scalar block pentadiagonal solver

Joachim · April 13, 2015, 19:00

Hello everyone!

I am looking for a code that would solve a block pentadiagonal system of equations, in which all 5 blocks are diagonal. Basically, I have

Ax(i-2) + Bx(i-1) + Cx(i) + Dx(i+1) + Ex(i+2) = F

in which x is a vector of dimension N, and A, B, C,... are diagonal matrices of dimension N by N.

Would you know an efficient way to solve this system (exact solution)? A fortran code would be perfect, but even if you only have the theory, I'll take it!

thank you!

Joachim

mprinkey · April 14, 2015, 09:45

I gave a lot of details and links to sample code here a week or so ago:

http://www.cfd-online.com/Forums/mai...tml#post540661

There is discussion above about block Thomas solvers too. You can easily take the scalar pentadiagonal code and turn the scalar elimination into block elimination. The only tricky part is replacing the scalar division with multiplication by matrix inverse (really, LU factorization of the divisor matrix and repeated LU evaluation for each block).

beer · April 14, 2015, 09:58

http://www.math.uakron.edu/~kreider/anpde/penta.f

Or use SIP (Strongly implicit procedure) if you want a more general approach. Apart from that I would always encourage people to use libraries like petsc or paralution. They are very fast, precise and stable. Also they are easy to use (some more, some less) and open source.

April 13, 2015, 19:00	scalar block pentadiagonal solver	#1
Joachim Senior Member Joachim Join Date: Mar 2012 Location: Paris, France Posts: 145 Rep Power: 15	Hello everyone! I am looking for a code that would solve a block pentadiagonal system of equations, in which all 5 blocks are diagonal. Basically, I have Ax(i-2) + Bx(i-1) + Cx(i) + Dx(i+1) + Ex(i+2) = F in which x is a vector of dimension N, and A, B, C,... are diagonal matrices of dimension N by N. Would you know an efficient way to solve this system (exact solution)? A fortran code would be perfect, but even if you only have the theory, I'll take it! thank you! Joachim

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April 14, 2015, 09:45		#2
mprinkey Senior Member Michael Prinkey Join Date: Mar 2009 Location: Pittsburgh PA Posts: 363 Rep Power: 25	I gave a lot of details and links to sample code here a week or so ago: http://www.cfd-online.com/Forums/mai...tml#post540661 There is discussion above about block Thomas solvers too. You can easily take the scalar pentadiagonal code and turn the scalar elimination into block elimination. The only tricky part is replacing the scalar division with multiplication by matrix inverse (really, LU factorization of the divisor matrix and repeated LU evaluation for each block).

April 14, 2015, 09:58		#3
beer Member Join Date: Dec 2012 Posts: 92 Rep Power: 13	http://www.math.uakron.edu/~kreider/anpde/penta.f Or use SIP (Strongly implicit procedure) if you want a more general approach. Apart from that I would always encourage people to use libraries like petsc or paralution. They are very fast, precise and stable. Also they are easy to use (some more, some less) and open source.