the best of authors’ knowledge, that also many high‐order edge elements, recently proposed in the engineering literature for the analysis of electromagnetic problems, provide the same kind of reliable approximation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 21 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 May 2013

Leilei Wei, Xindong Zhang and Yinnian He

The purpose of this paper is to develop a fully discrete local discontinuous Galerkin (LDG) finite element method for solving a time‐fractional advection‐diffusion equation.

405

Abstract

Purpose

The purpose of this paper is to develop a fully discrete local discontinuous Galerkin (LDG) finite element method for solving a time‐fractional advection‐diffusion equation.

Design/methodology/approach

The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space.

Findings

By choosing the numerical fluxes carefully the authors' scheme is proved to be unconditionally stable and gets L2 error estimates of O(hk+1+(Δt)2+(Δt)α/2hk+(1/2)). Finally Numerical examples are performed to illustrate the effectiveness and the accuracy of the method.

Originality/value

The proposed method is different from the traditional LDG method, which discretes an equation in spatial direction and couples an ordinary differential equation (ODE) solver, such as Runger‐Kutta method. This fully discrete scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. Numerical examples prove that the authors' method is very effective. The present paper is the authors' first step towards an effective approach based on the discontinuous Galerkin method for the solution of fractional‐order problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 2000

P. Alotto, A. Castagnini, P. Girdinio and M. Nervi

An adaptive FEM for 3D magnetostatic problems involving non‐linear materials and permanent magnets is presented. The problems are formulated in terms of scalar potentials and…

215

Abstract

An adaptive FEM for 3D magnetostatic problems involving non‐linear materials and permanent magnets is presented. 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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

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