===firstname:
Kevin
===firstname3:
Ray
===affil6:

===lastname3:
Tuminaro
===email:
ktcarlb@sandia.gov
===keyword_other2:

===lastname6:

===affil5:

===lastname4:

===lastname7:

===affil7:

===postal:
7011 East Ave, MS 9159
Livermore, CA 94550
===ABSTRACT:
This talk presents a new Krylov-subspace-recycling method for efficiently
solving sequences of linear systems of equations characterized by varying
right-hand sides and symmetric-positive-definite matrices. As opposed to
typical truncation strategies used in recycling such as deflation, we propose
a truncation method based on a technique from nonlinear model reduction:
goal-oriented proper orthogonal decomposition (POD).

This idea is inspired by the observation that model reduction aims to compute a
low-dimensional subspace that contains an \textit{accurate} solution; as such,
we expect the proposed method to generate a low-dimensional subspace that is
well suited for computing solutions that can satisfy \textit{inexact}
tolerances. In particular, we propose specific goal-oriented POD `ingredients'
that align the optimality properties of POD with the objective of
Krylov-subspace recycling.

To efficiently compute solutions in the resulting `POD-augmented' Krylov
subspace, we propose a novel hybrid direct/iterative three-stage method that
leverages 1) the optimal ordering of POD basis vectors, and 2)
well-conditioned reduced matrices.  Numerical experiments performed on
solid-mechanics problems highlight the benefits of the proposed method over
existing approaches for Krylov-subspace recycling.
===affil3:
Sandia National Laboratories
===title:
Applying model reduction to Krylov-subspace recycling: the POD-augmented conjugate-gradient method
===affil2:
University of Maryland
===lastname2:
Forstall
===firstname4:

===keyword1:
Hybrid direct-iterative solvers
===workshop:
no
===lastname:
Carlberg
===firstname5:

===keyword2:
Surrogate modeling/model reduction
===otherauths:

===affil4:

===competition:
no
===firstname7:

===firstname6:

===keyword_other1:

===lastname5:

===affilother:

===firstname2:
Virginia