2 edition of **investigation of preconditioners suitable for parallel implementation** found in the catalog.

investigation of preconditioners suitable for parallel implementation

C.A Rostron

- 162 Want to read
- 18 Currently reading

Published
**1994** by UMIST in Manchester .

Written in English

**Edition Notes**

Statement | C.A. Rostron ; supervised by R.W. Thatcher. |

Contributions | Thatcher, R.W., Mathematics. |

ID Numbers | |
---|---|

Open Library | OL21239365M |

MINRES is suitable for any symmetric \(A\), including positive definite systems. It might terminate considerably sooner than CG [4]. REFERENCES: [1] C. C. Paige and M. A. Saunders (). Solution of sparse indefinite systems of linear equations, SIAM J. Numerical Analy Books Authored or Co-Authored (Original Editions) “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” EMTS International Symposium on Electromagnetic Theory, Berlin, Germany, Aug. “Parallel preconditioners for solutions of dense. A parallel version of ANSOR scheme was investigated on distributed memory (DM) machines. The algorithm was proven suitable for parallel environments due to its high speedups, reasonable number of iterations, and reliability to converge for heavily loaded large power systems.

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This book mainly explores the use of polynomial preconditioners in iterative solvers for large-scale sparse linear systems Ax = b. Polynomial preconditioners have several advantages over other popular preconditioners -- they may be implemented easily, they are highly parallel Cited by: 7.

A multilevel approach with parallel implementation is developed for obtaining fast solutions of the Navier–Stokes equations solved on domains with non-matching grids. The method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors.

@article{osti_, title = {The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners}, author = {Falgout, R D and Jones, J E and Yang, U M}, abstractNote = {The increasing demands of computationally challenging applications and the advance of larger more powerful computers with more complicated architectures have necessitated the development of new.

original preconditioners would appear suitable for effective parallel implementation, although such implementation details have not been explored before.

That the original preconditioner leads to a small number of iterations, which is independent of the number of time-steps when employed with the widely used GMRES method [12], is established in [11]. We describe and test spaia parallel MPI implementation of the Sparse Approximate Inverse (SPAI) preconditioner.

We show that SPAI can be very effective for solving a set of very large and. () Parallel Implementation and Practical Use of Sparse Approximate Inverse Preconditioners with a Priori Sparsity Patterns.

The International Journal of High Performance Computing ApplicationsThe Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners t,andUlrikeMeierYang. This motivates the investigation of space decomposition preconditioners, which are efficient and suitable for parallel implementation.

These preconditioners exist in additive, multiplicative and combined hybrid forms. All variants require solution of sub-problems defined on individual sub-spaces of the considered space decomposition.

Design and implementation issues that concern the development of a package of parallel algebraic two-level Schwarz preconditioners are discussed. The computations are based on the Parallel Sparse. The resulting algorithms are well suited for implementation on computers with parallel architecture.

In this paper, we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners. The itera-tive algorithms using these new preconditioners converge to. Parallel implementation. As already stated, 3-D EM problems are typically large-scale problems whose solutions require enormous amounts of computation.

Nowadays, parallel computing has been widely accepted as a means of handling very large and demanding computational tasks. for parallel implementation as shown by Grote and Huckle [9], and Chow [8].

However, preconditioning quality may lag that of ICT preconditioners. Incomplete Cholesky with Selective Inversion Our parallel incomplete Cholesky with SI uses many of the ideas from parallel sparse direct multifrontal solution.

We start with a good ll-reducing. preconditioners are defined as a sum of independent operators on a sequence of nested subspaces of the full approximation space. On a parallel computer, the evaluation of these operators and hence of the preconditioner on a given function can be computed concurrently.

We shall study this new technique for developing preconditioners first in. Abstract. We describe the implementation and performance of a novel class of preconditioners. These preconditioners were proposed and theoretically analyzed by Pravin Vaidya inbut no report on their implementation or performance in practice has ever been published.

linear systems, with a focus on algebraic methods suitable for general sparse ma-trices. Covered topics include progress in incomplete investigation of preconditioners suitable for parallel implementation book methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.

Some of the challenges ahead are also discussed. An extensive bibliog. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The linear systems associated with large, sparse, symmetric, positive definite matrices are often solved iteratively using the preconditioned conjugate gradient method.

We have developed a new class of preconditioners, support tree preconditioners, that are based on the connectivity of the graphs corresponding to the. matrices and are well-structured for parallel implementation. In this paper, we evaluate the performance of support tree precondi-tioners by comparing them against two common types of precon-ditioners: diagonal scaling, and incomplete Cholesky.

Support tree preconditioners require less overall storage and less work per. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We consider iterative solvers for large linear systems, and develop a theoretical analysis for parallel implementation techniques which resort to overlapping decompositions, i.e.

in which some unknowns are replicated on two or more processors to facilitate the parallelization. advantage of being well-structured for parallel implementation, both in construction and in evalua-tion.

In this paper, we evaluate the performance of support tree preconditioners by comparing them against two common types of preconditioners: those arising from diagonal scaling, and from the incomplete Cholesky decomposition. ory parallel environment. Concluding remarks based on these tests are given in section 4.

2 Computation-Free Preconditioners The conjugate gradient method is inherently paral- lel. Its parallelism degrades significantly with the use of ILU preconditioners. This can be prevented by a highly 1 preconditioner, such as an approximate parti. Specifically, we assessed the performance of parallel multigrid preconditioners for a conjugate gradient solver.

We compared two different approaches: the Geometric and Algebraic Multigrid Methods. The implementation is based on the PETSc library. Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model.

After outlining the parallel implementation in the LFRic framework in Section 4, an investigation of the mixed solver is not the focus of this article and so only this method, as used in Melvin et al., is considered.

A new Newton–Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs.

However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. Here we discuss a parallel version of the coarsening algorithm described above and its integration into the library of parallel AMG preconditioners MLD2P4, to obtain preconditioners that are robust and efficient on large and sparse linear systems arising from anisotropic elliptic PDE problems discretized on general meshes.

solar potential, not every building site will be suitable for a solar installation. The first step in the design of a photovoltaic system is determining if the site you are considering has good solar potential. Some questions you should ask are: • Is the installation site free from shading by nearby trees, buildings or other obstructions.

preconditioners rely on an LUfactorization of an a priori unknown subset of the constraint matrix columns instead. We also develop some theoretical properties of the preconditioned matrix and reduce it to a positive deﬁnite one.

Several techniques for an efﬁcient implementation of these preconditioners are presented. Among the tech. Chronopoulos and C. Gear. Implementation of preconditioned s-step conjugate gradient methods on a multiprocessor system with memory hierarchy. Parallel Comput.,Google Scholar Cross Ref; E.

Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices. In 24th National Conference, pages Preconditioning for linear systems. In linear algebra and numerical analysis, a preconditioner of a matrix is a matrix such that − has a smaller condition number is also common to call = − the preconditioner, rather than, since itself is rarely explicitly available.

In modern preconditioning, the application of = −, i.e., multiplication of a column vector, or a block of column. A technique to assemble global stiffness matrix stored in sparse storage format and two parallel solvers for sparse linear systems based on FEM are presented.

The assembly method uses a data structure named associated node at intermediate stages to finally arrive at the Compressed Sparse Row (CSR) format. The associated nodes record the information about the connection of nodes in the mesh. Parallel Implementation and Preconditioning. In the domain decomposition system used in this work, computation models are firstly divided into several parts before the domain decomposition computation; parts are further decomposed into subdomains, and for each parts, domain decomposition is performed by the current processor element (PE), see.

preconditioners have not been available despite the fact that they have been used for more than twenty years [12]. We report the design, analysis, implementation, and computational evaluation of a parallel algorithm for computing ILU preconditioners.

Our parallel algorithm assumes that. Parallel preconditioners for Newton-Krylov methods 3 ILU-based Additive Schwarz Let P i be the rectangular matrix that projects a global n-vector onto a local vector corresponding to the unknowns stored on pro- cess ngP i to the linear system (3), and considering local solutions of the form x=PT i x i,weobtaintheblockdiagonalsystem A ix i =b i, (4) where b i ≡ P.

Abstract: The need for higher frequency in state estimation execution covering larger supervised networks has led to the investigation of faster and numerically more stable state estimation algorithms. However, technical developments in distributed Energy Management Systems, based on fast data communication networks, open up the possibility of parallel or distributed state estimation.

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader.

Further, a basic knowledge of the finite element method and its. A numerical investigation of Schwarz domain decomposition techniques for elliptic problems on unstructured grids. Mathematics and Computers in Simulation, Vol. 44, Issue. 4, p. ‘ Parallel multilevel preconditioners ’ Math.

‘ A parallel implementation of an iterative substructuring algorithm for problems in three dimensions. Parallel Preconditioning 7 • Block Jacobi type Localized Preconditioners • Simple problems can easily converge by simple preconditioners with excellent parallel efficiency.

• Difficult (ill-conditioned) problems cannot easily converge – Effect of domain decomposition on convergence is significant, especially for ill-conditioned problems. Parallel Techniques and Algorithms. Parallel Sorting Algorithms. Solution of a System of Linear Algebraic Equations.

The Symmetric Eigenvalue Problem: Jacobi's Method. QR Factorization. Singular Value Decomposition and Related Problems. Ortega (). Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, New York. PRECONDITIONERS D A VID HYSOM AND ALEX POTHEN y Abstract.

W e rep ort the dev elopmen t of a parallel algorithm for computing ILU preconditioners. The algorithm attains a high degree of parallelism through emplo ymen tofat w o-lev el ordering strategy, coupled with a sub domain gr aph c onstr aint that regulates the lo cation of nonzeros in Sc.

a nested deﬁnition of the preconditioner. In addition it is suitable for parallel computation. The methods can be seen as a multilevel extension of classical preconditioners as SSOR and modiﬁed ILU (MILU) (see for example [2, 15]).

The method of NSSOR is built by approximating the Schur complements simply by the diagonal blocks of. iv Master Thesis within Military Logistics Title: Management Information System (MIS) Implementation Challenges, Success Key Issues, Effects and Consequences: A Case Study of Fenix System Author: Artit Kornkaew Tutor: Leif-Magnus Jensen Place and Date: Jönköping, May Subject terms: Management Information System (MIS), Information System (IS).

M. Karl, G. Seemann, F. Sachse, O. Dössel, and V. Heuveline. Time and memory efficient implementation of the cardiac bidomain equations. In 4th European Conference of the International Federation for Medical and Biological Engineering, IFMBE Proceedings, vol.

22, For a parallel circuit, the total equivalent resistance, R eq, is: 1 R eq = 1 R1 + 1 R2 + 1 R3 ++ 1 R N = XN i=1 1 R i () (Resistors in Parallel) Figure Parallel Circuit Schematic The third type of circuit you will construct is a com-bination circuit(Fig.

and .where, M = M 1 M 2, M 2 x = x ~, M b = b ~, and M is a preconditioner, which represents A in some sense (Barrett et al. ; Meurant ).In the most extreme case, M is identical to A, and therefore, the linear equation can be solved without any far, no definitive preconditioner has been determined, thus developing preconditioner have been drawing attention from many.