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How coefficient matrix property change with dt?

  1. Jul 23, 2009 #1
    My work is on implicit FDTD method which allows time step (delta_t) above CFL limit. Implicit methods require one to solve a large sparse matrix. If delta_t is increased the the solution of this sparse matrix becomes slower (slow convergence). I can see this when I do the simulation with the implicit scheme. But my query is about mathematical explanation of what happens when I increase delta_t. How the properties of the matrix change with the change of delta_t which ultimately lead to poor convergence. Which properties of the sparse matrix do I actually need to look into. I think with the increase of delta_t the matrix characteristics change - how one observe this and relate this with the convergence.

    Can someone please advise me on this. Any advice on some simple literature / books where I can get a good understanding on this would be highly appreciated. If this is not a suitable forum for this can you please refer me to some other more appropriate forum where I can get advice on mathematical issues like this. Thank you very much.
     
  2. jcsd
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