Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices

We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifrontal factorization that is valid irrespective of the amount of dynamic pivoting performed during factorization. Finally, we describe an unsymmetric-pattern multifrontal algorithm for Gaussian elimination with partial pivoting that uses the task- and data-dependency graphs computed during the symbolic phase. These algorithms have been implemented in WSMP—an industrial strength sparse solver package—and have enabled WSMP to significantly outperform other similar solvers. We present experimental results to demonstrate the merits of the new algorithms

On-line cascading event tracking and avoidance decision support tool

Cascading outages in power systems are costly events that power system operators and planners actively seek to avoid. Such events can quickly result in power outages for millions of customers. Although it is unreasonable to claim that blackouts can be completely prevented, we can nonetheless reduce the frequency and impact of such high consequence events. Power operators can take actions if they have the right information provided by tools for monitoring and managing the risk of cascading outages. Such tools are being developed in this research project by identifying contingencies that could initiate cascading outages and by determining operator actions to avoid the start of a cascade.;A key to cascading outage defense is the level of grid operator situational awareness. Severe disturbances and complex unfolding of post-disturbance phenomena, including interdependent events, demand critical actions to be taken on the part of the operators, thus making operators dependent on decision support tools and automatic controls. In other industries (e.g., airline, nuclear, process control), control operators employ computational capabilities that help them predict system response and identify corrective actions. Power system operators should have a similar capability with online simulation tools.;To create an online simulator to help operators identify the potential for and actions to avoid cascades, we developed a systematic way to identify power system initiating contingencies for operational use. The work extends the conventional contingency list by including a subset of high-order contingencies identified through topology processing. The contingencies are assessed via an online, mid-term simulator, designed to provide generalized, event-based, corrective control and decision support for operators with very high computational efficiency. Speed enhancement is obtained algorithmically by employing a multi-frontal linear solver within an implicit integration scheme. The contingency selection and simulation capabilities were illustrated on two systems: a test system with six generators and the IEEE RTS-96 with 33 generators. Comparisons with commercial grade simulators indicate the developed simulator is accurate and fast

Resilience for Asynchronous Iterative Methods for Sparse Linear Systems

Large scale simulations are used in a variety of application areas in science and engineering to help forward the progress of innovation. Many spend the vast majority of their computational time attempting to solve large systems of linear equations; typically arising from discretizations of partial differential equations that are used to mathematically model various phenomena. The algorithms used to solve these problems are typically iterative in nature, and making efficient use of computational time on High Performance Computing (HPC) clusters involves constantly improving these iterative algorithms. Future HPC platforms are expected to encounter three main problem areas: scalability of code, reliability of hardware, and energy efficiency of the platform. The HPC resources that are expected to run the large programs are planned to consist of billions of processing units that come from more traditional multicore processors as well as a variety of different hardware accelerators. This growth in parallelism leads to the presence of all three problems. Previously, work on algorithm development has focused primarily on creating fault tolerance mechanisms for traditional iterative solvers. Recent work has begun to revisit using asynchronous methods for solving large scale applications, and this dissertation presents research into fault tolerance for fine-grained methods that are asynchronous in nature. Classical convergence results for asynchronous methods are revisited and modified to account for the possible occurrence of a fault, and a variety of techniques for recovery from the effects of a fault are proposed. Examples of how these techniques can be used are shown for various algorithms, including an analysis of a fine-grained algorithm for computing incomplete factorizations. Lastly, numerous modeling and simulation tools for the further construction of iterative algorithms for HPC applications are developed, including numerical models for simulating faults and a simulation framework that can be used to extrapolate the performance of algorithms towards future HPC systems