Mark Seager

Parallelizing conjugate gradient for the CRAY X-MP

Abstract A standard preconditioned conjugate gradient algorithm for the solution of symmetric linear systems is studied in the context of multiprocessing. A totally parallel approach is taken based on a computational model of an MIMD machine with shared global memory. In order to assure mathematical correctness of the algorithm, four barrier syncs are required during each iteration. Large linear systems are solved with this parallel adaptation of conjugated gradient and efficiencies near one observed on the CRAY X-MP24 running COS 1.13. Further, segments of the code which could be considered independent (i.e. between syncs) clocked in at speedups very close to the number of tasks. The latter indicates that the loss efficiency in this implementation of the algorithm on the X-MP24 is connected with the cost of barrier syncs. On the CRAY X-MP48 running COS 1.15 similar results are observed utilizing two CPUs. When all four CPUs execute parallel tasks in vector mode memory bank conflicts cause a 30% loss of overall speedup.

Adaptive domain extension and adaptive grids for unbounded spherical elliptic PDEs

The problem of approximating the solution to a class of (PDEs) posed on unbounded domains using finite domain approximations is considered. A finite-element method is formulated for the approximation on the finite subregions, and a domain extension strategy that “balances” the finite-element error and domain-truncation error is developed. It is shown that this scheme yields asymptotically optimal finite-element approximation properties to the solution on the unbounded domain as the grid is extended. Error estimates for adaptive refinement and domain truncation are developed.

A Collaboration and Commercialization Model for Exascale Software Research

We propose a coordinated strategy for exascale software development that includes the incorporation of successful research and development (R&D) into development and engineering (D&E) projects and harvesting the successful D&E projects into products with vendor support (P&S). This allows the most flexible R&D agenda while at the same time providing a commercialization path. This process is described as a natural extension of current focus areas and funding agents for R&D, D&E and P&S, but adds stake holders from the next stage in the process in the upstream processes. This model allows the flexibility to encourage development and competition of ideas in the research, development and productization phases. We anticipate that multiple iterations through this process from R&D through P&S are required to achieve appropriate software for Exascale systems.

The sub-implicit method: New multiprocessor algorithms for old implicit codes☆

Abstract This paper presents a new approach to the parallel solution of an implicit system of difference equations. The sub-implicit method operates on sub-regions of the data which are evaluated at spatial points and synchronous times. Each sub-region has a border node which is shared with an adjacent sub-region (in one dimension). Values for this shared node are computed independently by the two solution processes for two adjacent sub-regions. Nodes outside the sub-region are treated as having fixed values during the solution. At the finish of the two sub-region solutions, the two sub-regions are blocked against further changes (a pairwise synchronization) and the two different values for the shared node are reconciled. This can be done in such a way that energy conservation is exact. Results for test problems for heat diffusion in one dimension are given and compared against standard methods and analytic results. Implementation of the method into a demonstration two-dimensional hydrodynamics code SIMPLE is described. The best speedups observed for parallel execution of this version of SIMPLE on a twelve CPU Sequent multiprocessor were 9.6 for 50 by 50 grid and 10.4 for a 95 by 95 grid. Some generalization of this approach are discussed.

A Scalable System Architecture to Addressing the Next Generation of Predictive Simulation Workflows with Coupled Compute and Data Intensive Applications

Trends in the emerging digital economy are pushing the virtual representation of products and services. Creating these digital twins requires a combination of real time data ingestion, simulation of physical products under real world conditions, service delivery optimization and data analytics as well as ML/DL anomaly detection and decision making. Quantification of Uncertainty in the simulations will also be a compute and data intensive workflow that will drive the simulation improvement cycle. Future high-end computing systems designs need to comprehend these types of complex workflows and provide a flexible framework for optimizing the design and operations under dynamic load conditions for them.

Banquet and Invited Speech Why Peta-Scale is Different: An Ecosystem Approach to Predictive Scientific and Engineering Simulation

With the recent advent of 100s of teraFLOP/s-scale simulations capability at Lawrence Livermore National Laboratory and other sites, it has become clear that the scientific method has changed. This transition has taken us from theory and experiment to theory and experiment being tightly integrated by simulation. With the advent of peta-scale simulations on the horizon it is appropriate to take stock of the recent advances and to look forward to the coming wave of future systems. In this talk we focus on some areas of science that open up with peta-scale systems and how this is VERY different from the science one can accomplish with a single workstation (giga-scale simulation). In actual fact, the science enabled by tera-scale and peta-scale systems require a whole new approach to the scientific method. One of the things we are starting to realize being at the leading edge of applying this new technology, is that with the coming onset of peta-scale simulations (systems, visualization, and applications) is that we may be headed for huge scientific breakthroughs enabled

The challenges and rewards of petascale clusters

Building, integrating and using petascale systems have many challenges including system power and cooling, system stability, scalablity, simulation environment and the development of petascale applications. In this talk, we discuss these challenges and provide some approaches to addressing these challenges. In addition, we discuss some recent scientific results from petascale systems that make the whole effort worthwhile.

Exploring largeness, complexity and scalability from the OOT perspective (panel)

This panel will lay the foundation for understanding the needs of Large Systems so that OO practitioners can:• appreciate the problems faced;• understand the issues involved; and• re-orient the approaches to provide a viable solution when participating in similar efforts.Specifically, this panel will establish the foundation for discussions on Large Systems by establishing concepts, exposing terminology, and highlighting the state-of-the art.Large applications are usually complex and display one or more of the following dimensions of largeness:• Processing power: requiring tens to hundreds of gigabytes of memory and hundreds of gigaflops performance• High connectivity: highly-connected, systems can show aggregate behavior with complex characteristics: they can become chaotic.• Online access: Archival of terabytes of information, with the need to provide online access to information• Archival and online retrieval: The two technologies (database and archival storage), however, currently do not interoperate. There is a need to develop interfaces to integrate these two technologies.• Data-intensive scientific applications: These involve constructing a data handling infrastructure that simplifies the effort required to maintain petabyte archives, identify relevant data sets within the archive, move, the data to processing platforms, and distribute the data sets across multiple nodes.• Internet access: Large applications often require simultaneous access of information by millions of users worldwide;they must provide acceptable response times.• Scaleable architecture: The systems must be prepared to support exponential growth of application load.Is OOT up to the task? OO practitioners will be encountering some of these application domains in the near future. Some may have already gained some experience in trying to solve these problems. However, the literature in OO does not provide sufficient evidence to believe that OO is ready for such large systems today. Part of the problem is the cross-disciplinary nature of these problems requires a steep learning curve for OO practitioners to be effective. The modeling of these problems with an OO approach is also a challenge. Current 00 methods do not do a good job of supporting multiple views of a domain, and multiple layers of a complex application domain.