微波仿真论坛_Yee的经典论文_FDTD鼻祖Yee1966年的经典论文 AP-1966-FDTD

obstacle is moderately large compared to that of an incoming n-ave. A set of finite difference equations for the system of partial differential equations will be introduced in the early partof this paper. We shall then show that with an appropriate choice of the points at which the various INTRODUCTION field components are to be evaluated, the set of finite OLUTIONS to the time-dependent Maxwell's equa- difference equations can be solved and the solution will tions general in form unknown are except for satisfy the boundary condition. The latter part of this a few special cases.T h e difficulty is due mainly to paper will specialize in two-dimensional problems, and the imposition of theboundary conditions. LT,7e shall an example illustrating scattering of a n incoming pulse by a perfectly conducting square will be presented. show in this paper how to obtain the solution numerically when the boundary condition is that appropriate AND for a perfect conductor. In theory, this numerical attack AIAXTT-ELL'S EQVATION THE EQUIVALENT SET OF FINITE DIFFERENCE EQUATIONS can be employed for the most general case. However, because of the limited memory capacity of present dal: llaxwell's equations in an isotropic medium [ l ] are:' computers, numerical solutions to a scattering problem aB for which the ratio of the characteristic linear dimen-+VXE=O, at sion of the obstacle to the m-avelength is largestill seem to be impractical. We shall show by an example t h a t in the case of two dimensions, numerical solutions are practical even when the characteristic length the of
801
D = E,
1
In M K S system of units.
YEE: SOLUTION OF INITIAL BOUNDARY VALUE PROBLEMS
303
where J , p , and E are assumed to be given functions of space and time. In a rectangular coordinate system, (la) and (lb) are equivalent to the following system of scalar equations:
s
Manuscript received August 24, 1965; revised January 28, 1966. This work was performed under the auspices of the U. S. Atomic Energy Commission. The author is with the Lawrence Radiation Lab., University of California, Livermore, Clf ai.
examined. Kumerical results of the surface wave characteristics are given for one typicalcase.
Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media
KANE S. YEE
Abstracf-Maxwell's equations are replacedbya set of finite difEerence equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for aboundaryconditioninvolvingperfectlyconductingsurfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
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VOL. AP-14, so. 3
MAY, 1Ybb
V. CONCLUSION
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REFERENCES
P. S. Epstein, of T h e characteristics of the waves guided along a plane [I] waves," Proc. "Onthe c a d . possibility vol. electromagneticsurface Nat'l d Sciences, 40, pp. 1158-1165, Deinterface which separates a semi-infinite region of free cember 1954. T. Tamir and A. spectrum of electromagnetic space from that of a magnetoionic medium are investi- [2] waves guided by aA. Oliner, "TheProc. IEEE, vol. 51, pp. 317plasma layer," gated for the case in which the static magnetic field is 332, February 1963. &I. A. Gintsburg, "Surface waves on the boundary of a plasma oriented perpendicular the to plane interface. I t is [3] in magnetic a field," Rasprost. Radwvoln i Ionosf., Trudy found that surface waves exist only when w , < w p and N I Z M I R A N L'SSR, no. 17(27), pp. 208-215,1960. from a source near a t h a t also only for angular frequencies which lie bet\\-een [4]S. R. Seshadri and A. Hessel, "Radiation gyrotropic dielectric," plane interface between an isotropic and a w e and 1 / 4 2 times the upper hybrid resonant frequency. Canad. J . Phys., vol. 42, pp. 2153-2172, November 1964. [5] G. H. Owpang and S. R. Seshadri, "Guided waves propagating T h e surfacewavespropagatewithaphasevelocity along the magnetostatic field a t a planeboundary of asemiwhich is always less than the velocity of electromagnetic infinite magnetoionic medium," IEEE Trans. on M i o m a v e T o y and Techniques, vol. MTT-14, pp. waves in free space.The attenuation rates normal to the S.bR.rSeshadri and T. T. \Vu, "Radiation136144, March 1966. [6] condition for a maginterface of the surface wave fields inboth the media are netoionic medium." to be Dublished.
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(2b) (2c) (24 (24 (20 BOUNDARY CONDITIONS The boundary condition appropriate for a perfectly conducting surface is that the tangential components of the electric field vanish.Thisconditionalsoimplies that the normal component of the magnetic field vanishes on the surface. The conducting surface will thereforebeapproximatedbya collection of surfaces of cubes, the sides of which are parallel to the coordinate axes. Plane surfaces perpendicular to the x-axis will be chosen so astocontainpointswhere E , and E, are defined. Similarly, plane surfaces perpendicular to the other axes are chosen. GRID SIZE AND STABILITY CRITERION