Engineering topics

Poole, W. G., Jr.

Publications and source records attributed to Poole, W. G., Jr..

9 records

NASA NTRS1978

Incomplete nested dissection for solving n by n grid problems

Nested dissection orderings are known to be very effective for solving sparse positive definite linear systems which arise from n by n grid problems. In this paper we consider incomplete nested dissection, an ordering which corresponds to the premature termination of nested dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given and the ordering is shown to be competitive with nested dissection with regard to arithmetic operations and superior to that ordering in storage requirements.

George, A.↗

NASA NTRS1978

Analysis of dissection algorithms for vector computers

Recently two dissection algorithms (one-way and incomplete nested dissection) have been developed for solving the sparse positive definite linear systems arising from n by n grid problems. Concurrently, vector computers (such as the CDC STAR-100 and TI ASC) have been developed for large scientific applications. An analysis of the use of dissection algorithms on vector computers dictates that vectors of maximum length be utilized thereby implying little or no dissection; on the other hand, minimizing operation counts suggest that considerable dissection be performed. In this paper we discuss the resolution of this conflict by minimizing the total time required by vectorized versions of the two algorithms.

George, A.↗

NASA NTRS1977

Timing formulas for dissection algorithms on vector computers

The use of the finite element and finite difference methods often leads to the problem of solving large, sparse, positive definite systems of linear equations. MACSYMA plays a major role in the generation of formulas representing the time required for execution of the dissection algorithms. The use of MACSYMA in the generation of those formulas is described.

Poole, W. G., Jr.↗

NASA NTRS1976

A variant of nested dissection for solving n by n grid problems

Nested dissection orderings are known to be very effective for solving the sparse positive definite linear systems which arise from n by n grid problems. In this paper nested dissection is shown to be the final step of incomplete nested dissection, an ordering which corresponds to the premature termination of dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given, and the ordering is shown to be competitive with nested dissection under certain conditions.

George, A.↗

NASA NTRS1976

An algorithm for reducing the bandwidth and profile of a sparse matrix

A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill-McKee algorithm, yet requires significantly less computation time.

Gibbs, N. E.↗

NASA NTRS1975

System balance analysis for vector computers

The availability of vector processors capable of sustaining computing rates of 10 to the 8th power arithmetic results pers second raised the question of whether peripheral storage devices representing current technology can keep such processors supplied with data. By examining the solution of a large banded linear system on these computers, it was found that even under ideal conditions, the processors will frequently be waiting for problem data.

Knight, J. C.↗

NASA NTRS1975

Matrix bandwidth and profile reduction

This program, REDUCE, reduces the bandwidth and profile of sparse symmetric matrices, using row and corresponding column permutations. It is a realization of the algorithm described by the authors elsewhere. It was extensively tested and compared with several other programs and was found to be considerably faster than the others, superior for bandwidth reduction and as satisfactory as any other for profile reduction.

Crane, H. L., Jr.↗

NASA NTRS1975

An interactive graphics package for the automatic node renumbering of finite element matrices

An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile. Although the primary application of the package has been to the finite element analysis of structures, it is equally well suited to the many other areas of engineering and science which use sparse matrices.

Boisvert, R. F.↗

NASA NTRS1973

A geometric theory for the QR, LU and power iterations.

Consideration of the task of computing the invariant subspaces of a given matrix. For this purpose the LU, QR, treppen and bi-iterations have been presented, used, and studied more or less independently of the old-fashioned power method. Each of these methods generates implicitly a sequence of subspaces which determines the convergence properties of the method. The iterations differ in the way in which a basis is constructed to represent each subspace. This aspect largely determines the usefulness of the method. It is shown that the first four iterations produce exactly the same sequence of subspaces as do direct and inverse iteration started from appropriate subspaces. Their convergence properties are therefore the same, and a complete geometric convergence theory is presented in terms of the power method. It is shown that Hessenberg matrices are associated with ideal starting spaces.

Parlett, B. N.↗