FDTD 法入門 Introduction to the FDTD method

1 MWE 2018 FR6A-2. FDTD . Introduction to the FDTD method . Jun shibayama .. (FDTD) . Maxwell Yee .. FDTD . Yee . Abstract The finite-difference time-domain (FDTD) method has widely been used to treat electromagnetic problems. The formulation of the FDTD method is quite simple, , Maxwell's equations are directly discretized with the finite- difference scheme with Yee's mesh. For practical simulations, several techniques should be incorporated into the FDTD method . For example, we need to impose an absorbing boundary condition, excite an incident field and display electromagnetic fields. In this presentation, we study the basic of the FDTD method with a lecture note.. 1. 3. Yee . (FDTD) [1]-[7] 1(a) Yee . (b) .. FDTD .. FDTD.

2 2. Maxwell .. Maxwell (a) Yee . H. E (1). t E. H (2). t E H .. 6 (b) . H x E y E z 1 . (3). t z y 1(a) . H y E E. z x (4) Staggered grid . t x z x y z x . y z x=i x y=j y z=k z . H z Ex E y (5) i j k 0 . t y x . Yee . Ex H z H y (6) 1(b) . t y z FDTD .. E y H x H z (7) . t z x Ez H y H x 4.. (8) (3) (3) . t x y n . (3)-(8) Yee Hx 1(b) n n+1/2. FDTD n-1/2 . n 1/2 n 1/2 Yee 4 . H x,i, n j +1/2 ,k +1/2 H x,i, j+1/2 ,k+1/2 H x,i, j+1/2 ,k+1/ 2. (9) . t t (2) . Hx 1(a) (i j+1/2 k+1/2) Yee . (9) Hx FDTD . (3) Maxwell . n 1(a) Yee . (3) 1 . (9) Hx (i j+1/2 k+1/2) Hx 5.. (i j+1/2 k+1) (i j+1/2 k) . Ey .. E yn, i, j+1/2 ,k+1/ 2 E yn, i, j+1/2, k+1 E yn, i, j+1/2 ,k (10). z z 1 . (3) 2 Hx . 2 .. E zn, i, j+1/2, k+1/ 2 E zn, i, j+1,k+1/ 2 E zn, i, j,k 1 / 2 (11).

3 3 FDTD FDTD . y y 4 . (9)-(11) (3) . 5 Yee Yee .. H xn, i ,1/2j+1/2 ,k+1/ 2 H xn, i,1/2. j+1/2 ,k+1 / 2. 6 1,2,3 1,2,3 FDTD . t En z y , i, j+1/2 ,k+1. E yn, i, j+1/2, k 7 (1) Mur Higdon . 8 (2) Perfectly Matched Layer . t . En y z , i, j+1,k+1/2. Ezn, i, j,k 1/ 2 (12) 9 . 10 . n n-1/2 11 (1) FDTD . (12) n+1/2 Hx . 2 3 12 (2) Drude, Debye, Lorentz . n 13 BOR BOR . n+1/2 n+1 FDTD . FDTD n=0 -1/2 14 FDTD . t .. 6.. t Courant FDTD FDTD .. 1. v t . 2 2 2. 1 1 1 FDTD .. x y z .. v . FDTD . Maxwell Yee FDTD . (1) .. [1] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, . IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 302 307, May 1966. [2] A. Taflove and S.

4 C. Hagness, Computational Electro- dynamics: The Finite-Difference Time-Domain method . Norwood, MA: Artech House, 2005. [3] , FDTD , . , , 1998. [4] : . FDTD , , 2016. [5] , FDTD , , , 2006. [6] , . ( ): , . , vol. 86, no. 4, pp. 327-330, 2017. [7] , . ( ): , . , vol. 86, no. 5, pp. 408-411, 2017.