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Wednesday, October 14, 2020 | History

2 edition of Parallel and sequential algorithms for second-order parabolic equations with applications. found in the catalog.

Parallel and sequential algorithms for second-order parabolic equations with applications.

Abba Babandi Gumel

# Parallel and sequential algorithms for second-order parabolic equations with applications.

## by Abba Babandi Gumel

Written in English

Edition Notes

The Physical Object ID Numbers Contributions Brunel University. Department of Mathematics and Statistics. Pagination 163p. : Number of Pages 163 Open Library OL20681438M

Sometimes, you use a sequence of seeds when using parallelism. So, every run will give the same results, but not the same as the sequential version. So, basically, you would get the same results only if using the same seed AND the same numbers of cores. Is this the case here? – F. Privé Oct 7 '18 at The book is intended to quickly bring researchers and graduate students working on numerical solutions of partial differential equations with various applications into the area of parallel processing. The book starts from the basic concepts of parallel processing, like speedup, efficiency and different parallel architectures, then introduces.

Parallel Algorithm for Gauss Elimination Method In the Parallel execution using the Multi thread mechanism. If the size of the linear equation is n, n processors are used. Each thread represent one processor. In the Parallel execution processing time is less compared to sequential execution. for k = 1 to n-1 for i = k+1 to n do in parallel u. Multigrid algorithms have been mainly developed to solve linear system of equations which arise from the discretization of elliptic and parabolic PDEs. Smoothers like Jacobi, Gauss-Seidel, and CG, which work in the case of these PDEs do not work for inverse problems because of the different eigen-structure of the reduced Hessian operator.

Parallel and sequential algorithms for second-order parabolic equations with applications. Author: Gumel, Abba Babandi. ISNI: Awarding Body: Brunel University Current Institution: Brunel University Date of Award: Parallel Algorithms and Parallel Architectures 13 Relating Parallel Algorithm and Parallel Architecture 14 Implementation of Algorithms: A Two-Sided Problem 14 Measuring Beneﬁ ts of Parallel Computing 15 Amdahl’s Law for Multiprocessor Systems 19 Gustafson–Barsis’s Law 21 Applications of Parallel Computing

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### Parallel and sequential algorithms for second-order parabolic equations with applications by Abba Babandi Gumel Download PDF EPUB FB2

We may combine these two schemes with parallel or sequential solving of, -three-diagonal system parallel variant of Thomas algorithm (factorization method) we are utilizing Konovalov-Yanenko algorithm 3, which has in comparison of others famous algorithms better characteristic in sense of speed-up, and combinations of domain decomposition ways Author: Alexander I.

Sukhinov. This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems.

It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by Cited by: () Unconditional stability of parallel difference schemes with second order accuracy for parabolic equation.

Applied Mathematics and Computation() Unconditional Stability of Corrected Explicit‐Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat by: Key words: parallel algorithms, finite-difference schemes, parabolic problems, nonlocal conditions.

Problem Formulation Many physical and technological processes are described by mathematical. Time-parallel iterative solvers for parabolic evolution equations Martin Neumuller y and Iain Smearsz Febru Abstract We present original time-parallel algorithms for the solution of the implicit Euler dis-cretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial : Martin Neumuller, Iain Smears.

Parallel Algorithms and Applications website: Other titles: Parallel algorithms and applications (Online) ISSN: OCLC: Material type: Document, Periodical, Internet resource. The standard numerical algorithms for solving parabolic partial differential equations are inherently sequential in the time direction.

This paper describes an algorithm for the time-accurate solut. Gumel, Parallel and sequential algorithms for second-order parabolic equations with applications, Ph.D. thesis, Brunel University ().  A. Khaliq, Numerical methods for ordinary differential equations with applications to partial differential equations.

Parallel Algorithms and Applications Volume 6, NumberFrancisco Almeida and Felix García and Daniel Gonzalez and Casiano Rodríguez A Parallel Algorithm for the Integer Knapsack Problem for Pipeline Networks Reid Baldwin and Moon Jung Chung and Yunmo Chung Overlapping Window Algorithm for Computing GVT in Time Warp.

Related work on parallel multigrid. Excellent surveys on parallel algorithms for multigrid can be found in  and .1 Here, we give a brief (and incomplete!) overview of distributed memory message-passing based parallel multigrid algorithms.

The two basic approaches are. Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers.

Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray parallelism in a sequential algorithm might not always lead to an efficient parallel algorithm.

It turns out that for certain types of problems a better approach is to adopt a parallel algorithm that solves a problem similar to, but different from, the given problem. Another approach is to design a totally new parallel.

Abstract. We describe a parallel implementation of a di erence scheme for the advection equation with time delay on a hybrid architecture com-putation system.

The di erence scheme has the second order in space and the rst order in time and is unconditionally stable. Performance of a sequential algorithm and several parallel implementations with.

Abstract. We consider the problem of solving time-dependent partial differential equations on a’ MIMD computer. Conventional methods for the solution of this type of equation when discretized by an implicit method such as backward Euler proceed by solving a sequence of problems iteratively.

algorithm that speciﬁes multiple operations on each step, i.e., a parallel algorithm. As an example, consider the problem of computing the sum of a sequence A of n numbers. The standard algorithm computes the sum by making a single pass through the sequence, keeping a running sum of the numbers seen so far.

In this paper, a new parallel algorithm for solving parabolic equations is proposed. The new algorithm includes two domain decomposition methods, each method is applied to compute the values at (n + 1) \$(n+1)\$ st time level by use of known numerical solutions at nth time level, respectively.

Then the average of two above values is chosen to be the numerical solutions at (n + 1) \$(n+1)\$ st. The Gauss Algorithm Gauss method is a well known direct algorithm of solving systems of linear equations, the coefficient matrices of which are a system of linear equations is nondegenerate, then the Gauss method guarantees solving the.

In these methods first- and second-order spatial derivatives are approximated by finite-difference approximations which produce systems of ordinary differential equations expressible in vector-matrix forms.\ud Solutions of these systems satisfy recurrence relations which lead to the development of parallel algorithms suitable for computer.

Algorithms: Sequential and Parallel takes an innovative approach to a traditional algorithms-based course of study. This new approach addresses the changing challenges of computer scientists in the fields of computational science and engineering. With the onset of parallel computing becoming more mainstream, the authors address this dynamic by merging the application and analysis of.

A propagation matrix method for the solution of the parabolic equation in ocean acoustics is presented, where the sound fields at an arbitrary distance are expressed as a product of the initial fields and a sequential multiplication of the propagation matrices.

The first algorithm is sequential while the second is parallel. Both algorithms, unlike existing ones, perform addition on blocks or tokens of 60 bits (18 digits), and thus boosting the execution time by a factor of Keywords: computer algorithm, large numbers addition, sequential algorithm, parallel algorithm 1 Introduction.

2. Algorithms Sequential and Parallel does not compete with Cormen et al. in the scope of topics covered. The Cormen et al. text, whose 3rd edition is over pages, seems designed for at least a year sequence in the study of algorithms.

By contrast, Algorithms Sequential and Parallel, 3rd edition, is just over s: 5.In this work, we propose a new dynamic model on the basis of the physical transmission of heat by conduction governed by a second-order parabolic partial differential equation with suitable initial and boundary conditions to analyze and forecast thermal stresses in the plate of a P64 OSCAR B airplane.