摘要:

AbstractA relaxation‐like method for the numerical solution of a class of partial differential equations of mixed type is presented. The equations of this class have not yet been solved by functional outlines. The numerical method does not add artificial terms to the original equatio

ISSN:1069-8299    

DOI:10.1002/cnm.1640090302

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe paper is concerned with the solution of non‐linear wave distribution in structural fibre members subjected to dynamic kinematic forcing. The development of reliable and efficient techniques for numerical handling of wave distribution based on the application of combined finite‐element and transfer matrix approaches is emphasized. Illustrative numerical solutions are presen

ISSN:1069-8299    

DOI:10.1002/cnm.1640090303

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper deals with the solution of the one‐dimensional advection–diffusion equation. The method of solution is based on the process‐splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite‐element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed

ISSN:1069-8299    

DOI:10.1002/cnm.1640090304

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA posteriori error indicators for strain energy error in finite‐element solutions have recently been shown to be effective. A popular error indicator, usually denoted by η, makes use of ‘error energy’, i.e. strain energy associated with the difference between the conventional element stresses σ and a smoothed stress field constructed from σ. It is intended that η be constructed by summing element contributions and that it be applied at the global level. The present study suggests that an error indicator applicable at the element level can be obtained by combining an element value of η with information about stress gradient and strain energy density. It is also shown how the stress gradient information can be used to obtain more accurate stresses at mesh

ISSN:1069-8299    

DOI:10.1002/cnm.1640090305

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe symmetric boundary‐element method for mixed boundary‐value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive‐definite finite‐element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite‐element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2ntypes of boundary data for self‐adjoint problems of order 2nand solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2‐D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher‐order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0continuous

ISSN:1069-8299    

DOI:10.1002/cnm.1640090306

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe Neumann–Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite‐element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are repor

ISSN:1069-8299    

DOI:10.1002/cnm.1640090307

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe potential distribution of bipolar, strongly reverse‐biasedpn‐junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self‐adaptive finite‐element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse‐biasedpn‐junction with multistep field plate and stop electrode to illustrate its efficiency and

ISSN:1069-8299    

DOI:10.1002/cnm.1640090308

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA modification has been introduced to the new superconvergent patch derivative recovery technique recently developed (Zienkiewicz and Zhu, 1991). By use of a locally normalized co‐ordinate system, the application of this technique can now be applied to higher‐order finite‐element shape functions. Numerical studies are carried out for up to 6th‐order elements in one dimension and for up to quartic elements in two dimensions, and superconvergent results are obtained for all examples

ISSN:1069-8299    

DOI:10.1002/cnm.1640090309

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractTwo graph‐theoretical algorithms are developed for bandwidth reduction of rectangular matrices. A K‐total graph is defined for a selected cycle basis, generalized cycle basis and cut set basis of a graph. This transforms a simultaneous ordering of the elements of a basis and members of a graph into that of a nodal numbering of its K‐total graph.The first algorithm uses the K‐total graph and results in banded equilibrium and self‐stress matrices. The second employs a nodal ordering algorithm followed by a member ordering process. This algorithm can be used for optimizing the bandwidth of member‐cocycle incidence matrices, resulting in banded equilibri

ISSN:1069-8299    

DOI:10.1002/cnm.1640090310

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:1069-8299    

DOI:10.1002/cnm.1640090311

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY