The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multi-physics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking.Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software.

Over the last twenty years, the open source community has provided more and more software on which the world's High Performance Computing (HPC) systems depend for performance and productivity. The community has invested millions of dollars and years of effort to build key components. But although the investments in these separate software elements have been tremendously valuable, a great deal of productivity has also been lost because of the lack of planning, coordination, and key integration of technologies necessary to make them work together smoothly and efficiently, both within individual PetaScale systems and between different systems. It seems clear that this completely uncoordinated development model will not provide the software needed to support the unprecedented parallelism required for peta/exascale computation on millions of cores, or the flexibility required to exploit new hardware models and features, such as transactional memory, speculative execution, and GPUs. This report describes the work of the community to prepare for the challenges of exascale computing, ultimately combing their efforts in a coordinated International Exascale Software Project.

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We describe a new high-performance conjugate-gradient (HPCG) benchmark. HPCG is composed of computations and data-access patterns commonly found in scientific applications. HPCG strives for a better correlation to existing codes from the computational science domain and to be representative of their performance. HPCG is meant to help drive the computer system design and implementation in directions that will better impact future performance improvement.

Cover Cover art by George Kitrinos, a derivative of "Circuit board elements background" from freedesignfile.com, used under Creative Commons Attribution 3.0. Equations from a far-field approximation of the Green's function solution to the acoustic analogy equation with thermoacoustic sources.

Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real vafued systems, or deal with complex valued systems as an afterthought.One obvious approach to addressing this problem is to recasb the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach.At the same time, our experience has shown us that there are situations where using an equivalent real form can be very effective.In this paper, we explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be usefuf for a number of practical situations. Furthermore, we show that by making good use of some of the advance features of modem solver packages, we can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using our techniques, we are able to solve very ili-condi tioned complex valued linear systems for a variety of large scale applications.However, more importantly, we shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.

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