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Post-seminar working session

The purpose of this session is for the applied math group to work through some problems cooperatively. Anyone is welcome to attend. We normally meet Fridays from 4pm-6pm in EAA 1100 after seminar. Here are notes from certain session.

• Feb 10th, 2006 - Vorticity in a box (part II)
  • Asymptotic expansion of \nabla(psi) = lambda*psi + epsilon*psi^3 ( jpg)
  • Order conditions to check psi = psi_0 + epsilon*psi_1 + epsilon^2*psi_2 + ... (jpg)
  • Using self-adjoint properties (jpg)
  • Summary of what we found out. (jpg)
  • The resulting first order equation expanded. What is c_kl?? (jpg)
  • The second order equation, can we get c_kl from there? no. We get lambda_2 in terms of c_kl again. (jpg)
  • Ben and Colin's optimization scheme (jpg)
  • set c_kl = 1, k = 1, l = 1, and appropriate lambda_0 and psi_0, N = 20 (chebychev points for accuracy). Convergence results jpg)
  • set c_kl = 1, k = 1, l = 1, and appropriate lambda_0 and psi_0, N = 10 (chebychev points for accuracy). Convergence results jpg). Noticed that our two norm definition wasn't normalized properly for non-equidistributed grids, did a quick test of max norm instead.
  • changed c_kl =2, convergence results. jpg)
• Oct 10th,2003 - A Contour Integration Exercise.   pdf | cosz.m | integrand.m
• September 26th,2003 - Breaking down an equation.   ps | pdf

Last updated: Wednesday, 29-Aug-2007 13:31:44 PDT