Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS) ap- proach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the div-curl system with added slack vari- ables, and hence it is quite complicated. In this paper, we apply the FOSLL* approach to the div system and establish its well-posedness. For the corresponding finite ele- ment approximation, we obtain a quasi-optimal a priori error bound under the same regularity assumption as the standard Galerkin method, but without the restriction to sufficiently small mesh size. Unlike the FOSLS approach, the FOSLL* approach does not have a free a posteriori error estimator, we then propose an explicit residual error estimator and establish its reliability and efficiency bound

Time Traces: Cultural Memory and World War II in Pohnpei

While conducting fieldwork in Pohnpei, Micronesia, in the 1980s and 1990s, Suzanne Falgout heard poignant accounts of the Islanders’ experiences during World War II. The stories and songs that she recorded reveal that for Pohnpeians the effects of the war were local and personal—a catastrophe visited on a landscape that they know in intimate terms. In this paper we discuss not only the content of these memories but also the broader role of memory in human culture. First, we critique common understandings of memory. We highlight the ability of memory to transcend time, the diversity of forms that memory can take, and the active role of humans as agents in the process of remembering. Next, we examine the similarities and diff e rences between personal and cultural memory and the p rocesses of transformation from individual experience to collective identity. F i n a l l y, we discuss the nature of Pohnpeian experiences in World War II and what has made them such enduring and compelling cultural memories sixty years after the war. We relate these wartime memories to traditional Pohnpeian understandings of historical knowledge and to the genres, tropes, characters, concerns, and contexts used by Pohnpeians to remember and to articulate the past. We also examine the changing nature and use of war memories as a strategic resource in the context of contemporary Micronesia

Novel design for transparent high-pressure fuel injector nozzles

The efficiency and emissions of internal combustion (IC) engines are closely tied to the formation of the combustible air-fuel mixture. Direct-injection engines have become more common due to their increased practical flexibility and efficiency, and sprays dominate mixture formation in these engines. Spray formation, or rather the transition from a cylindrical liquid jet to a field of isolated droplets, is not completely understood. However, it is known that nozzle orifice flow and cavitation have an important effect on the formation of fuel injector sprays, even if the exact details of this effect remain unknown. A number of studies in recent years have used injectors with optically transparent nozzles (OTN) to allow observation of the nozzle orifice flow. Our goal in this work is to design various OTN concepts that mimic the flow inside commercial injector nozzles, at realistic fuel pressures, and yet still allow access to the very near nozzle region of the spray so that interior flow structure can be correlated with primary breakup dynamics. This goal has not been achieved until now because interior structures can be very complex, and the most appropriate optical materials are brittle and easily fractured by realistic fuel pressures. An OTN design that achieves realistic injection pressures and grants visual access to the interior flow and spray formation will be explained in detail. The design uses an acrylic nozzle, which is ideal for imaging the interior flow. This nozzle is supported from the outside with sapphire clamps, which reduces tensile stresses in the nozzle and increases the nozzle\u27s injection pressure capacity. An ensemble of nozzles were mechanically tested to prove this design concept

A PETSc parallel-in-time solver based on MGRIT algorithm

We address the development of a modular implementation of the MGRIT (MultiGrid-In-Time) algorithm to solve linear and nonlinear systems that arise from the discretization of evolutionary models with a parallel-in-time approach in the context of the PETSc (the Portable, Extensible Toolkit for Scientific computing) library. Our aim is to give the opportunity of predicting the performance gain achievable when using the MGRIT approach instead of the Time Stepping integrator (TS). To this end, we analyze the performance parameters of the algorithm that provide a-priori the best number of processing elements and grid levels to use to address the scaling of MGRIT, regarded as a parallel iterative algorithm proceeding along the time dimensio

Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by B\"{o}rm and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend the analysis to three dimensions under slightly weakened assumptions, and numerically demonstrate its efficiency for the solution of the elliptic PDE for the global pressure correction in atmospheric forecast models. For this we compare the performance of different multigrid preconditioners on a tensor-product grid with a semi-structured and quasi-uniform horizontal mesh and a one dimensional vertical grid. The code is implemented in the Distributed and Unified Numerics Environment (DUNE), which provides an easy-to-use and scalable environment for algorithms operating on tensor-product grids. Parallel scalability of our solvers on up to 20,480 cores is demonstrated on the HECToR supercomputer.Comment: 22 pages, 6 Figures, 2 Table

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics

We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts, one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.Comment: accepted by ApJS, 27 pages, 20 figures, high-resolution version available at https://ccse.lbl.gov/Publications/wqzhang/castro3.pd