Peter, What the hay is this R. E. Bank and D. J. Rose, ``Global Approximate Newton Methods,'' Numer. Math., vol. 37, pp. 279-295, 1981. and should it be a “line search” or something in SNES?
Thanks Barry On Jan 18, 2014, at 5:59 PM, Dharmendar Reddy <[email protected]> wrote: > On Sat, Jan 18, 2014 at 3:54 PM, Karl Rupp <[email protected]> wrote: >> Hi, >> >> >> >>> I am solving a set of equations with SNES >>> >>> F1 (x1,x2,x3) = 0 >>> F2 (x1,x2,x3) = 0 >>> F3 (x1,x2,x3) = 0 >>> >>> The system of equations is shown on page 1 of pdf here >>> http://dunham.ee.washington.edu/ee531/notes/SemiRev.pdf >>> >>> F1 = equation 1 >>> F2 = equation 2 >>> F3 = equation 5 >>> >>> x1 = n, X2=p and X3 = psi, >>> X1 and X2 have an exponential dependance on X1 >>> after i scale the variables, X3 typically varies between say +/- 100 >>> where as X1 and X2 vary between 0 to 2. norm(X) then may usually >>> dominated by solution values of X3. >> >> >> If you are solving the drift-diffusion system for semiconductors, which >> discretization do you use? How did you stabilize the strong advection? >> >> > > My plan is to use the discretization method described here. > (http://www.iue.tuwien.ac.at/phd/triebl/node30.html ). > > The method typically used for for stabilizing the advection term is > called Scharfetter-Gummel method described the above link. > > When i intially started the code design, i wanted to implement the > approach mentioned in this paper (dx.doi.org/10.2172/1020517) . I am > still learning about this things so..i am not sure which is the right > way to go. > > For stabilizing, i implemented the bank n rose algorithm via > SNESPostCheck, i am yet to test the efficacy of this method over the > defualt snes methods. > (http://www.iue.tuwien.ac.at/phd/ceric/node17.html) > > > >> >>> Can you suggest me the snes options that i need to use to achieve the >>> following: >>> >>> 1. X1 > 0 and X2 > 0 (as per previous emails, i can use >>> SNESSetVariableBounds) >> >> >> Have you considered a transformation to quasi-fermi potentials, i.e. >> n ~ exp(phi_n), p ~ exp(phi_p) >> or Slotboom variables? This way you could get rid of the constraint >> entirely. Even if you solve for (n,p,psi), my experience is that positivity >> is preserved automatically when using a good discretization and step size >> control. >> >> >> >>> 2. I want the updates to solution to have an adaptive stepping based >>> on norm of (F) or norm(X). If norm(F) is decreasing as the iteration >>> progresss, larger stepping others wise reduce the step size.. >>> Similarly for Norm of X. >> >> >> A good damping for the drift-diffusion system is tricky. I know a couple of >> empirical expressions, but would be interested to know whether this can be >> handled in a more black-box manner as well. >> >> Best regards, >> Karli >>
