Patrick Sanan, Dave May and I submitted a paper entitled
Pipelined, Flexible Krylov Subspace Methods
The abstract reads
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 2x can be observed. We conclude by analyzing our new methods with a performance model targeted at future exascale machines.
Please find the preprint on arxiv.
UPDATE Sep/7 2016: The article is published in SIAM J. Sci. Comput., 38(5), C441–C470. (30 pages). Please find it here.
I am starting a new position tomorrow — and will convert into a geophysicist (watch this for some background info). These are my new utensils:
I wish to thank the Alexander von Humboldt-Foundation for supporting me over the last two years.
Particularly, I wish to thank Prof. Christian Hafner and the Institute of Electromagnetic Fields at ETH Zurich. Prof. Hafner was as welcoming as anyone can possibly be. Experiencing how he still enjoys his research after more than 35 years made a strong impression on me. Thank you!
Starting from August I am with the Geophysical Fluid Dynamics group of Prof. Tackley at ETH. They give me the opportunity to join the GeoPC project, which deals with infrastructure development for hybrid parallel smoothers for multigrid preconditioners. GeoPC is part of the larger PASC (Platform for Advanced Scientific Computing) initiative. The abstract of the project proposal reads:
The GeoPC project is developing computational infrastructure to enable massively parallel, scalable smoothers and coarse grid solvers to be used within multigrid preconditioners. This infrastructure is intended to (i) facilitate the execution of high resolution, 3D geodynamic models of the planetary evolution; (ii) provide the Earth Science community (and others) with a suite of continually maintained and re-usable HPC components to build robust multi-level preconditioners (iii) position Swiss computational geosciences in the emerging exa-scale era.
GeoPC is a PASC co-design project involving the University of Lugano (USI), the Swiss Federal Institute of Technology (ETH), University of Chicago (UC), Vienna University of Technology (TU Wien), as well as other stakeholders.
Our developments will become part of PETSc, the Portable, Extensible Toolkit for
Scientific Computation. I am very much looking forward to contributing to a library as renowned as PETSc!
My new coordinates are:
Institute of Geophysics – Geophysical Fluid Dynamics
NO H23, Sonneggstrasse 5, 8092 Zurich, Switzerland
Phone: +41 44 632 0244