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Segregated method for numerical solution of a PDE system

  1. Oct 19, 2012 #1

    I have a system of three coupled PDE and I discretized the equations using finite difference method.

    It results in a block matrix equations as:

    [A11 A12 A13] [x1] = [f1]
    [A21 A22 A23] [x2] = [f2]
    [A31 A32 A33] [x3] = [f3]

    where, any of Aij is a square matrix.

    I use segregated method to solve the system of equations iteratively as:

    0 - initial values: x2=0, x3=0

    1 - A11 * x1 = f1 - A12 * x2 - A13 * x3

    2- update x1

    3- A22 * x2 = f2 - A21 * x1 - A23 * x3

    4- update x2

    5- A33 * x3 = f3 - A31 * x1 - A32 * x2

    6- update x3 and repeat 1 to 6 until convergence.

    The issue I encountered is that when I change the order of the steps above I will get different results. For example if I first assume x1=x2=0 and I start by solving

    A33 * x3 = f3 - A31 * x1 - A32 * x2 and continue with the other unknowns, I will get completely different results.

    I hope you can help me to find out what is wrong in my method.


  2. jcsd
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