Monolithic nonlinear system of equations

[saikat mukherjee]

Hello,

I am looking for some tutorials on solving a time dependent, nonlinear system of equations monolithically, in parallel using deal.ii. I am using Trilinos and p4est for the parallel mesh and linear solvers. I tried solving using some of the examples but so far none has been successful. Could someone suggest some tutorial or example code that I could begin with ??

Thanks,

Saikat 

[Wolfgang Bangerth]

It all depends on how exactly you want to solve your nonlinear problem. If you
use a Newton method, you will end up with a block system which you can solve
like we always solve block systems -- with an iterative solver, using a block
preconditioner. You can also use parallel direct solvers for the Newton system.

My suggestion would be first formulate what the linear systems are that you
need to solve in each iteration, and then think about how one can use the
structure of these linear systems to define efficient solvers. This is really
no different from linear problems -- each Newton step, for example, is just a
linear problem.

Best
W.

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