摘要:

AbstractA modified version of the method of fundamental solutions which incorporates the singular behavior of the problem under consideration is introduced. The method is tested on potential and biharmonic problems and its performance is compared to the performance of the standard method of fundamental solutions.

ISSN:0749-159X    

DOI:10.1002/num.1690080101

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractWe attempt to obtain a two‐level implicit finite difference scheme using nine spatial grid points ofO(k2+kh2+h4) for solving the 2D nonlinear parabolic partial differential equationv1uxx+ v2uyy=f(x,y,t,u,ux,uy,u1) wherev1andv2are positive constants, with Dirichlet boundary conditions. The method, when applied to a linear diffusion‐convection problem, is shown to be unconditionally stable. Computational efficiency and the results of numerical experiments are discus

ISSN:0749-159X    

DOI:10.1002/num.1690080102

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractPenlty coupling techniques on an interface boundary, artificial or material, are first presented for combining the Ritz–Galerkin and finite element methods. An optimal convergence rate first is proved in the Sobolev norms. Moreover, a significant coupling strategy,L+ 1 =O(|lnh|), between these two methods are derived for the Laplace equation with singularities, whereL+ 1 is the total number of particular solutions used in the Ritz–Galerkin method, andhis the maximal boundary length of quasiuniform elements used in the linear finite element method. Numreical experiments have been carried out for solving the benchmark model: Motz's problem. Both theoretical analysis and numreical experiments clearly display the importance of penalty‐combined methods is solving elliptic equations with singular

ISSN:0749-159X    

DOI:10.1002/num.1690080103

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractWe compare the relative performances of two iterative schemes based on projection techniques for the solution of large sparse nonsymmetric systems of linear equations, encountered in the numerical solution of partial differential equations. The Block–Symmetric Successive Over‐Relaxation (Block‐SSOR) method and the Symmetric–Kaczmarz method are derived from the simplest of projection methods, that is, the Kaczmarz method. These methods are then accelerated using the conjugate gradient method, in order to improve their convergence. We study their behavior on various test problems and comment on the conditions under which one method would be better than the other. We show that while the conjugate‐gradient‐accelerated Block‐SSOR method is more amenable to implementation on vector and parallel computers, the conjugate‐gradient accelerated Symmetric–Kaczmarz method provides a viable alternative for use on

ISSN:0749-159X    

DOI:10.1002/num.1690080104

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this paper the optimal control of uncertain parabolic systems of partial differential equations is investigated. In order to search for controllers that are insensitive to uncertainties in these systems, an iterative optimization procedure is proposed. This procedure involves the solution of a set of operator valued parabolic partial differential equations. The existence and uniqueness of solutions to these operator equations is proved, and a stable numerical algorithm to approximate the uncertain optimal control problem is proposed. The viability of the proposed algorithm is demonstrated by applying it to the control of parabolic systems having two different types of uncertainty.

ISSN:0749-159X    

DOI:10.1002/num.1690080105

出版商:John Wiley&Sons, Inc.    

年代:1992

数据来源: WILEY