Dimplementationofmaxwell’s Equationsin Matlabtostudythe Effect Of Absorption Using Pml

Algebra Calculus Education Finance

1-D Implementation of Maxwell’s Equations in MATLAB to Study the Effect of Absorption Using PML . Pranav K Shrivastava,Vikas Rathi, Hemant S Pokhariya Graphic Era Unversity ,Dehradun e-mail:{pranav.shantikunj,vikas.rth}@gmil.com . . Abstract: The Finite Difference Time Domain method   (FDTD)     uses     centre-difference representations   of   the   continuous   partial The 3D source free( J =0) Mxwell’s curl equations[5]  a homogeneous medium are: . ∂Ez − ∂Ey = −µ ∂Hx ∂y differential equations to create iterative numerical  dH  ∂Ex ∂z ∂Ez ∂t ∂Hy models of wave propagation. First we study the ∇×E = −µ → ∂z   − ∂x   = −µ ∂t propagation behavior of the wave in single dt  ∂Ey ∂Ex ∂Hz dimension without PML and in second part we study the absorption using PML for the same wave  ∂x   − ∂y = −µ ∂t using MATLAB environment. . I. INTRODUCTION . Finite-difference  time-domain  (FDTD)  is  a  popular computational electrodynamics modeling technique. Since it is a . ∇ × H = ε  ∂Hz d E      ∂Hx dt    ∂Hy →   ∂y ∂z  ∂x ∂Hy −   ∂z    = ε ∂Hz = −    ∂t  ε ∂Hx −   ∂y    = ε ∂Ex ∂t ∂Ey ∂t ∂Ez ∂t time-domain method, solutions can cover a wide frequency range with a single simulation run. ∂Ex   = −µ ∂Hy ∂z  ∂t ∂Hy   = −ε ∂Ex The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. The time- dependent Maxwell’s equations (in partial differential form) are discretized using central-difference approximations to the space and time partial   derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved. . When Maxwell’s differential equations are examined, it can be seen that the change in the E-field in time (the time derivative) is dependent on the change in the H-field across space (the curl). This results in the basic FDTD time-stepping relation that, at any point in space, the updated value of the E-field in time is dependent on the stored value of the E-field and the numerical curl of the local distribution of the H-field in space.[4] . The H-field is time-stepped…

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