摘要:

AbstractPoint iterative methods at which, at any one time, only a single equation of the linear system is treated are well known. However, in recent times block (or line) iterative methods, in which a group of equations (or points on the grid mesh) are treated implicity and solved directly by a specialized algorithm, have become the standard techniques for solving the sparse linear systems derived from the finite difference/element discretization of a self‐adjoint elliptic partial differential equation on a two‐dimensional grid. The main concern of this paper is to construct new groupings of the mesh points of the network into four and nine points using the high order accurate nine‐point finite difference equations and to investigate their advantages when used explicity in the standard iterative methods

ISSN:0748-8025    

DOI:10.1002/cnm.1630020502

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the numerical construction of Hermite interpolatory product integration rules at arbitrarily prescribed nodes. The heart of the computational scheme is the efficient construction of Hermite functions of any order for any set of points. For the purpose of illustration, quadrature formulae based on the use of Basu. Clenshaw, Filippi, Filon and Polyá nodes are generated for oscillatory integrals. Of the nodes considered. Basu nodes yield the most accurate results in the interesting case of rapid oscillations, while Filippi nodes give rise to efficient common‐point quadrature rules when the integrand has slight oscillations. The results also demonstrate that Hermite rules compare well with the Lagrange quadrature for the same number of function evaluatio

ISSN:0748-8025    

DOI:10.1002/cnm.1630020503

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630020504

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper presents some new finite difference methods for computing eigenvalues of two‐point boundary value problems of the formy″ + λq(x)y= 0,y(a) =y(b) = 0. The approximations Λ for λ are computed from a generalized seven‐band symmetric matrix eigenvalue problem resulting from a suitable discretization of this boundary value problem. The numerical approximations are 0(h4)‐convergent. It is shown that the accuracy of the numerical results can be pushed to 0(h5) and 0(h6), provided that the functionq(x)vanishes atx = aandb.Some numerical evidence is included to demonstrate the practical usefulness of the

ISSN:0748-8025    

DOI:10.1002/cnm.1630020505

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe Riccati equation arises in various problems, particularly in practical engineering problems. It is required to solve the resulting Riccati algebraic matrix equation instead of solving the time‐invariant optimal control problem in one of its standard forms. In this paper an unconstrained minimization technique referred to as the Davidon–Fletcher–Powell (DFP) method is used in solving such an equation by minimizing its norm. The positive‐definite solution of the equation is also obtained, which is desirable in most engineering p

ISSN:0748-8025    

DOI:10.1002/cnm.1630020506

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe frontal solution method for finite element linear systems is well known to be especially useful for small and medium‐sized computing equipment. Even memory sizes from 1 to 8 MB, which are now possible, put severe space limitations on three‐dimensional calculations run on a time‐sharing system. This paper describes a programming technique which greatly increases the applicability of the frontal solution method without using the automatic paging of modern operating systems, which would result in extreme ineffic

ISSN:0748-8025    

DOI:10.1002/cnm.1630020507

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe discretization, by means of the usual 5‐point difference formulae, of an elliptic partial differential equation can give rise to an unsymmetric and sparse linear system of equations in which the matrixAof coefficients is anM‐matrix such that each element in the upper/lower triangular part is greater than or equal to the respective element in the lower/upper triangular part. In other applications, dense matrices with the same property can arise. A FORTRAN subroutine called OAHM is presented for the solution of such systems which can be easily modified to deal efficiently with the sparse case. The OAHM subroutine uses a regular splitting and the convergence is therefore guarant

ISSN:0748-8025    

DOI:10.1002/cnm.1630020508

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractIn finite element analysis, each element is defined by a set of node numbers and stored. In this paper, it is shown that by storing the three neighbouring triangles of each triangular element, In addition to the three vertices, the interactivity and automation of the design station may be greatly enhanced. This enhancement results from the use of the data on neighbours in:1Identifying triangles pointed to on a graphics screen, through a digitizer. This is used for extracting potentials and field intensities at points, for refining meshes by adding points, and for imposing Neumann boundary conditions on the boundary edges and performing integrations, such as of force, over trianggles.2Following a path defined as a straight line for extracting graphs of potential and field intensity and performing contour integrations, like Maxwell stress, along such lines.3Checking the optimality of the mesh using the Delaunay criterion.4Determining discontinuities of field intensity at material interfaces.5Comparing the field intensities in adjacent triangles to measure error for adaptive refinement.Alternatively, in an environment where memory for storing the neighbours is scarce, such as when using microcomputers, it is shown that the values may be computed when they are required, at the expense of speed.

ISSN:0748-8025    

DOI:10.1002/cnm.1630020509

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractNon‐unique flows are possible in a coiled tube when the axial pressure gradient driving the flow exceeds a critical value. For a tube of square cross‐section, it is shown that the rate of convergence of the critical value with mesh size depends strongly on the mesh pattern. In the particular, the predictions obtained with mesh patterns which respect the symmetry of the problem converge more rapidly as the mesh size is redu

ISSN:0748-8025    

DOI:10.1002/cnm.1630020510

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractAn explicit from of the plastic matrix for a Mohr–Coulomb material in two dimensions is presented. The derivation, which assumes elastic–perfectly plastic behaviour is obtained by direct differentiation of a non‐invariant expression for the Mohr–Coulomb yield function. A FORTRAN 77 subroutine is also p

ISSN:0748-8025    

DOI:10.1002/cnm.1630020511

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY