3,941 research outputs found
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
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
Recent Advances in Computational Methods for the Power Flow Equations
The power flow equations are at the core of most of the computations for
designing and operating electric power systems. The power flow equations are a
system of multivariate nonlinear equations which relate the power injections
and voltages in a power system. A plethora of methods have been devised to
solve these equations, starting from Newton-based methods to homotopy
continuation and other optimization-based methods. While many of these methods
often efficiently find a high-voltage, stable solution due to its large basin
of attraction, most of the methods struggle to find low-voltage solutions which
play significant role in certain stability-related computations. While we do
not claim to have exhausted the existing literature on all related methods,
this tutorial paper introduces some of the recent advances in methods for
solving power flow equations to the wider power systems community as well as
bringing attention from the computational mathematics and optimization
communities to the power systems problems. After briefly reviewing some of the
traditional computational methods used to solve the power flow equations, we
focus on three emerging methods: the numerical polynomial homotopy continuation
method, Groebner basis techniques, and moment/sum-of-squares relaxations using
semidefinite programming. In passing, we also emphasize the importance of an
upper bound on the number of solutions of the power flow equations and review
the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016
American Control Conferenc
Precision analysis for hardware acceleration of numerical algorithms
The precision used in an algorithm affects the error and performance of individual computations, the
memory usage, and the potential parallelism for a fixed hardware budget. However, when migrating
an algorithm onto hardware, the potential improvements that can be obtained by tuning the precision
throughout an algorithm to meet a range or error specification are often overlooked; the major reason
is that it is hard to choose a number system which can guarantee any such specification can be met.
Instead, the problem is mitigated by opting to use IEEE standard double precision arithmetic so as to be
‘no worse’ than a software implementation. However, the flexibility in the number representation is one
of the key factors that can be exploited on reconfigurable hardware such as FPGAs, and hence ignoring
this potential significantly limits the performance achievable.
In order to optimise the performance of hardware reliably, we require a method that can tractably
calculate tight bounds for the error or range of any variable within an algorithm, but currently only a
handful of methods to calculate such bounds exist, and these either sacrifice tightness or tractability,
whilst simulation-based methods cannot guarantee the given error estimate. This thesis presents a new
method to calculate these bounds, taking into account both input ranges and finite precision effects,
which we show to be, in general, tighter in comparison to existing methods; this in turn can be used to
tune the hardware to the algorithm specifications.
We demonstrate the use of this software to optimise hardware for various algorithms to accelerate
the solution of a system of linear equations, which forms the basis of many problems in engineering
and science, and show that significant performance gains can be obtained by using this new approach in
conjunction with more traditional hardware optimisations
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
Custom Integrated Circuits
Contains reports on nine research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAALO03-86-K-0002)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI SemiconductorU.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryDARPA/U.S. Navy - Office of Naval Research (Contract N00014-80-C-0622)DARPA/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)National Science Foundation (Grant ECS-83-10941)AT&T Bell Laboratorie
Modeling and Simulation of Nonlinearly Loaded Electromagnetic Systems via Reduced Order Models - A Case Study: Energy Selective Surfaces
L'abstract è presente nell'allegato / the abstract is in the attachmen
Parallel solution of power system linear equations
At the heart of many power system computations lies the solution of a large sparse set of linear equations. These equations arise from the modelling of the network and are the cause of a computational bottleneck in power system analysis applications. Efficient sequential techniques have been developed to solve these equations but the solution is still too slow for applications such as real-time dynamic simulation and on-line security analysis. Parallel computing techniques have been explored in the attempt to find faster solutions but the methods developed to date have not efficiently exploited the full power of parallel processing. This thesis considers the solution of the linear network equations encountered in power system computations. Based on the insight provided by the elimination tree, it is proposed that a novel matrix structure is adopted to allow the exploitation of parallelism which exists within the cutset of a typical parallel solution. Using this matrix structure it is possible to reduce the size of the sequential part of the problem and to increase the speed and efficiency of typical LU-based parallel solution. A method for transforming the admittance matrix into the required form is presented along with network partitioning and load balancing techniques. Sequential solution techniques are considered and existing parallel methods are surveyed to determine their strengths and weaknesses. Combining the benefits of existing solutions with the new matrix structure allows an improved LU-based parallel solution to be derived. A simulation of the improved LU solution is used to show the improvements in performance over a standard LU-based solution that result from the adoption of the new techniques. The results of a multiprocessor implementation of the method are presented and the new method is shown to have a better performance than existing methods for distributed memory multiprocessors
Custom optimization algorithms for efficient hardware implementation
The focus is on real-time optimal decision making with application in advanced control
systems. These computationally intensive schemes, which involve the repeated solution of
(convex) optimization problems within a sampling interval, require more efficient computational
methods than currently available for extending their application to highly dynamical
systems and setups with resource-constrained embedded computing platforms.
A range of techniques are proposed to exploit synergies between digital hardware, numerical
analysis and algorithm design. These techniques build on top of parameterisable
hardware code generation tools that generate VHDL code describing custom computing
architectures for interior-point methods and a range of first-order constrained optimization
methods. Since memory limitations are often important in embedded implementations we
develop a custom storage scheme for KKT matrices arising in interior-point methods for
control, which reduces memory requirements significantly and prevents I/O bandwidth
limitations from affecting the performance in our implementations. To take advantage of
the trend towards parallel computing architectures and to exploit the special characteristics
of our custom architectures we propose several high-level parallel optimal control
schemes that can reduce computation time. A novel optimization formulation was devised
for reducing the computational effort in solving certain problems independent of the computing
platform used. In order to be able to solve optimization problems in fixed-point
arithmetic, which is significantly more resource-efficient than floating-point, tailored linear
algebra algorithms were developed for solving the linear systems that form the computational
bottleneck in many optimization methods. These methods come with guarantees
for reliable operation. We also provide finite-precision error analysis for fixed-point implementations
of first-order methods that can be used to minimize the use of resources while
meeting accuracy specifications. The suggested techniques are demonstrated on several
practical examples, including a hardware-in-the-loop setup for optimization-based control
of a large airliner.Open Acces
Risk-based security-constrained optimal power flow: Mathematical fundamentals, computational strategies, validation, and use within electricity markets
This dissertation contributes to develop the mathematical fundamentals and computational strategies of risk-based security-constrained optimal power flow (RB-SCOPF) and validate its application in electricity markets. The RB-SCOPF enforces three types of flow-related constraints: normal state deterministic flow limits, contingency state deterministic flow limits (the N-1 criteria), and contingency state system risk, which depends only on contingency states but not the normal state. Each constraint group is scaled by a single parameter setting allowing tradeoffs between deterministic constraints and system risk. Relative to the security-constrained optimal power flow (SCOPF) used in industry today, the RB-SCOPF finds operating conditions that are more secure and more economic. It does this by obtaining solutions that achieve better balance between post-contingency flows on individual circuits and overall system risk. The method exploits the fact that, in a SCOPF solution, some post-contingency circuit flows which exceed their limits impose little risk while other post-contingency circuit flows which are within their limits impose significant risk. The RB-SCOPF softens constraints for the former and hardens constraints for the latter, thus achieving simultaneous improvement in both security and economy. Although the RB-SCOPF is more time-intensive to solve than SCOPF, we have developed efficient algorithms that allow RB-SCOPF to solve in sufficient time for use in real-time electricity markets. In contrast to SCOPF, which motivates market behavior to offload circuit flows exceeding rated flows, the use of RB-SCOPF provides price signals that motivate market behavior to offload circuit flows and to enhance system-wide security levels. Voltage stability testing has demonstrated that the dispatch result based on RB-SCOPF has higher reactive margins at normal state and after a contingency happens, thus has better static voltage stability performance
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