Solving System of Linear equations

shchepan · September 29, 2009, 09:33

Hi!
I need to solve in OpenFOAM system of linear equation like
A*b = c
where A is tensor (rank 2) and c is vector. A and c are constants.

How can I solve this equation?
Thank you

shchepan · September 30, 2009, 02:03

Thank you, Stanley!
Can you show how to use this function?
What H-file I should include solve function to work?

shchepan · October 1, 2009, 01:09

//I've created tensor A:
tensor A(Axx, Axy, Axz, Ayx, Ayy, Ayz, Azx, Azy, Azz);
//and vector c:
vector c(cx, cy, cz);

and now I want to get vector b: A*b=c

akidess · October 1, 2009, 20:05

Why use OpenFOAM instead of MATLAB / Octave for this?

shchepan · October 2, 2009, 01:46

Anton, because it is only one step of big programm.
First I solve MHD turbulent equations in crucible. Then I solve lagrangian equation for solid particle motion. I take into acount lift force to (proportional U x rot(U)). And to solve this aquation I need to solve system of linear algebraic equations.

nikwin · November 14, 2010, 14:03

Hi Mihails,

I would also be able to solve a system of linear equations in OF as a part of a larger code. Did you ever find out if there is a possibility to solve a system of linear equations i OF?

Thanks

Lukasz · November 14, 2010, 16:04

Why don't you use our GPU-baed code (speedit.vratis.com)? It can be easily plugged to OF. So far we support CG/BiCGSTAB for solving symmetric/unsymmetric matrices in single/double precision (soon also with complex values).

shchepan · November 15, 2010, 03:50

Year ago I decided that it is much easier for me to write my own code that solve systems of linear equation using Gauss method.

Lukasz · November 15, 2010, 05:30

But happens if the matrix is huge and sparse. The memory requirements are quite high for Gauss method.

shchepan · November 15, 2010, 05:40

Of course you are right, Lukasz. I am solving my specific problem and I have no goal to write universal code for systems of linear equations.

nikwin · November 16, 2010, 05:27

Thanks both of you!

The simplest way for me is to go for Michails suggestion, which I've already implemented in Matlab. Now I will just need to rewrite it into OF which for me will be the tricky part.

Regards

herbert · November 16, 2010, 05:36

Hi,

if you want to use Gauss-algorithm only, you don't have to hardcode it. There is already a class called simpleMatrix which can do this job. The source is located in src/OpenFOAM/matrices/simpleMatrix/ .

I don't know if there is an example in any solver, but it is quite simple to use.

Regards,
Stefan

nikwin · November 16, 2010, 07:52

Perfect!

It works as expected.

Thanks
/NW

Danath · December 5, 2013, 11:40

Hello ! can you tell me how you add simpleMatrix to your code ?

I am trying to do the same thing but i have a lot of problems !

September 29, 2009, 09:33	Solving System of Linear equations	#1
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	Hi! I need to solve in OpenFOAM system of linear equation like Ab = c* where A is tensor (rank 2) and c is vector. A and c are constants. How can I solve this equation? Thank you

November 15, 2010, 03:50		#8
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	Year ago I decided that it is much easier for me to write my own code that solve systems of linear equation using Gauss method. __________________ Mihails Ščepanskis Laboratory for Mathematical Modelling of Environmental and Technological Processes University of Latvia

November 15, 2010, 05:40		#10
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	Of course you are right, Lukasz. I am solving my specific problem and I have no goal to write universal code for systems of linear equations. __________________ Mihails Ščepanskis Laboratory for Mathematical Modelling of Environmental and Technological Processes University of Latvia

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September 30, 2009, 02:03		#2
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	Thank you, Stanley! Can you show how to use this function? What H-file I should include solve function to work?

October 1, 2009, 01:09		#3
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	//I've created tensor A: tensor A(Axx, Axy, Axz, Ayx, Ayy, Ayz, Azx, Azy, Azz); //and vector c: vector c(cx, cy, cz); and now I want to get vector b: A*b=c

October 1, 2009, 20:05		#4
akidess Senior Member Anton Kidess Join Date: May 2009 Location: Germany Posts: 1,377 Rep Power: 30	Why use OpenFOAM instead of MATLAB / Octave for this?

October 2, 2009, 01:46		#5
shchepan Member Mihails Ščepanskis Join Date: Jul 2009 Posts: 36 Rep Power: 17	Anton, because it is only one step of big programm. First I solve MHD turbulent equations in crucible. Then I solve lagrangian equation for solid particle motion. I take into acount lift force to (proportional U x rot(U)). And to solve this aquation I need to solve system of linear algebraic equations.

November 14, 2010, 14:03		#6
nikwin Member Niklas Winkler Join Date: Mar 2009 Location: Stockholm, Stockholm, Sweden Posts: 73 Rep Power: 17	Hi Mihails, I would also be able to solve a system of linear equations in OF as a part of a larger code. Did you ever find out if there is a possibility to solve a system of linear equations i OF? Thanks

November 14, 2010, 16:04		#7
Lukasz Member Lukasz Miroslaw Join Date: Dec 2009 Location: Poland Posts: 66 Rep Power: 16	Why don't you use our GPU-baed code (speedit.vratis.com)? It can be easily plugged to OF. So far we support CG/BiCGSTAB for solving symmetric/unsymmetric matrices in single/double precision (soon also with complex values).

November 15, 2010, 05:30		#9
Lukasz Member Lukasz Miroslaw Join Date: Dec 2009 Location: Poland Posts: 66 Rep Power: 16	But happens if the matrix is huge and sparse. The memory requirements are quite high for Gauss method.

November 16, 2010, 05:27		#11
nikwin Member Niklas Winkler Join Date: Mar 2009 Location: Stockholm, Stockholm, Sweden Posts: 73 Rep Power: 17	Thanks both of you! The simplest way for me is to go for Michails suggestion, which I've already implemented in Matlab. Now I will just need to rewrite it into OF which for me will be the tricky part. Regards

November 16, 2010, 05:36		#12
herbert Senior Member Stefan Herbert Join Date: Dec 2009 Location: Darmstadt, Germany Posts: 129 Rep Power: 17	Hi, if you want to use Gauss-algorithm only, you don't have to hardcode it. There is already a class called simpleMatrix which can do this job. The source is located in src/OpenFOAM/matrices/simpleMatrix/ . I don't know if there is an example in any solver, but it is quite simple to use. Regards, Stefan

November 16, 2010, 07:52		#13
nikwin Member Niklas Winkler Join Date: Mar 2009 Location: Stockholm, Stockholm, Sweden Posts: 73 Rep Power: 17	Perfect! It works as expected. Thanks /NW

December 5, 2013, 11:40		#14
Danath Member Evangelos Join Date: Sep 2011 Posts: 87 Rep Power: 15	Hello ! can you tell me how you add simpleMatrix to your code ? I am trying to do the same thing but i have a lot of problems !