摘要:

AbstractAn algorithm is presented to accelerate the convergence of the inverse iteration method for the solution of algebraic symmetric eigensystems. The algorithm is based on the use of the Ritz analysis during inverse iteration to generate improved trial vectors at virtually no extra cost. Examples are shown to illustrate the computational advantages of the method. The results are compared with those obtained using the subspace iteration method, the determinant search method and the accelerated subspace iteration method.

ISSN:0029-5981    

DOI:10.1002/nme.1620200702

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractTo estimate wave motion, the finite element method is presented based on the linear interpolation function and two‐step explicit numerical integration in time. For the determination of free surface position, the two‐step scheme based on the Eulerian technique is usefully employed. Travel and run‐up of solitary wave have been analysed and compared with the analytical solution. Both results are reasonably well in agreement. This method is applied to estimate the wave force on the practical breakwater to show the validity of the m

ISSN:0029-5981    

DOI:10.1002/nme.1620200703

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA wide variety of methods have been proposed for solving implicit second‐order systems of differential equations such as arise in structural and mechanical vibration analyses. Here we discuss a class of methods, based on second derivative formulae, some of which have previously been used by Enright.1We show them to have desirable analytic and implementation properties. We relate these methods to others recently proposed by Brusa and Nigro and by Serbin, showing that we obtain algorithms which have all the desirable properties of their methods and which can also be extended to classes of practical problems which were not considered by these other authors. Since implicit first‐order systems are also important in practice, for example in finite element analyses of heat conduction problems, we demonstrate the efficient implementation of the second derivative formulae in this case

ISSN:0029-5981    

DOI:10.1002/nme.1620200704

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA constructive approach for the treatment of Stummel's examples to the patch test is presented, together with generalizations of these examples. The strange convergence phenomenon of nonconforming approximations is discussed in detail, and a kind of modified variational equation for remedying these defects is introduced. Our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh‐dependent nor

ISSN:0029-5981    

DOI:10.1002/nme.1620200705

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA general finite difference scheme has been proposed along with a three‐dimensional co‐ordinate transformation procedure for the prediction of three‐dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three‐dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three‐dimensional flows of t

ISSN:0029-5981    

DOI:10.1002/nme.1620200706

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractAnalytical comparative solutions are often needed to assess the accuracy of proposed elements or proposed iterative schemes for potential flow numerical calculations. Traditionally, the flow over a circular cylinder, placed in a wind tunnel, has served for such a test and the results compared to what is thought to be an exact solution. We point out here that there is no exact solution for the flow over a circular cylinder in a wind tunnel, for practical values of wind tunnel height to cylinder radius, but that an exact solution can only be found for the flow over an oval cylinder. We derive that exact solution and provide numerical comparisons, using triangular elements, with both the stream function and the velocity potential for the incompressible case. In addition, numerical results for compressible flows up to critical Mach number are presented.

ISSN:0029-5981    

DOI:10.1002/nme.1620200707

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractGeneralized Petrov–Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths.9,10The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co‐workers4–6and Herbst et al.7,8can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are

ISSN:0029-5981    

DOI:10.1002/nme.1620200708

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA numerical method of solution is proposed for optimization problems of distributed parameter systems. Two model problems from continuum mechanics are investigated by means of constructing the problems as the steady‐state optimal control problems governed by elliptic partial differential equations.The basis of the suggested method of solution lies in the space discretization of the necessary conditions for optimality by the boundary element method, and the minimization of the performance indices by the conjugate gradient method of optimizatio

ISSN:0029-5981    

DOI:10.1002/nme.1620200709

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractWe discuss properties of methods proposed recently by Gellert1and by Brusa and Nigro2for solving systems of second‐order ordinary differential equations. In both cases, we extend the derivations to obtain whole families of methods with improved stability properties (roughly equivalent toL‐stability for first‐order systems) and we show that obtaining improvement in stability properties results in a deterioration in accuracy and/or implementation properties. Also we bring out the relationship (and in some cases equivalence) of these methods to others proposed in the literature. In particular, we show that the methods proposed by the above authors are essentially equivalent to well‐known methods of long standing, namely Padé approximant methods for equivalent first‐order systems of ordinary differential

ISSN:0029-5981    

DOI:10.1002/nme.1620200710

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractHybrid analysis techniques based on the combined use of finite elements and the classical Bubnov–Galerkin approximation are presented for predicting nonlinear steady‐state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees‐of‐freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global‐temperature modes, or basis vectors. The Bubnov–Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global–temperature modes).The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal–temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem‐adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations.The potential of the proposed reduction methods for the solution of large‐scale, nonlinear steady‐state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer.This study shows that the use of the uniform‐temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large‐scale, n

ISSN:0029-5981    

DOI:10.1002/nme.1620200711

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY