CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Tridiagonal system

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

Reply
 
LinkBack Thread Tools Display Modes
Old   April 17, 2014, 03:29
Default Tridiagonal system
  #1
New Member
 
Robert Celi
Join Date: Apr 2014
Posts: 2
Rep Power: 0
celi is on a distinguished road
I need a method for solving a linear system (x1..xn) of type
A*x=B
where A is a tridiagonal matrix

x x
x x x
. x x x

with (generic) structure

first row
x1*(k11+k11a/(x1+x2+..xn) x2*k13

second row
x1*k21 x2*(k22+k22a/(x1+x2+..xn) x3*k23

third row
x2*k32 x3*(k33+k33a/(x1+x2+..xn) x4*k34

and so on, size N about 400 x 400 (sparse),
I am unable to find a solution which allow to use Thomas or similar efficient methods
cause diagonal elements contains K/(x1+x2+...+xn) which require separate processing,
what am I missing here ?
Is there any simple solution for these systems ?
Thanks for help.

Last edited by celi; April 17, 2014 at 05:50.
celi is offline   Reply With Quote

Old   April 17, 2014, 12:55
Default
  #2
agd
Senior Member
 
Join Date: Jul 2009
Posts: 191
Rep Power: 7
agd is on a distinguished road
Pardon me if this is a stupid question, but if I understand your notation it looks like you have a system of quadratic equations rather than linear equations. If you multiply through by the denominator of the diagonal terms don't you get a bunch of quadratic terms?
agd is offline   Reply With Quote

Old   April 17, 2014, 13:08
Default
  #3
New Member
 
Robert Celi
Join Date: Apr 2014
Posts: 2
Rep Power: 0
celi is on a distinguished road
thanks for the comment,
it looks like there is a quadratic contribute,
my problem is to identify an efficient method for solving such kind of systems,
a iterative method could be Ok providing there is a way (which I do not know) to generate accurate estimates for vector [x1..xn]
celi is offline   Reply With Quote

Old   April 17, 2014, 13:16
Default
  #4
agd
Senior Member
 
Join Date: Jul 2009
Posts: 191
Rep Power: 7
agd is on a distinguished road
If you want to use a linear solver, then try linearizing the system first. A Newton-Raphson procedure would probably be sufficient, at which point you could use a linear iterative solver to solve the resulting linear system.
agd is offline   Reply With Quote

Reply

Tags
thomas, tridiagonal

Thread Tools
Display Modes

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 Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
CFX11 + Fortran compiler ? Mohan CFX 20 March 30, 2011 18:56
block tridiagonal system solver for periodic bc Abdullah Main CFD Forum 8 February 23, 2007 14:15
Tridiagonal System Zhong Lei Main CFD Forum 3 May 24, 2001 14:18
On the block tridiagonal linear system zhanglei Main CFD Forum 2 July 24, 2000 06:15
On the block tridiagonal linear system zhanglei Main CFD Forum 0 July 18, 2000 08:55


All times are GMT -4. The time now is 08:08.