Bernhard Steffen

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

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. >

A particle–particle particle-multigrid method for long-range interactions in molecular simulations

Abstract A fast method of order O ( N ) is proposed to calculate interaction energies and forces in molecular systems with open boundaries, exerted by long range Coulomb interactions. The method consists of a fast multigrid Poisson solver for the far field smooth part of the potential and a particle–particle based method for the near field contribution. Boundary conditions are calculated with a multipole expansion method. Test cases are performed for the performance of the method.

2D and 3D computations of lossy eigenvalue problems

An approach utilizing the finite integral method in frequency-domain is applied to the computation of resonance frequencies and propagation constants of both inhomogeneous (electric and magnetic), anisotropic and lossy cavities (3D) and waveguides (2D). In this method only the physical solutions are calculated and only the interesting modes are looked for. >

The 3-D MAFIA group of electromagnetic codes

The MAFIA group of fully three-dimensional computer codes for solving Maxwells equations for a wide range of applications is discussed. The MAFIA family consists of a number of independent programs that interact through a common file base. A single preprocessor acts as the input program, which defines the geometry of the problem, the mesh, and the different materials of the various bodies. Extensive comparisons with measurements have demonstrated the accuracy of the computations. The authors describe the mathematical approach taken by the MAFIA codes for the solution of Maxwells equations in the time and frequency domains in three dimensions. >

Use of a multigrid solver in the MAFIA module S3 for electro- and magnetostatic problems

The MAFIA codes are fully 3-D codes for solving Maxwells equations by the finite integration algorithm. SOR schemes are a well tested standard for finite-difference (FD) methods in electromagnetic calculations. Since for 3-D problems requiring high accuracy, the necessary fine meshes give a large number of unknowns and so SOR becomes very slow, therefore a multigrid (MG) scheme, a technique developed for the solution of problems with many unknowns, has been incorporated into the S3 code. The performance and accuracy of the new scheme has been compared to that of SOR. The tests demonstrated that multigrid is much faster and more accurate than SOR. It also converges for matrices where SOR fails. >

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.