Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pipelined, Flexible Krylov Subspace Methods   We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR),
and Generalized Minimal Residual (GMRES) methods which are both pipelined and
flexible. These allow computation of inner products and norms to be overlapped
with operator and nonlinear or nondeterministic preconditioner application.The
methods are hence aimed at hiding network latencies and synchronizations which
can become computational bottlenecks in Krylov methods on extreme-scale systems
or in the strong-scaling limit. The new variants are not arithmetically
equivalent to their base flexible Krylov methods, but are chosen to be
similarly performant in a realistic use case, the application of strong
nonlinear preconditioners to large problems which require many Krylov
iterations. We provide scalable implementations of our methods as contributions
to the PETSc package and demonstrate their effectiveness with practical
examples derived from models of mantle convection and lithospheric dynamics
with heterogeneous viscosity structure. These represent challenging problems
where multiscale nonlinear preconditioners are required for the current
state-of-the-art algorithms, and are hence amenable to acceleration with our
new techniques. Large-scale tests are performed in the strong-scaling regime on
a contemporary leadership supercomputer, where speedups approaching, and even
exceeding $2\times$ can be observed. We conclude by analyzing our new methods
with a performance model targeted at future exascale machines.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph