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JacobiPC and SliceJacobiPC for all-at-once-system #162
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…emove `current_state` from AllAtOnceJacobian
colinjcotter
approved these changes
Feb 27, 2024
JHopeCollins
commented
Feb 27, 2024
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Labels
Core functionality
Adding to the main paradiag functionality
enhancement
New feature or request
performance
Improving or fixing the computational performance
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This PR implements two new preconditioners for the all-at-once system. Each one builds an approximation to the all-at-once Jacobian and applies an (approximate) solve.
A block Jacobi preconditioner
JacobiPC
. This forms the preconditioner from the blocks on the diagonal of the all-at-once system. These blocks are real-valued and have no time average approximation (unless you ask for it), but there is no coupling between the timesteps.A "slice Jacobi" preconditioner
SliceJacobiPC
. This forms a preconditioner from blocks of several timesteps of the all-at-once Jacobian. The timesteps are coupled within each block, but not between blocks. Another all-at-once preconditioner can be applied to each of these blocks, for example applyingCirculantPC
to smaller slices of the full timeseries. In this case, the circulant preconditioner in each slice would use the time average from the local slice which would hopefully reduce this error source.Other additions in this PR
DiagFFTPC
->CirculantPC
LinearSolver
class that solves aksp
with theAllAtOnceJacobian
. This does not build the rhs including the initial condition like theAllAtOnceSolver
does so unless you provide it with an appropriate rhs it will not solve for an all-at-once-system timeseries.split_ensemble
function for taking a largeEnsemble
and creating smaller subEnsembles
defined over only part of the large one.