We start the talk by discussing the size of problems that can currently be solved by sparse direct methods. We then consider the limitations of such methods, where current research is going in moving these limitations, and how far we might expect to go with direct solvers in the near future.

This leads us to the conclusion that very large systems, by which we mean three dimensional problems in more than a million degrees of freedom, require the assistance of iterative methods in their solution. However, even the strongest advocates and developers of iterative methods recognize their limitations when solving difficult problems, that is problems that are poorly conditioned and/or very unstructured. It is now universally accepted that sophisticated preconditioners must be used in such instances.

A very standard and sometimes successful class of preconditioners are based on incomplete factorizations or sparse approximate inverses, but we very much want to exploit the powerful software that we have developed for sparse direct methods over a period of more than thirty years. We thus discuss various ways in which a symbiotic relationship can be developed between direct and iterative methods in order to solve problems that would be intractable for one class of methods alone. In these approaches, we will use a direct factorization on a ``nearby'' problem or on a subproblem.

We examine the use of a symmetric indefinite solver in constrained optimization problems that is used in the first way, and the use of a direct solver within domain decomposition techniques in the second.

We also discuss some ways in which this approach can provide a good basis for the exploitation of parallelism.

The technology directions of manufacturers, life sciences companies, automotive companies, energy and media and broadcast enterprises must innovate and take time out of their market delivery. This talk is about the technological application to business design and innovation that enables this time to market acceleration. Mr. Greenwald will also discuss key technology areas that have not yet found their way into the commercial mainstream applications and what the future in 2006-2008 holds for this HPC marketplace.

Clusters are now widely used in technical and commercial computing, but there are a number of open issues ranging across hardware, software design and system deployments. This talk will address using COTS solutions to take advantage of the economics of standard building blocks and the unique solutions in the industry around these building blocks. It will address key challenges we face in the years ahead including managing clusters, uptime for deployments, and managing power issues. Intel's vision of the roles that Intel and other industry vendors will play in providing solutions to address these challenges will be discussed. Specifics will be presented in terms of Intel hardware and software roadmaps. Conflicts within the clustering community will be discussed, including COTS vs. custom hardware, open vs. proprietary software, as well as various components of what customers see as productivity objectives.

Computational field problems; such as computational fluid dynamics (CFD), electromagnetic field simulation, and weather modeling -- essentially any problems whose physics can be modeled effectively by ordinary and/or partial differential equations--constitute the majority of computational science and engineering simulations. The output of such simulations might be a single field variable (such as pressure or velocity) or a combination of fields involving a number of scalar fields, vector fields, and/or tensor fields. As such, scientific visualization researchers have concentrated on effective ways to visualize large-scale computational fields. Much current and previous visualization research has focused on methods and techniques for visualizing a computational field variables (such as the extraction of a single scalar field variable as an isosurface). While single variable visualization often satisfies the needs of the user, it is clear that it would also be useful to be able to effectively visualize multiple fields simultaneously.

In this talk I will describe some of our recent work in scalar, vector, and tensor visualization techniques as applied to the domain of computational field problems. I will present recent research results for the integration of techniques for creating computational multi-field visualizations.

This talk addresses High Performance Computing (HPC) outside the popular context associated with the raw processor performance (i.e. teraflops-petaflops), networking technologies (i.e. the GRID) performance, computational architectures and all collaborative efforts on tools, systems and applications that the greater community has been spending most of its development and utilization time on. It approaches the subject from the perspective of the question: “How successful HPC has been in enabling High Performing People and Projects?” HPC pathology is therefore expressed in terms of the various cases that provide negative answers to this question. Our interest on HPC pathology is rooted on our goal to quantify HPC productivity since we can’t improve what we can’t measure, and on overcoming the principle of technological aggravation that states “cheap, fast, good: choose any two”.

We begin by pointing to naval engineering application areas where all recent and astonishing progress on HPC hardware has had almost no impact. Such areas are the design, tailoring, prototyping, manufacturing, certification, qualification and mission/lifetime functional adaptivity of traditional multi-mission naval platforms and more contemporary coupled multi-field multi-domain ones where tradition-bound approaches are still in use. It also addresses why vertically produced HPC products are not used by people who create horizontally produced HPC products, and vice versa. The paradox of computational productivity is addressed as well.

In an effort to identify the pathological roots of these incongruences, a multidimensional context vector space is introduced for those HPC performance attributes that can serve as bases for this space. A point in this space represents the performance of every technological artifact. Most common understanding of performance focuses on wall-clock performance, ease and speed of behavior modeling and application development, and efficient use and availability of computational resources. The proposed performance space extends and enriches this understanding by introducing contextual and usability typing on all of these focal points according to the various characters and stakeholders who are involved in the development, management and utilization of HPC and Information Technology (IT) products in general. The attribute bases of systemic modeling, computational implementation, business execution, technology transfer, and application industry specialization performances form a coarse view of this space. Each one of these bases represents folded subspaces of additional attribute bases. For example, systemic analytical modeling performance subspace is spanned by the direction of modeling approach performance (i.e. forward, inverse and mixed), by the methodology of modeling performance (i.e. physics-based, physics-agnostic and mixed), representation media performance (i.e. syntactic and semantic dimensionality metrics based on order of division algebra employed), scaled behavior-modeling performance (i.e. scale model composition, trans-scalar formalisms etc.), modeling confidence/reliability/validation performance (i.e. hypothetico-deductive use of data, inductive and industrialized-inductive use of data in modeling). Similarly, computational implementation subspace is spanned by the hardware efficiency (i.e. xFLOPS, Architecture, portability, power consumption), application development efficiency (i.e. agile modeling, Extreme Programming etc.), application usage easiness (i.e. requirements specification through UML-use-cases, OMT, Mana-Pnueli, Promela, SDL, Message Sequence Charts etc.), application correctness (i.e. formal validation and verification), application compositionality and integrability (i.e. easiness of application co-operation, integration with existing and new resources etc), application language implementation (i.e. object-oriented, procedural, declarative), algorithmic efficiency (i.e. complexity metrics), autonomic efficiency (i.e. self maintainability, self reparability etc), hardware matching, networking transparency, networking performance (i.e. Mbps), networking heterogeneity, integration ubiquity (i.e. ad-hoc networking), network security, etc.

Space and time limitations for the presentation do not allow further or detailed expansion on the rest of the subspaces/bases. Thus, focus is given on some carefully selected section of the pathology space where the domain of Problem Solving Environments (PSE) is realizable. Some historical perspective in this area from NRL’s first hardware-PSE and subsequent multidimensional robotic loaders through today’s distributed PSEs, establishes the idea that today it is possible to use the industrialized-inductive methods based on data-driven approaches for automated computing of analytical models and their computational implementations in order to embed validity and reliability within systemic behavior simulations.

The paradigm introduced by how of the evolution of the printing industry has affected science and technology brakes down when viewed from the perspective of lack of similar behavior expected from the proliferation of the Internet and the associated technologies. It is subsequently used to show that most (if not all) pathological issues with IT/HPC are consequences of certain limitations of the human cognitive process, and corresponding approaches employed in problem solving. These are classified in the problems of the “self” and the problems of the “group” in terms of the usage of research media (i.e. natural and formal language, etc.). They all relate to how our individual rational processes are themselves a part of the system used to solve a problem and how we keep this fact is ignored during its usage. This is why we generally do not realize that IT and HPC have been very successful in automating information/data/products production but not consumption. Tradition-bound behavior of stakeholders worsens this situation. Thus, the term “high performance” may be claimed for very few of the basis cases (such as hardware/networking evolution) of this context/performance space but there are quite a few areas where the opportunity of acting is much higher than the progress exhibited. The talk concludes with suggestions on utilizing HPC to improve HPC itself and human performance aspects (i.e. time integration of knowledge, response consistency, additivity and compositionality of expertise in group environments) and is based on multi-level meta-automation and meta-context implementation ideas leading to industrialization of the research and development processes.

Acknowledgement. The author acknowledges the support by the National Science Foundation under grant ITR-0205663.

Distributed computing as well as remote resource sharing have existed for several decades. Yet, grids, commonly perceived as distributed resource sharing frameworks, are receiving levels of attention normally reserved for radically new technologies. In this talk, we attempt to analyze the precise characteristics and attributes of grids that set them apart from other distributed computing frameworks. We suggest that the myriad rotocols, software tools, and other mechanisms required to deploy and operate grids can all be traced back to two simple concepts: resource and user virtualization, with the latter contributing much of the burden. With regard to this issue, we propose alternative schemes that localize sharing policies at each resource, thereby reducing the amount of state involved in (virtual) user management. With regard to resource virtualization, orthogonal issues, namely the suitability of service oriented paradigms for high performance computing, are explored. In particular, existing and proposed models for programming grids are discussed, and their strengths and drawbacks highlighted. In particular, the relationship between service-oriented grid programming and conventional parallel processing is analyzed. The talk will conclude by summarizing the essential features and characteristics of grids, the tension between infrastructural complexity and usability, and factors in distributed-parallel programming, and outline alternative approaches to addressing these issues.