currents in the moving copper strip by the solid cones and the magnetic field by the gray scaled contours. This modest problem was modeled with 5,664 degrees of freedom(No. of equations) and needed 198 cp seconds running on a workstation rated at SPECfp9296.5. However most industrial problems will require many more degrees of freedom, and typically a non-linear magnetostatic problem with 200,000 equations needed 75 mintues and 25 Mbytes of RAM on the same machine. The resources needed for transient non-linear problems will be far greater Defining Terms Biot savart law: =x,×V2 There r is the distance from the source point to the field point. Interface conditions: (B,-B,.n=0 (D2-D (H2-H1)×n=K (E2-E1)×n=0 where K and o are the surface current and charge densities, respectively. Maxwells equations: VD=p (Gauss's law VxH=dr (Ampere's law displacement current) Related Topics 35. 1 Maxwell Equations. 45.1 Introduction.45.3 Analytical Issues in Developing a Computer Model References A. Bossavit," Rationale for 'edge elements' in 3-D field computation, "IEEE Trans. on Magnetics, voL. 24, no. 1 P L. Tasuo(Ed. ) Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, New York: John D. A. Lowther, " Knowledge-based and numerical optimization techniques for the design of electromagnetic devices, "IJ Num. Mod, voL. 9, no. 1, 2, Pp 35-44, 1996 I. Mayergoyz, Mathematical Models of Hysteresis, New York: Springer-Verlag, 1990. . Owen, STEP An Introduction, Information Geometers Ltd, 47 Sockers Avenue, winchester, UK, 1993. Russenschuck, Synthesis, inverse problems and optimization in computational electromagnetics, "IJ Num. Mod,vol.9,no.1,2,pp.45-58,1996. PP Silvester and R L. Ferrari, Finite Elements for Electrical Engineers, 2nd ed, Cambridge: Cambridge University Press, 1990 c 2000 by CRC Press LLC© 2000 by CRC Press LLC currents in the moving copper strip by the solid cones and the magnetic field by the gray scaled contours. This modest problem was modeled with 5,664 degrees of freedom (No. of equations) and needed 198 cp seconds running on a workstation rated at SPECfp92 96.5. However most industrial problems will require many more degrees of freedom, and typically a non-linear magnetostatic problem with 200,000 equations needed 75 mintues and 25 Mbytes of RAM on the same machine. The resources needed for transient non-linear problems will be far greater. Defining Terms Biot Savart law: where R is the distance from the source point to the field point. Interface conditions: (B2 – B1) • n = 0 (D2 – D1) • n = v (H2 – H1) 3 n = K (E2 – E1) 3 n = 0 where K and v are the surface current and charge densities, respectively. Maxwell’s equations: Related Topics 35.1 Maxwell Equations • 45.1 Introduction • 45.3 Analytical Issues in Developing a Computer Model References A. Bossavit, “Rationale for ‘edge elements’ in 3-D field computation,” IEEE Trans. on Magnetics, vol. 24, no. 1, p. 74, 1988. I. Tasuo (Ed.), Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, New York: John Wiley, 1989. D. A. Lowther, “Knowledge-based and numerical optimization techniques for the design of electromagnetic devices,” IJ Num. Mod., vol. 9, no. 1,2, pp. 35–44, 1996. I. Mayergoyz, Mathematical Models of Hysteresis, New York: Springer-Verlag, 1990. J. Owen, STEP An Introduction, Information Geometers Ltd, 47 Sockers Avenue, Winchester, UK, 1993. S. Russenschuck, “Synthesis, inverse problems and optimization in computational electromagnetics,” IJ Num. Mod., vol. 9, no. 1,2, pp. 45–58, 1996. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 2nd ed., Cambridge: Cambridge University Press, 1990. H J s s R = ¥— d Ú 1 4 1 p W W —× = —× = —¥ =- —¥ = + D (Gauss's law) B E (Faraday's law) H J (Ampere's law + displacement current) r ¶ ¶ ¶ ¶ 0 B D t t