165 research outputs found
Parallel dichotomy algorithm for solving tridiagonal SLAEs
A parallel algorithm for solving a series of matrix equations with a constant
tridiagonal matrix and different right-hand sides is proposed and studied. The
process of solving the problem is represented in two steps. The first
preliminary step is fixing some rows of the inverse matrix of SLAEs. The second
step consists in calculating solutions for all right-hand sides. For reducing
the communication interactions, based on the formulated and proved main
parallel sweep theorem, we propose an original algorithm for calculating share
components of the solution vector. Theoretical estimates validating the
efficiency of the approach for both the common- and distributed-memory
supercomputers are obtained. Direct and iterative methods of solving a 2D
Poisson equation, which include procedures of tridiagonal matrix inversion, are
realized using the mpi technology. Results of computational experiments on a
multicomputer demonstrate a high efficiency and scalability of the parallel
sweep algorithm.Comment: 18 page
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized
Iterative and doubling algorithms for Riccati-type matrix equations: a comparative introduction
We review a family of algorithms for Lyapunov- and Riccati-type equations
which are all related to each other by the idea of \emph{doubling}: they
construct the iterate of another naturally-arising fixed-point
iteration via a sort of repeated squaring.
The equations we consider are Stein equations , Lyapunov
equations , discrete-time algebraic Riccati equations
, continuous-time algebraic Riccati equations
, palindromic quadratic matrix equations , and
nonlinear matrix equations . We draw comparisons among these
algorithms, highlight the connections between them and to other algorithms such
as subspace iteration, and discuss open issues in their theory.Comment: Review article for GAMM Mitteilunge
Parallel Algorithm with Parameters Based on Alternating Direction for Solving Banded Linear Systems
An efficient parallel iterative method with parameters on distributed-memory multicomputer is investigated for solving the banded linear equations in this work. The parallel algorithm at each iterative step is executed using alternating direction by splitting the coefficient matrix and using parameters properly. Only it twice requires the communications of the algorithm between the adjacent processors, so this method has high parallel efficiency. Some convergence theorems for different coefficient matrices are given, such as a Hermite positive definite matrix or an M-matrix. Numerical experiments implemented on HP rx2600 cluster verify that our algorithm has the advantages over the multisplitting one of high efficiency and low memory space, which has a considerable advantage in CPU-times costs over the BSOR one. The efficiency for Example 1 is better than BSOR one significantly. As to Example 2, the acceleration rates and efficiency of our algorithm are better than the PEk inner iterative one
Concurrent DASSL Applied to Dynamic Distillation Column Simulation
The accurate, high-speed solution of systems of ordinary differential-algebraic equations (DAE’s) of low index is of great importance in chemical, electrical and other engineering disciplines. Petzold’s Fortran-based DASSL is the most widely used sequential code for solving DAE’s. We have devised and implemented a completely new C code, Concurrent DASSL, specifically for multicomputers and patterned on DASSL. In this work, we address the issues of data distribution and the performance of the overall algorithm, rather than just that of individual steps. Concurrent DASSL is designed as an open, application-independent environment below which linear algebra algorithms may be added in addition to standard support for dense and sparse algorithms. The user may furthermore attach explicit data interconversions between the main computational steps, or choose compromise distributions. A “problem formulator” (simulation layer) must be constructed above Concurrent DASSL, for any specific problem domain. We indicate performance for a particular chemical engineering application, a sequence of coupled distillation columns. Future efforts are cited in conclusion
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
Parallel Algorithms for Time and Frequency Domain Circuit Simulation
As a most critical form of pre-silicon verification, transistor-level circuit simulation
is an indispensable step before committing to an expensive manufacturing process.
However, considering the nature of circuit simulation, it can be computationally
expensive, especially for ever-larger transistor circuits with more complex device models.
Therefore, it is becoming increasingly desirable to accelerate circuit simulation.
On the other hand, the emergence of multi-core machines offers a promising solution
to circuit simulation besides the known application of distributed-memory clustered
computing platforms, which provides abundant hardware computing resources. This
research addresses the limitations of traditional serial circuit simulations and proposes
new techniques for both time-domain and frequency-domain parallel circuit
simulations.
For time-domain simulation, this dissertation presents a parallel transient simulation
methodology. This new approach, called WavePipe, exploits coarse-grained
application-level parallelism by simultaneously computing circuit solutions at multiple
adjacent time points in a way resembling hardware pipelining. There are two
embodiments in WavePipe: backward and forward pipelining schemes. While the
former creates independent computing tasks that contribute to a larger future time
step, the latter performs predictive computing along the forward direction. Unlike
existing relaxation methods, WavePipe facilitates parallel circuit simulation without jeopardizing convergence and accuracy. As a coarse-grained parallel approach, it requires
low parallel programming effort, furthermore it creates new avenues to have a
full utilization of increasingly parallel hardware by going beyond conventional finer
grained parallel device model evaluation and matrix solutions.
This dissertation also exploits the recently developed explicit telescopic projective
integration method for efficient parallel transient circuit simulation by addressing the
stability limitation of explicit numerical integration. The new method allows the
effective time step controlled by accuracy requirement instead of stability limitation.
Therefore, it not only leads to noticeable efficiency improvement, but also lends itself
to straightforward parallelization due to its explicit nature.
For frequency-domain simulation, this dissertation presents a parallel harmonic
balance approach, applicable to the steady-state and envelope-following analyses of
both driven and autonomous circuits. The new approach is centered on a naturally-parallelizable
preconditioning technique that speeds up the core computation in harmonic
balance based analysis. The proposed method facilitates parallel computing
via the use of domain knowledge and simplifies parallel programming compared with
fine-grained strategies. As a result, favorable runtime speedups are achieved
The Sixth Copper Mountain Conference on Multigrid Methods, part 2
The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth
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