Reference text for some of the theory with linear systems and block matricies

[Matthew Rich]

Hi all, 

I sort of crashed into a knowledge barrier in my learnings with the library, more specifically with Steps 20-22, which introduce block matrices and crafty manipulations to get the system ready for the CG solver. I am sort of lost with these tutorials and I think it is due to gaps in my understanding. 

I have been relying on Zienkiewicz texts to really get a solid understanding of FEM and work towards my aspirational use it for analyzing biological structures. However, those resources don't touch the numerical topics like Schur's compliment, preconditioners etc.... 

Is there a good textbook that consolidates these ideas or am I at the point, I just need to sift through journal articles? I am trying to apply some of the techniques utilized in the tutorials on different problems but the leap is too big at the moment.

Thanks in advance.  

[Wolfgang Bangerth]

> I have been relying on Zienkiewicz texts to really get a solid understanding
> of FEM and work towards my aspirational use it for analyzing biological
> structures. However, those resources don't touch the numerical topics like
> Schur's compliment, preconditioners etc....
>
> Is there a good textbook that consolidates these ideas or am I at the point, I
> just need to sift through journal articles? I am trying to apply some of the
> techniques utilized in the tutorials on different problems but the leap is too
> big at the moment.

I would start with Elman, Silvester, Wathen: "Finite elements and fast
iterative solvers". The canonical book on iterative solvers is the one by
Saad, but it only has a few pages about block methods.

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/