Sparse approximate inverse preconditioners on high performance GPU platforms

Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs)

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

High-performance direct solution of finite element problems on multi-core processors

A direct solution procedure is proposed and developed which exploits the parallelism that exists in current symmetric multiprocessing (SMP) multi-core processors. Several algorithms are proposed and developed to improve the performance of the direct solution of FE problems. A high-performance sparse direct solver is developed which allows experimentation with the newly developed and existing algorithms. The performance of the algorithms is investigated using a large set of FE problems. Furthermore, operation count estimations are developed to further assess various algorithms. An out-of-core version of the solver is developed to reduce the memory requirements for the solution. I/O is performed asynchronously without blocking the thread that makes the I/O request. Asynchronous I/O allows overlapping factorization and triangular solution computations with I/O. The performance of the developed solver is demonstrated on a large number of test problems. A problem with nearly 10 million degree of freedoms is solved on a low price desktop computer using the out-of-core version of the direct solver. Furthermore, the developed solver usually outperforms a commonly used shared memory solver.Ph.D.Committee Chair: Will, Kenneth; Committee Member: Emkin, Leroy; Committee Member: Kurc, Ozgur; Committee Member: Vuduc, Richard; Committee Member: White, Donal

Interstitial-Scale Modeling of Packed-Bed Reactors

Packed-beds are common to adsorption scrubbers, packed bed reactors, and trickle-bed reactors widely used across the petroleum, petrochemical, and chemical industries. The micro structure of these packed beds is generally very complex and has tremendous influence on heat, mass, and momentum transport phenomena on the micro and macro length scales within the bed. On a reactor scale, bed geometry strongly influences overall pressure drop, residence time distribution, and conversion of species through domain-fluid interactions. On the interstitial scale, particle boundary layer formation, fluid to particle mass transfer, and local mixing are controlled by turbulence and dissipation existing around packed particles. In the present research, a CFD model is developed using OpenFOAM: www.openfoam.org) to directly resolve momentum and scalar transport in both laminar and turbulent flow-fields, where the interstitial velocity field is resolved using the Navier-Stokes equations: i.e. no pseudo-continuum based assumptions. A discussion detailing the process of generating the complex domain using a Monte-Carlo packing algorithm is provided, along with relevant details required to generate an arbitrary polyhedral mesh describing the packed-bed. Lastly, an algorithm coupling OpenFOAM with a linear system solver using the graphics processing unit: GPU) computing paradigm was developed and will be discussed in detail

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

Austrian High-Performance-Computing meeting (AHPC2020)

This booklet is a collection of abstracts presented at the AHPC conference

A NUMA Aware Scheduler for a Parallel Sparse Direct Solver

Over the past few years, parallel sparse direct solvers made significant progress and are now able to solve efficiently industrial three-dimensional problems with several millions of unknowns. To solve efficiently these problems, PaStiX and WSMP solvers for example, provide an hybrid MPI-thread implementation well suited for SMP nodes or multi-core architectures. It enables to drastically reduce the memory overhead of the factorization and improve the scalability of the algorithms. However, today's modern architectures introduce new hierarchical memory accesses that are not handle in these solvers. We present in this paper three improvements on PaStiX solver to improve the performance on modern architectures : memory allocation, communication overlap and dynamic scheduling and some results on numerical test cases will be presented to prove the efficiency of the approach on NUMA architectures