Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table

The volume of earth's ocean

Author Posting. © Oceanography Society, 2010. This article is posted here by permission of Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 23, no. 2 (2010): 112-114.Despite playing a significant role in the global water cycle, ocean volume has not been re-examined in over 25 years. The main uncertainty associated with ocean volume is the mean ocean depth. The earliest studies tended to overestimate ocean depth due to undersampling of seamounts and ocean ridges. The advent of the echosounder in the 1920s and subsequent ship-borne technologies rapidly increased aerial coverage of the ocean; hence, over time there has been a gradual decrease in calculated mean ocean depth. Today, however, in situ measurements span only ~ 10% of the ocean’s surface area. Here, we use satellite altimetry data to estimate the ocean’s volume, which is lower by a volume equivalent to 500 times the Great Lakes or five times the Gulf of Mexico when compared to the most recent published estimates.This work was funded in part by the EarthWater Institute (http://www. earthwaterinstitute.org) in concert with the institute’s ongoing Global Water Audit

Experimental Synthetic Aperture Radar with Dynamic Metasurfaces

We investigate the use of a dynamic metasurface as the transmitting antenna for a synthetic aperture radar (SAR) imaging system. The dynamic metasurface consists of a one-dimensional microstrip waveguide with complementary electric resonator (cELC) elements patterned into the upper conductor. Integrated into each of the cELCs are two diodes that can be used to shift each cELC resonance out of band with an applied voltage. The aperture is designed to operate at K band frequencies (17.5 to 20.3 GHz), with a bandwidth of 2.8 GHz. We experimentally demonstrate imaging with a fabricated metasurface aperture using existing SAR modalities, showing image quality comparable to traditional antennas. The agility of this aperture allows it to operate in spotlight and stripmap SAR modes, as well as in a third modality inspired by computational imaging strategies. We describe its operation in detail, demonstrate high-quality imaging in both 2D and 3D, and examine various trade-offs governing the integration of dynamic metasurfaces in future SAR imaging platforms