SUMMARYComponent mode synthesis (CMS) is a classical method for the reduction of large-scale finite element models in linear elasticity. In this paper we develop a methodology for adaptive refinement of CMS models. The methodology is based on a posteriori error estimates that determine to what degree each CMS subspace influence the error in the reduced solution. We consider a static model problem and prove a posteriori error estimates for the error in a linear goal quantity as well as in the energy and L 2 norms. Automatic control of the error in the reduced solution is accomplished through an adaptive algorithm that determines suitable dimensions of each CMS subspace. The results are demonstrated in numerical examples.
We discuss a technique for query evaluation based on storing intermediary results as trees and study two applications. We first consider the problem of computing the transitive closure of a graph for a specific set of source nodes. Algorithms for this problem can be directly applied to many nonrecursive queries as well. We give a new algorithm and show that it is superior to several previous algorithms.We then consider Warshall's transitive closure algorithm. This algorithm is not O(n e), but we show that by using trees instead flat representations of intermediary results, we can derive a new of the algorithm with an O(n e) upper bound.
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