Preconditioner reuse

[reverendbedford]

Reason

Preconditioner reuse is a good trick to effectively reduce the computational cost of a simulation. The idea is that forming the preconditioner can be quite expensive, but often the structure of the problem only changes slowly over time. So you can reuse an old preconditioner at subsequent time steps quite effectively, avoiding the cost of reforming for many time steps.

As an example, imagine you use a full LU factorization as your preconditioner for GMRES. The first time you form the LU factorization the linear solve will converge in 1 iteration. If you keep reusing that LU factorization for multiple nonlinear iterations across multiple time steps it will often continue to work quite well.

Design

Use the new libmesh preconditioner reuse functionality to provide new options in the Executioner block:

• reuse_preconditioner -- a bool, if true enable preconditioner reuse
• reuse_preconditioner_max_its -- the heuristic is to continue to reuse the previously-constructed preconditioner until it takes this number of linear iterations to solve the linearized system. At that point reform a new preconditioner.

Impact

This will add a new feature and (should) not affect any existing functionality.