SUMMARYNumerical integration of stiff first-order systems of differential equations is considered. It is shown how a Co-continuous polynomial time discretization, in conjunction with a weighted residual method, can be used to derive methods corresponding to the diagonal and first subdiagonal Pade approximants. In this manner A-stable schemes of order 2k and L-stable schemes of order 2k -1 are obtained, at least for k -5 4.The methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower-order methods that have the same stability type. We show how this feature may be utilized to perform partial refinements in the integration process, and how an error estimation by an embedding approach naturally follows. An adaptive algorithm based on the error estimator is suggested. Some numerical experiments that illustrate the ideas are included.

This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the-advancing front concept in a natural way.

A load identification problem in structural dynamics has in general multiple solutions. Therefore, additional information, such as the locations of the unknown forces, has to be supplied a priori in order to make a unique solution possible. The present study focuses on cases where such information is not readily available. First, it is shown that, given (tentatively) the spatial shape and position of the load, the Betti reciprocal theorem together with a reference load case may be used to calculate the required magnitude of the unknown load so that the response fits the measurement data as well as possible in a defined sense. In this manner a large number of trial loads may be evaluated with only little computational effort, since no equation system needs to be solved. Second, the situation where several loads, each reproducing the same measurement data, have been identified is investigated. An optimization problem with added discrete masses as design variables is suggested. The solution of this problem yields a structure such that each set of responses generated by each one of the previously identified loads is clearly distinguishable at the transducer positions. The proposed method is a novel approach and should be useful in the load identification problem for an existing structure. A numerical example illustrates the application of the method.

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SUMMARYAn adaptive procedure for the solution of the generalized linear eigenvalue problem within the hierarchical finite element method is described. The problem offinding, for a given discretization, an upper limit eigenvalue that is accurate within a prescribed tolerance is especially studied. An error estimator is presented and a recomputational scheme for improved solutions is proposed. A numerical example is included.