[Q-e-developers] Yet another way to avoid overflow in ESM.

[Minoru Otani]

Dear Dr. Nishihara,

Thank you for giving me a clever way to avoid the overflow. I will consider this
for all the boundary conditions.

Best regards,
Minoru 

> On Nov 2, 2015, at 9:58 PM, <nisihara225 at gmail.com> <nisihara225 at gmail.com> wrote:
> 
> Dear Minoru Otani,
> 
> I am trying to use ESM implemented in Q.E. and reading your code (esm.f90).
> In ESM calculation, terms of “exp(x) * erfc(y)” often become overflow because of huge exp(x).
> Thus, you prepare a special subroutine “exp_erfc(x, y)” to avoid the overflow.
> Now, I have another idea to avoid the overflow, as following:
> 
> Operating an unit “exp(log( ))” to “exp(x) * erfc(y)”, one can obtain
>     exp(x) * erfc(y) = exp( x + log(erfc(y)) ) .
> For boundary condition bc1, bc2, and bc3, it is easy to prove “x + log(erfc(y))” has 
> finite upper-bound. Thus, “exp( x + log(erfc(y)) )” does not become overflow.
> Using “exp( x + log(erfc(y)) )” instead of “exp(x) * erfc(y)” in ESM calculation,
> the overflow will be avoided. This method is accurate, not including numerical approximations.
> 
> Unfortunately, I have not ensured that this method is reliable for 
> exponential attenuated metal medium (bc4).
> It would be great if my idea could help you to develop ESM code.
> 
> Regards,
> Satomichi Nishihara