摘要:

AbstractSensitivity analysis allows for analyzing the effects of parameter uncertainty. For functional parameters, the sensitivity of the system is described by the functional derivatives of the output variables with respect to the parameters. Approximation of each of the functional parameters by a finite number of scalars (via the finite element representation) allows one to use elementary sensitivity analysis. The functional sensitivities are easily approximated from elementary sensitivities and, being objective quantities, they allow one to evaluate the numerical quality of sensitivities. The grid density necessary for computing functional sensitivities may differ significantly from the grid required for the numerical solution of the governing equation.

ISSN:0749-159X    

DOI:10.1002/num.1690070202

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

摘要:

AbstractThis paper presents three innovative methods for solving eigenvalue problems for differential equations based upon the techniques of implicit decomposition developed by Luo and Friedman. An eigenvalue problem can be written as an approximate algebraic system of the form [K]{X} + λ[M]{X} = 0 by employing finite elements. These methods provide robust techniques to compute the real eigenpair, λ and {X}, where [K] and [M] can be asymmetric, indefinite, and even singula

ISSN:0749-159X    

DOI:10.1002/num.1690070203

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

摘要:

AbstractWe present an algorithm for nonlinear parabolic equations that uses a linear semigroup approach to decouple the nonlinearity, thus allowing simpler techniques to be used for the solution. The basic method is applicable only to a restricted class of problems, but can be extended with little loss of utility. Stability and error estimates are given, along with example computations.

ISSN:0749-159X    

DOI:10.1002/num.1690070204

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

摘要:

AbstractOperator splitting for evolution equations which involve linear operators is investigated. A systematic method for identifying multifactor fractional‐step operator splittings is proposed. The classical second‐order accurate splittings of Strang readily emerge, as well as various third‐order splittings of nonstandard type. Factorizations possessing mixed positive‐negative fractional steps are discovered, as well as bizarre splittings whose factors include complex fractional steps. It is found that no higher‐order accurate splitting which employs all positive fractional steps and which possesses less than nine operator factors can exist. For the linear case this implies second‐order accurate splittings are optimal, as a further increase of one power in accuracy essentially requires a three‐fold increase in work. This estimate slightly improves, for cases where the nonstandard splittings can be employed. Some numerical experiments which illustrate the theory

ISSN:0749-159X    

DOI:10.1002/num.1690070205

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

摘要:

AbstractThe system of two quasilinear elliptic equations is approximated by the method of lines, which has the truncation errorO(h2) at points neighboring the boundary andO(h4) at the most interior points. It is proved that the global error of the method isO(h4) at all mesh points. The two‐point boundary value problem for the system of ordinary differential equations that arises from the method of lines is solved by theO(h4) convergent finite difference scheme, suitable to the equations of the formuxx=f(x, u) without the first derivativeux. The system of algebraic equations obtained by the full discretization is solved by Gauss elimination method for three diagonal matrices combined with the method of iterations. A numerical example is presente

ISSN:0749-159X    

DOI:10.1002/num.1690070206

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

摘要:

AbstractFinite element solutions of the Euler and Navier‐Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak‐Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two‐dimensional transonic inviscid flows and two‐ and three‐dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler

ISSN:0749-159X    

DOI:10.1002/num.1690070207

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690070201

出版商:John Wiley&Sons, Inc.    

年代:1991

数据来源: WILEY