P. Molfino

A user oriented modular package for the solution of general field problems under time varying conditions

In this paper a modular package, named COMPELL, for the solution of two-variable time-varying problems of the elliptic type is presented. The package allows the solution of standard magnetic problems, also under quasi-stationary or rapidly time-varying conditions, in the cases with nonlinear, anisotropic and nonhomogeneous materials with eddy currents, but can also face different problems, taking into account for instance the presence of moving bodies or the reciprocal interaction between magnetic fields, thermal fields and so on. The procedures used for field solution are generalized finite differences, least square finite differences, first presented in this paper, or finite elements. In the paper examples of magnetic field solutions are given, in particular by showing the field in a Tokamak structure accounting for the Hall effect. The data deck and the obtained results are displayed and the main features of the package are discussed.

A mixed face-edge finite element formulation for 3D magnetostatic problems

A mixed variational formulation for the solution of three dimensional magnetostatic problems, based on both the magnetic field H and the magnetic induction field B, has been developed. The approach is based upon the minimisation of the residual in the fulfilment of the constitutive relationship, imposing Maxwells equations as constraints. A finite element discretisation has been realised by using face and edge elements to interpolate B and H, respectively, in order to guarantee the physical continuity properties. The mathematical formulation, its code development and computational results are presented and discussed in detail.

A package for computer aided design for power electrical engineering

A package developed for both research and industrial application for computer aided design of electromagnetic devices is presented and the main features are discussed. From the research point of view the main feature of the package is to allow the definition of the differential equations of the problem to be solved in their analytical form by means of input data for both finite differences and finite elements. From the point of view of practical application, the main features are based on an input processor allowing the input of data in a parametric form. Besides, procedures for optimization of integral and differential quantities and for profile optimization are implemented in the package. For both purposes, automatic grid generation procedures controlled by the user are at disposal and grid optimization is at an advanced stage of development.

Numerical computation of fields in electrostatic devices: experience and applications

A computer package developed for the numerical field computation of electrostatic fields is presented. The package is composed of an interactive preprocessor for data definition, a field computation program based on the general purpose field computation code COMPELL, and a program for the interactive analysis of results and postprocessing. It has been devised to simplify as far as possible its management by users not skilled in numerical methods and is provided with a quasiautomatic grid-generation algorithm and a powerful data definition system for advanced users. The package has been field proven with good results on many practical cases, both of scientific and technical interest, and some obtained results are shown and discussed. >

A computer approach to the nonlinear hysteretic problem of electromagnetic field computation in hard superconductors for loss evaluation

The computation of the losses in superconducting wires requires the solution of electromagnetic problems with a complicated constitutive equation of the superconducting material, which is nonlinear with hysteresis, under time-varying conditions. Analytical and numerical procedures which can be found in the literature about this problem present a very limited application range and cannot be applied to cases of practical interest. In the paper a procedure is presented, by which most of the drawbacks are eliminated. The critical state model developed by Bean, Kim et al is used, in both the forms with constant critical current density and with critical current density function of the magnetic field. In this model the magnetic field penetrates the superconductor entering from the boundary by fronts. These fronts cannot reverse their velocity and represent interfaces with unknown geometric shapes. A package has been implemented to solve this problem, some example of field solution are given and the results are discussed.

Finite difference and finite element grid optimization by the grid iteration method

A grid optimization iterative procedure is presented in the paper. It represents the first step of a two step algorithm and is named grid iteration method. Together with the second step, named metric iteration method, it has been developed previously by the authors for simple examples and has been proven to be potentially very efficient. In this paper the grid iteration method is further developed. It is extended to problems with various unknowns; more efficient techniques are developed in order to apply the method to more complex geometries, to improve the convergence tests and to better solve magnetic problems.

Finite difference and finite element discretization procedures with improved continuity of interpolation functions

In the paper, procedures oriented to improve the continuity of interpolation functions in both finite difference and finite element methods are presented. The mathematical formulation of a new method, the least square finite difference method, is given and the features of the method are discussed. Analogously, in the area of finite element method a new procedure is presented allowing to obtain complete polynomial interpolation functions by minimization of quadratic continuity errors on the lower order derivatives not constrained to exact continuity. In both cases, the first results are very encouraging; in the paper, some of them are outlined and discussed.

The versatility of a multiformulational approach in the solution of electromagnetic field problems

In this paper the usefulness of a multiformulational approach to the numerical computation of electromagnetic fields of technical interest, including coupled problems, is discussed. Several field computation problems arising from various application areas are presented to sample some of the many formulations required to face the existing computational needs. The problems are solved by means of a code designed for a multiformulational management of field computation, and the versatility of the approach and the obtained results are discussed.

A generalized finite element discretization procedure allowing the definition of the problem to be solved by input data

The new version of the package COMPELL (rev. 2.0) is designed to extend to the finite element method the generalized data input already present in the finite difference version (rev. 1.0). The algorithm used is based on the Galerkin method, generalized to allow the discretization of any system of partial differential equations. In the package the procedure is designed only for plane or axisymmetrical second order partial differential equations under nonlinear time-varying conditions; the extension to higher order equations is straightforward in principle.

Comparison of conditions V=0 and A center dot n=0 on conductor boundaries in A,V-A-Psi formulations

Drago et al. (1994) proposed a Coulomb gauge A,V-A-/spl Psi/ formulation for quasi-static transient eddy current problems using V=0, instead of A/spl middot/n=0, as gauge condition on the conductor boundary. Further numerical experimentation using either V=0 or A/spl middot/n=0 on different parts of the conductor boundary, however, has shown that, rather unexpectedly, J/spl middot/n=0 is numerically more weakly enforced where V=0 is used. Hence, in spite of some advantages of V=0, A/spl middot/n=0 still seems to be a better choice, after all. A theoretical explanation for this unexpected drawback of V=0 has been found and is presented in detail.