Peter Hahne

Solution of Maxwell's equations

Abstract A numerical approach for the solution of Maxwells equations is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms. A large variety of two- and three-dimensional field problems can be solved by computer programs based on this approach: electrostatics and magnetostatics, low-frequency eddy currents in solid and laminated iron cores, high-frequency modes in resonators, waves on dielectric or metallic waveguides, transient fields of antennas and waveguide transitions, transient fields of free-moving bunches of charged particles etc.

Maxwell's grid equations

A numerical approach for the solution of Maxwells equation is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms

MAFIA version 4

MAFIA Version 4.0 is an almost completely new version of the general purpose electromagnetic simulator known since 13 years. The major improvements concern the new graphical user interface based on state of the art technology as well as a series of new solvers for new physics problems. MAFIA now covers heat distribution, electro-quasistatics, S-parameters in frequency domain, particle beam tracking in linear accelerators, acoustics and even elastodynamics. The solvers that were available in earlier versions have also been improved and/or extended, as for example the complex eigenmode solver, the 2D–3D coupled PIC solvers. Time domain solvers have new waveguide boundary conditions with an extremely low reflection even near cutoff frequency, concentrated elements are available as well as a variety of signal processing options. Probably the most valuable addition are recursive sub-grid capabilities that enable modeling of very small details in large structures.

Status and future of the 3D MAFIA group of codes

An overview is presented of the MAFIA group of fully three-dimensional computer codes for solving Maxwells equations by the finite integration algorithm. The codes are well established. Extensive comparisons with measurements have demonstrated the accuracy of the computations. The latest additions include a static solver that calculates 3-D magnetostatic and electrostatic field and a self-consistent version of TBCI that solves the field equations and the equations of motion in parallel. Work on new eddy-current modules has started, which will allow treatment of laminated and/or solid iron cores by low-frequency current. Based on experience with the present releases 1 and 2, a complete revision of the whole user interface and data structure has begun that will be included in release 3. >

Determination of anisotropic equivalent conductivity of laminated cores for numerical computation

For the accurate electromagnetic simulation of devices containing laminated conductive cores including eddy current effects it often turns out that the full discretization of each sheet of a laminated core and the space between two sheets is computationally costly. The factors considered in reducing the effort refer to the finite integration method. By means of an analytical model the equivalent conductivity of a laminated iron core in the direction normal to the sheets is determined. The applicability of the model is demonstrated by comparison of measured shading ring sensor data and numerical results, performed by the W3 module of the program package MAFIA.

Mafia in Practice: the Capabilities of the Mafia Cad System

The program group MAFIA which solves Maxwells equations has been further improved by the inclusion of new programs, by the integration of both two and three dimensional modules under a unified user interface and by the extension of pre- and post-processor capabilities. In the present release, 3.1, a module for the calculation of eddy currents in solid or laminated iron cores is the latest addition to the family of codes, two and three dimensional particle-in-cell codes, which solve the equations of motion in parallel with the electromagnetic field equations, are also included and the time domain solver has been extended to calculate the transient fields of antennae and waveguide transitions. The programs are described and a series of large (up to a million mesh points), realistic examples are presented to indicate the range and complexity of the problems which MAFIA can solve.