# How to solve equations from Penalty FEM in Fluids?

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

 March 11, 2003, 11:14 How to solve equations from Penalty FEM in Fluids? #1 Yiling Guest   Posts: n/a Hi! everyone, I am learning and practicing penalty finite element method used to solve the incompressible flow. After the typical formulation of reduced integration method, a resultant systematic matrix is formed, but how to solve this equation whose some entries in the coefficient matrix are nearly infinite? General successive over-relaxation method fails to converge for this type of equaton, although the direct method such as Gaussian elemination method does work, but the extra requirment of storage forbides its use for large equation sets. Can you share your experience with me if you are skillful in this field? Any relative comments are also welcome. Thanks in advance. Yiling

 March 17, 2003, 20:45 Re: How to solve equations from Penalty FEM in Flu #2 carlslack Guest   Posts: n/a Yiling, You can optimize your Guassian elimination method by employing a skyline storage strategy. The idea is to trim all leading and trailing zero elements from each row of your system of equations. I've written an incompressible flow solver with Gaussian elimination, and this strategy results in an average reduction of 88% of storage space and computational effort. -Carl

 March 20, 2003, 05:11 Re: How to solve equations from Penalty FEM in Flu #3 Anthony Wachs Guest   Posts: n/a Try to switch to iterative solver like preconditioned conjugate gradient (PCG) with sparse matrix storage as suggested in the previous mail. PCG work fine for large matrix systems and combined with sparse storage you will save a great amount of memory. Anthony

 March 20, 2003, 15:58 Re: How to solve equations from Penalty FEM in Flu #4 carlslack Guest   Posts: n/a I thought that PCG was only suitable for symmetric systems... What strategy to you use to apply it to the (non-symmetric) NS equations? -CS

 March 25, 2003, 17:43 Re: How to solve equations from Penalty FEM in Flu #5 Yiling Guest   Posts: n/a Hi, Anthony I have tried the method of PCG, but still can't solve the equation. Firstly my PCG code has worked for general linear equation, and it does work even asymmetric equation. Secondly when I use this code for the equation generated from Penalty formulation, the convergent rate is very slow, if we set the tolerance as 1.e-4 at every point, it seems hopeless to reach that value. Another worry is: in the PCG algorithm, we have to involve the calculation of matrix by vector, while some entries in the nearly-singular matrix are very large in the order (1e+8), the result of multiplication of matrix by vector sometimes exceeds the range of real variables or even for the double precision variable. Yiling

 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 zyf Main CFD Forum 0 July 14, 2003 04:53 d Main CFD Forum 4 May 30, 2003 03:19 kai Main CFD Forum 39 April 7, 2000 12:48 Jian Xia Main CFD Forum 3 January 11, 2000 19:07 Mikhail Main CFD Forum 40 September 9, 1999 09:11

All times are GMT -4. The time now is 22:23.