How to put mur's absorbing boundary condition in 1d fdtd maxwell equation

[s_hy]

hi

can anyone teach me how to put Mur's ABC in my fortran code for 1d fdtd maxwell's equation as below

!1d fdtd Simulation in free space 
subroutine fd1d01(f0,miu,delta,S,E0)
implicit none

double precision                   :: f0               !frequency
double precision                   :: miu              !permittivity
double precision                   :: delta 
double precision                   :: S 
double precision                   :: E0
integer                            :: iinit 
integer                            :: ilast 
integer                            :: i,j
integer                            :: n
double precision                   :: Ca
double precision                   :: Da
double precision                   :: tdelta 
double precision                   :: c
double precision,dimension(202)    :: Ez
double precision,dimension(202)    :: Hy
double precision, parameter        :: pi = 3.14159265
double precision                   :: Cb
double precision                   :: Db
double precision                   :: lambda
character(len=20)                  :: filename

f0 = 100.0
miu = 1.0
delta = 1.e-3
S = 1.0001
E0 = 1.0
iinit = 1 
ilast = 100

c = 1.0
lambda = c/f0

tdelta = (delta/c)/sqrt(2.0)

!initialization
do j = 1, 2*ilast
 If (Mod(j,2) == 0) then  !j is even; hence di is whole number
    Hy(j) = 0
    else
    Ez(j) = 0
 End if
end do

Ca = 1.0
Cb = (tdelta/delta)

Da = 1.0
Db = tdelta/(miu*delta)

do n = 1,200
  write (filename, "('ez',I3.3,'.dat')") n
  open (unit=130,file=filename)
 
  do j = 2, 2*ilast-1
     if (Mod(j,2) /= 0) then  !j is odd; 
        Ez(j) = Cb*(Hy(j+1)-Hy(j-1)) + Ca*Ez(j)
!        Print*, 'n, j, Ez(j) = ', n, ' ', j, ' ' , Ez(j)
        write (130,*) Ez(j)
     end if
  end do !j

  !absorbing boundary condition
  Ez(2) = 0
  Ez(202) = 0

  do j = 2, 2*ilast-1
     if (Mod(j,2) == 0) then  !j is even;
        Hy(j) = Db*(Ez(j+1)-Ez(j-1)) + Da*Hy(j)
     end if 
  end do !j

  !plane wave source  
   Ez(101) = E0*sin (2*pi*f0*n*tdelta)

 close (unit=130)

end do !n

end SUBROUTINE fd1d01

i tried to put it after Ez and before Hy...but i guess my ABC algorithm is wrong. anyone can teach me?

thanks

 

[Future Bruno]

Mur's ABC algorithm can be used to implement an absorbing boundary condition in your Fortran code. The algorithm works by taking the difference between the values of the fields at two successive points and applying a damping factor to reduce the amplitude of the propagating wave. The damping factor is chosen such that it reduces the amplitude of the wave exponentially as it propagates away from the boundary. For example, for your code, you can add the following lines after the line that initializes the Hy and Ez arrays:do j = 1,2*ilast if (j <= 2) then !apply Mur's ABC to the left boundary Ez(j) = Ez(j) - dampingFactor*(Hy(j+1)-Hy(j)) end if if (j >= 2*ilast-1) then !apply Mur's ABC to the right boundary Ez(j) = Ez(j) + dampingFactor*(Hy(j)-Hy(j-1)) end ifend dowhere dampingFactor is a value chosen to reduce the amplitude of the wave exponentially as it propagates away from the boundary. The exact value of this parameter will depend on the physical characteristics of your problem, so it is best to experiment with different values until you find one that works well.