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George Pau

convergence criteria

In the input deck, the poisson convergence criterion is stated as 1e-3. What exactly is the convergence criteria used in omenwire? How much additional computational time will I need if I decrease the tolerance by a factor of 10?

Thanks, George

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    Mathieu Luisier

    The Poisson equation is solved using a Newton-Raphson scheme in OMEN. There is an outer loop where the Schrodinger and Poisson equations are self-consistently solved and an inner loop in the Poisson equation where the carrier density is updated using simple analytical formula.

    The convergence criterion that you currently see in the input deck is the criterion of the outer loop. It means that between two iterations, the normalized norm of the electrostatic potential should not vary by more than 1e-3. It is difficult to say how much longer the simulation will last if you set this criterion to 1e-4. The number of additional iterations that are required depends on the nanowire structure and on the bias conditions, as the time per iteration.

    The convergence criterion of the inner loop can also be changed. The default value is 1e-3 and refers to the value of the residual of the Poisson equation.

    Both convergence criteria are set so that the drain current of the device does not vary by more than ~1% (in the worst case) if more self-consistent iterations were allowed.


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    SungGeun Kim

    Hi George,

    Thank you for the question. For now, the convergence criterion used in omenwire is 1e-3. The next version of omenwire will allow users to change the criterion. The additional computing time, as you decrease it by a factor of 10, depends on the structure of nanowire and the environment which users setup. I will check this out and come back to you shortly, but reasonable explanation without running simulations with different criterion could be given after a while.

    Thank you

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