# Boundary condition in Spectral method

 Register Blogs Members List Search Today's Posts Mark Forums Read

April 5, 2013, 15:18
Boundary condition in Spectral method
#1
New Member

Join Date: Feb 2011
Posts: 23
Rep Power: 6
Hi All

I am playing with the boundary conditions in spectral method using Chebyshev grids.

Say, I want to solve the eigenfunction of . Analytically, the eigenfunction will be sin or cosine.

Indeed, in Matlab, the following small code will generate the eigenfunction with three different boundary conditions. I choose to plot from each boundary condition case an eigenfunction and attach here.

clear;
nrmod=357;

[y,DM]=chebdif(nrmod,4);

D2=DM(:,:,2);

% q is the eigenfunction.

% bc: q(-1)=0,q(1)=0
% [ef,ev]=eig(D2(2:end-1,2:end-1));

% bc: q(-1)=0,q(1)=1. Just change the last 1 to 2 for q(-1)=0,q(1)=2
% [ef,ev]=eig(D2(2:end-1,2:end-1)+diag(D2(2:end-1,1))*1);

% bc: q(-1)=1,q(1)=1
[ef,ev]=eig(D2(2:end-1,2:end-1)+diag(D2(2:end-1,1))*1+diag(D2(2:end-1,end))*1);

for i=nrmod-2:-1:1
plot(y(2:end-1),real(ef(:,i)),'-*b')
title([num2str(i) ' eigenvalue is ' num2str(ev(i,i))])
pause
end

My question is:

Does it make sense to require the eigenfunction to have boundary condition q(-1)=0,q(1)=2? I tried in Matlab, but strange things happens, it returns the results of q(-1)=0,q(1)=0. Why is this?

Jo
Attached Images
 bc01.jpg (80.5 KB, 4 views) bc00.jpg (70.3 KB, 2 views) nobc.jpg (65.7 KB, 2 views)

 April 5, 2013, 16:58 #2 New Member   Join Date: Feb 2011 Posts: 23 Rep Power: 6 I am sorry. I just realized that the way imposing the boundary condition as implemented here is not right. Could anyone tell me the right way?......Thanks. Jo

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post peob OpenFOAM Running, Solving & CFD 2 August 14, 2014 09:07 happy CFX 14 September 6, 2012 01:54 aaev OpenFOAM Bugs 2 December 15, 2011 15:03 thehexman Main CFD Forum 1 February 5, 2010 07:10 Frank Main CFD Forum 1 April 21, 2008 18:36

All times are GMT -4. The time now is 18:09.