MPI-based Parallel Solution of Sparse Linear Systems Using Chio's Condensation Algorithm and Test Data from Power Flow Analysis

MPI-based Parallel Solution of Sparse Linear Systems Using Chio's Condensation Algorithm and Test Data from Power Flow Analysis
Author: Robert Bernard Armistead
Publisher:
Total Pages: 96
Release: 2010
Genre:
ISBN:

Solving sparse systems of linear equations permeates power system analysis. Newton-Raphson, decoupled, and fast decoupled algorithms all require the repeated solving of sparse systems of linear equations in order to capture the steady state operational conditions of the power system under test. Solving these systems of equations is usually done using LU Factorization which has an order of complexity O(n3) where n represents the number of equations in the system. The Chio's condensation algorithm is an alternative approach, which in general has a complexity of O(n4). However, it has a straightforward formulation that can be easily implemented in a parallel computing architecture. Previous research has not investigated the application of the Chio's algorithm under sparse matrix, which is typical for power system analysis. This thesis presents a MPI-based parallel solution of sparse linear systems using Chio's condensation algorithm and realistic test data from power flow analysis. Different sparse matrix techniques are discussed, and a reordering scheme is applied to further improve the efficiency for solving the sparse linear system.

Parallel, Iterative Solution of Sparse Linear Systems: Models and Architectures

Parallel, Iterative Solution of Sparse Linear Systems: Models and Architectures
Author: D. A. Reed
Publisher:
Total Pages: 52
Release: 1984
Genre: Iterative methods (Mathematics)
ISBN:

"The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed" -- abstract.

Sparse Linear Solver for Power System Analysis Using FPGA.

Sparse Linear Solver for Power System Analysis Using FPGA.
Author:
Publisher:
Total Pages: 22
Release: 2005
Genre:
ISBN:

Load flow computation and contingency analysis is the foundation of power system analysis. Numerical solution to load flow equations are typically computed using Newton-Raphson iteration, and the most time consuming component of the computation is the solution of a sparse linear system needed for the update each iteration. When an appropriate elimination ordering is used, direct solvers are more effective than iterative solvers. In practice these systems involve a larger number of variables (50,000 or more); however, when the sparsity is utilized effectively these systems can be solved in a modest amount of time (seconds). Despite the modest computation time for the linear solver, the number of systems that must be solved is large and current computation platforms and approaches do not yield the desired performance. Because of the relatively small granularity of the linear solver, the use of a coarse-grained parallel solver does not provide an effective means to improve performance. In this talk, it is argued that a hardware solution, implemented in FPGA, using fine-grained parallelism, provides a cost-effective means to achieve the desired performance. Previous work 1, 2, 3 has shown that FPGA can be effectively used for floating-point intensive scientific computation. It was shown that high MFLOP rates could be achieved by utilizing multiple floating-point units, and FPGA could outperform PCs and workstations, running at much higherlock rates, on dense matrix computations. The current work argues that similar benefit can be obtained for the sparse matrix computations arising in power system analysis. These conclusions are based on operation counts and system analysis for a collection of benchmark systems arising in practice. Benchmark data indicates that between 1 and 3 percent of peak floating point performance was obtained using a state-of-the-art sparse solver (UMFPACK) running on 2.60 GHz Pentium 4.

TinyML

TinyML
Author: Pete Warden
Publisher: O'Reilly Media
Total Pages: 504
Release: 2019-12-16
Genre: Computers
ISBN: 1492052019

Deep learning networks are getting smaller. Much smaller. The Google Assistant team can detect words with a model just 14 kilobytes in size—small enough to run on a microcontroller. With this practical book you’ll enter the field of TinyML, where deep learning and embedded systems combine to make astounding things possible with tiny devices. Pete Warden and Daniel Situnayake explain how you can train models small enough to fit into any environment. Ideal for software and hardware developers who want to build embedded systems using machine learning, this guide walks you through creating a series of TinyML projects, step-by-step. No machine learning or microcontroller experience is necessary. Build a speech recognizer, a camera that detects people, and a magic wand that responds to gestures Work with Arduino and ultra-low-power microcontrollers Learn the essentials of ML and how to train your own models Train models to understand audio, image, and accelerometer data Explore TensorFlow Lite for Microcontrollers, Google’s toolkit for TinyML Debug applications and provide safeguards for privacy and security Optimize latency, energy usage, and model and binary size

Domain Decomposition Methods in Science and Engineering

Domain Decomposition Methods in Science and Engineering
Author: Ralf Kornhuber
Publisher: Springer Science & Business Media
Total Pages: 686
Release: 2006-03-30
Genre: Mathematics
ISBN: 3540268251

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Aquaculture Genome Technologies

Aquaculture Genome Technologies
Author: Zhanjiang (John) Liu
Publisher: John Wiley & Sons
Total Pages: 579
Release: 2008-02-28
Genre: Technology & Engineering
ISBN: 0470276339

Genomics is a rapidly growing scientific field with applications ranging from improved disease resistance to increased rate of growth. Aquaculture Genome Technologies comprehensively covers the field of genomics and its applications to the aquaculture industry. This volume looks to bridge the gap between a basic understanding of genomic technology to its practical use in the aquaculture industry.

Diesel and Gasoline Engines

Diesel and Gasoline Engines
Author: Richard Viskup
Publisher:
Total Pages: 202
Release: 2020-02
Genre: Technology & Engineering
ISBN: 178985248X

The internal combustion engine was invented around 1790 by various scientists and engineers worldwide. Since then the engines have gone through many modifications and improvements. Today, different applications of engines form a significant technological importance in our everyday lives, leading to the evolution of our modern civilization. The invention of diesel and gasoline engines has definitely changed our lifestyles as well as shaped our priorities. The current engines serve innumerable applications in various types of transportation, in harsh environments, in construction, in diverse industries, and also as back-up power supply systems for hospitals, security departments, and other institutions. However, heavy duty or light duty engines have certain major disadvantages, which are well known to everyone. With the increasing usage of diesel and gasoline engines, and the constantly rising number of vehicles worldwide, the main concern nowadays is engine exhaust emissions. This book looks at basic phenomena related to diesel and gasoline engines, combustion, alternative fuels, exhaust emissions, and mitigations.

Efficient High-Order Discretizations for Computational Fluid Dynamics

Efficient High-Order Discretizations for Computational Fluid Dynamics
Author: Martin Kronbichler
Publisher: Springer Nature
Total Pages: 314
Release: 2021-01-04
Genre: Technology & Engineering
ISBN: 3030606104

The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

Advanced Numerical Methods for Differential Equations

Advanced Numerical Methods for Differential Equations
Author: Harendra Singh
Publisher: CRC Press
Total Pages: 337
Release: 2021-07-29
Genre: Technology & Engineering
ISBN: 1000381080

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Modeling of Coupled Phenomena in Science and Engineering

Numerical Modeling of Coupled Phenomena in Science and Engineering
Author: Mario César Suárez Arriaga
Publisher: CRC Press
Total Pages: 496
Release: 2008-12-01
Genre: Technology & Engineering
ISBN: 0203886224

Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont