摘要:

AbstractThis paper presents three axisymmetric infinite elements for the elastodynamic problems in a multi‐layered half‐space. They are the horizontal, the vertical and the corner infinite elements that are developed by using the wave functions in the function spaces derived from approximate expressions of the analytical solutions. An efficient integration procedure is proposed for calculating the element matrices involving multiple wave components. Numerical example analyses are presented for rigid disks on homogeneous and layered half‐spaces, and for an embedded caisson. The numerical results obtained show the effectiveness of the proposed infinite ele

ISSN:0029-5981    

DOI:10.1002/nme.1620382202

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWhen applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non‐dispersive media. The numerical wave displays a phase velocity that depends on the parameterkof the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one‐dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates inH1‐norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximationp(h

ISSN:0029-5981    

DOI:10.1002/nme.1620382203

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper we describe the foundations of a new hierarchical modal basis suitable for high‐order (hp) finite element discretizations on unstructured meshes. It is based on a generalized tensor product of mixed‐weight Jacobi polynomials. The generalized tensor product property leads to a low operation count with the use of sum factorization techniques. Variablep‐order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations. Numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two‐ and three‐dmensional computational domains employing standa

ISSN:0029-5981    

DOI:10.1002/nme.1620382204

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe finite element formulation for a half‐space electric field integral equation is described. Sommerfeld integrals, appearing in the kernel of the integral equation are calculated by means of exponential approximations. This approach shows advantages over the usual techniques. Obtained results are compared with other results availabl

ISSN:0029-5981    

DOI:10.1002/nme.1620382205

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractConformal co‐ordinate transformations are used to map rectangular computational domains onto arbitrary simply and doubly connected regions with smooth boundaries. The efficient numerical schemes of Wegmann involving the solution of the inverse boundary correspondence function problems associated with the mapping of the unit disc or circular annulus onto simply or doubly connected domains, respectively, are employed. The numerical implementation of these schemes is emphasized. Examples are generated for regions with elliptic inner and outer boundaries. Additional examples are used to demonstrate the accuracy and convergence of the schemes and their practical limitations. The techniques are found to converge well if holomorphic functions are used to describe the boundaries. The use of preconditioning maps is also discusse

ISSN:0029-5981    

DOI:10.1002/nme.1620382206

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe present a new efficient and scalable domain decomposition method for solving implicitly linear and non‐linear time‐dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time‐independent problems. Computational results confirm that the optimal convergence properties of the time‐independent FETI method are preserved in the time‐dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large‐scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time‐dependent problems, including the fictitious domain decompo

ISSN:0029-5981    

DOI:10.1002/nme.1620382207

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAdaptive two‐step direct integration methods are constructed for the integration of second‐order semidiscrete evolution equations possessing oscillatory solutions. The methods are based on a class of adaptive multistep methods for a semilinear test model whose frequency is known. They are constructed following the notion of diagonally implicit RK‐methods by using efficient rational approximations to cosv,v≥ 0. Our interest is centered on thedispersion(orphase errors) of the dominant components in the numerical oscillations when these methods are applied to a linear homogeneous test model. Two‐step methods which have high order of dispersion (up to 12), whereas the algebraic order is relatively low (2 or 4), are derived. Applications of these methods to linear as well as non‐linear test models and to semidiscretized hyperbolic equations reveal a good behaviour with regard to error propagation when they are compared with other conventio

ISSN:0029-5981    

DOI:10.1002/nme.1620382208

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper describes a parallel algorithm based on discontinuoushp‐finite element approximations of linear, scalar, hyperbolic conservation laws. The paper focuses on the development of an effective parallel adaptive strategy for such problems. Numerical experiments suggest that these techniques are highly parallelizable and exponentially convergent, thereby yielding efficiency many times superior to conventional schemes for hyperbolic problem

ISSN:0029-5981    

DOI:10.1002/nme.1620382209

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620382210

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620382201

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY