Batched Linear Algebra Problems on GPU Accelerators

The emergence of multicore and heterogeneous architectures requires many linear algebra algorithms to be redesigned to take advantage of the accelerators, such as GPUs. A particularly challenging class of problems, arising in numerous applications, involves the use of linear algebra operations on many small-sized matrices. The size of these matrices is usually the same, up to a few hundred. The number of them can be thousands, even millions. Compared to large matrix problems with more data parallel computation that are well suited on GPUs, the challenges of small matrix problems lie in the low computing intensity, the large sequential operation fractions, and the big PCI-E overhead. These challenges entail redesigning the algorithms instead of merely porting the current LAPACK algorithms. We consider two classes of problems. The first is linear systems with one-sided factorizations (LU, QR, and Cholesky) and their solver, forward and backward substitution. The second is a two-sided Householder bi-diagonalization. They are challenging to develop and are highly demanded in applications. Our main efforts focus on the same-sized problems. Variable-sized problems are also considered, though to a lesser extent. Our contributions can be summarized as follows. First, we formulated a batched linear algebra framework to solve many data-parallel, small-sized problems/tasks. Second, we redesigned a set of fundamental linear algebra algorithms for high- performance, batched execution on GPU accelerators. Third, we designed batched BLAS (Basic Linear Algebra Subprograms) and proposed innovative optimization techniques for high-performance computation. Fourth, we illustrated the batched methodology on real-world applications as in the case of scaling a CFD application up to 4096 nodes on the Titan supercomputer at Oak Ridge National Laboratory (ORNL). Finally, we demonstrated the power, energy and time efficiency of using accelerators as compared to CPUs. Our solutions achieved large speedups and high energy efficiency compared to related routines in CUBLAS on NVIDIA GPUs and MKL on Intel Sandy-Bridge multicore CPUs. The modern accelerators are all Single-Instruction Multiple-Thread (SIMT) architectures. Our solutions and methods are based on NVIDIA GPUs and can be extended to other accelerators, such as the Intel Xeon Phi and AMD GPUs based on OpenCL

A survey of high level frameworks in block-structured adaptive mesh refinement packages

pre-printOver the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific domain areas, others have pursued a more general functionality, providing the building blocks for a larger variety of applications. In this survey paper we examine a representative set of SAMR packages and SAMR-based codes that have been in existence for half a decade or more, have a reasonably sized and active user base outside of their home institutions, and are publicly available. The set consists of a mix of SAMR packages and application codes that cover a broad range of scientific domains. We look at their high-level frameworks, their design trade-offs and their approach to dealing with the advent of radical changes in hardware architecture. The codes included in this survey are BoxLib, Cactus, Chombo, Enzo, FLASH, and Uintah

Laboratory Directed Research and Development FY2010 Annual Report

A premier applied-science laboratory, Lawrence Livermore National Laboratory (LLNL) has at its core a primary national security mission - to ensure the safety, security, and reliability of the nation's nuclear weapons stockpile without nuclear testing, and to prevent and counter the spread and use of weapons of mass destruction: nuclear, chemical, and biological. The Laboratory uses the scientific and engineering expertise and facilities developed for its primary mission to pursue advanced technologies to meet other important national security needs - homeland defense, military operations, and missile defense, for example - that evolve in response to emerging threats. For broader national needs, LLNL executes programs in energy security, climate change and long-term energy needs, environmental assessment and management, bioscience and technology to improve human health, and for breakthroughs in fundamental science and technology. With this multidisciplinary expertise, the Laboratory serves as a science and technology resource to the U.S. government and as a partner with industry and academia. This annual report discusses the following topics: (1) Advanced Sensors and Instrumentation; (2) Biological Sciences; (3) Chemistry; (4) Earth and Space Sciences; (5) Energy Supply and Use; (6) Engineering and Manufacturing Processes; (7) Materials Science and Technology; Mathematics and Computing Science; (8) Nuclear Science and Engineering; and (9) Physics

The Grand Challenge of Managing the Petascale Facility.

This report is the result of a study of networks and how they may need to evolve to support petascale leadership computing and science. As Dr. Ray Orbach, director of the Department of Energy's Office of Science, says in the spring 2006 issue of SciDAC Review, 'One remarkable example of growth in unexpected directions has been in high-end computation'. In the same article Dr. Michael Strayer states, 'Moore's law suggests that before the end of the next cycle of SciDAC, we shall see petaflop computers'. Given the Office of Science's strong leadership and support for petascale computing and facilities, we should expect to see petaflop computers in operation in support of science before the end of the decade, and DOE/SC Advanced Scientific Computing Research programs are focused on making this a reality. This study took its lead from this strong focus on petascale computing and the networks required to support such facilities, but it grew to include almost all aspects of the DOE/SC petascale computational and experimental science facilities, all of which will face daunting challenges in managing and analyzing the voluminous amounts of data expected. In addition, trends indicate the increased coupling of unique experimental facilities with computational facilities, along with the integration of multidisciplinary datasets and high-end computing with data-intensive computing; and we can expect these trends to continue at the petascale level and beyond. Coupled with recent technology trends, they clearly indicate the need for including capability petascale storage, networks, and experiments, as well as collaboration tools and programming environments, as integral components of the Office of Science's petascale capability metafacility. The objective of this report is to recommend a new cross-cutting program to support the management of petascale science and infrastructure. The appendices of the report document current and projected DOE computation facilities, science trends, and technology trends, whose combined impact can affect the manageability and stewardship of DOE's petascale facilities. This report is not meant to be all-inclusive. Rather, the facilities, science projects, and research topics presented are to be considered examples to clarify a point