[petsc-users] [Need Help] Time dependent split operator method

[Dharmendar Reddy]

Hello,
           I am trying to implement a split operator method to solve time
dependent Schrodinger euqation. I use a semi implicit discretization for
the time operator. I have not used petsc TS before, it will be helpful  if
you can give me some pointers to implementing this algorithm:

Actual equation:   i*hbar*ddt(x) = (H1+H2)*x  (linear problem)

A1 = i*hbar/dt * IdentityMat -  H1/2
B1 = i*hbar/dt * IdentityMat + H2/2

A2 = i*hbar/dt * IdentityMat  - H2/2
B2 = i*hbar/dt * IdentityMat + H1/2

x1,x2 are vectors
do ic=1,NumTimeSteps

  solve substep1 :   A1*x1 = B1*x2
  solve substep2 :   A2*x2 = B2*x1

   copy solution:  x(ic*dt) = x2

end do

I have following constraints:
1.) I Want the time step to be fixed user specified value
2.) Matrices A1 and A2 can be reorder to be tri or penta diagonal. I would
like to use this for fast direct solve. Typical matrix sizes 10^5 to 10^6
with 3 to 5 non zeros per row.
3.) based on the time it take for my matlab code, which seem to use
umfpack, i think a direct solve will be fast enough for my needs.


petsc TS has the theta method which seems like the one i should be using
but its not clear to me how to do the stepping

Thanks
Reddy

-- 
-----------------------------------------------------
Dharmendar Reddy Palle
Graduate Student
Microelectronics Research center,
University of Texas at Austin,
10100 Burnet Road, Bldg. 160
MER 2.608F, TX 78758-4445
e-mail: dharmareddy84 at gmail.com
Phone: +1-512-350-9082
United States of America.
Homepage: https://webspace.utexas.edu/~dpr342
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