FI2TD schemes for magnetic field simulations: new formulations and algorithmic improvements

Finite Integration Implicit Time Domain (FI2TD) methods are designed for the calculation of transient magnetic fields and are based on the Finite Integration Technique. To improve the geometric modeling capabilities of these methods while maintaining computationally efficient structured orthogonal grids, the Conformal Finite Integration Technique was introduced. A magnetic field formulation based on a reduced magnetic vector potential formulation also allows an improved geometrical modeling of excitation coils while at the same time reducing the computational work for FI2TD simulation s at typically low accuracy requirements. A new generalized linearization formulation is presented for the simulation of nonlinear ferromagnetic material behavior, which includes the standard linearization schemes as special cases and enables us to derive hybrid nonlinear iteration schemes.

[1]  Thomas Weiland,et al.  Triangle search method for nonlinear electromagnetic field computation , 2001 .

[2]  R. C. Pardo,et al.  Proceedings of the XIX international Linac conference , 1999 .

[3]  E. Süli,et al.  A convergence analysis of Yee's scheme on nonuniform grids , 1994 .

[4]  Oszkar Biro,et al.  Various FEM formulations for the calculation of transient 3D eddy currents in nonlinear media , 1995 .

[5]  Rolf Schuhmann,et al.  The Perfect Boundary Approximation Technique Facing the Big Challenge of High Precision Field Computation , 1998 .

[6]  Thomas Weiland,et al.  Magnetic field simulation using conformal FIT formulations , 2002 .

[7]  Akihisa Kameari,et al.  Analysis of eddy current and force in conductors with motion , 1992 .

[8]  Thomas Weiland,et al.  Numerical solution of 2- or 3-dimensional nonlinear field problems by means of the computer program PROFI , 1982 .

[9]  Adolf J. Schwab.  Begriffswelt der Feldtheorie , 1985 .

[10]  C.R.I. Emson.  SUMMARY OF RESULTS FOR HOLLOW CONDUCTING SPHERE IN UNIFORM TRANSIENTLY VARYING MAGNETIC FIELD (PROBLEM 11) , 1990 .

[11]  K. Stüben.  Algebraic multigrid (AMG): experiences and comparisons , 1983 .

[12]  T. Weiland.  Time Domain Electromagnetic Field Computation with Finite Difference Methods , 1996 .

[13]  K. Preis,et al.  Finite element analysis of 3-D eddy currents , 1990 .

[14]  Thomas Weiland,et al.  Transient eddy-current calculation with the FI-method , 1999 .

[15]  Thomas Weiland,et al.  Numerical calculation of nonlinear transient field problems with the Newton-Raphson method , 2000 .

[16]  Thomas Weiland,et al.  A CONSISTENT SUBGRIDDING SCHEME FOR THE FINITE DIFFERENCE TIME DOMAIN METHOD , 1996 .

[17]  R. Mittra,et al.  A conformal finite difference time domain technique for modeling curved dielectric surfaces , 2001, IEEE Microwave and Wireless Components Letters.