The Boundary-Domain Integral Method for Elliptic Systems by Andreas Pomp (auth.)

By Andreas Pomp (auth.)

This monograph provides an outline of all algorithmic steps and a mathematical starting place for a different numerical procedure, particularly the boundary-domain crucial strategy (BDIM). this technique is a generalization of the well known boundary point approach, however it can be acceptable to linear elliptic platforms with variable coefficients, specially to shell equations. The textual content can be comprehensible first and foremost graduate-level. it truly is addressed to researchers within the fields of numerical research and computational mechanics, and should be of curiosity to every person critical choices to the well-established finite point methods.

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We proved theoretically that the method converges to the global optimum. We also presented examples where our algorithm actually gives better solutions than the solutions given by the state-of-the-art heuristics which explore the index configuration space. The method does not require any phase for preparatory candidate index selection. In addition it shows very low sensitivity to parameter settings, therefore it can be especially useful in the implementations of self-tuning, autonomic database systems.

7 Convergence curves for the TPC-H workload Fig. 8 Estimated costs of TPC-H workload as a function of the storage space limit We have also checked how the plan selection algorithm affects the performance of the method. As a reference, we have implemented the uniform plan selection algorithm. The proportional selection gave much better average results over the uniform selection (Fig. 5). When using the uniform selection, sometimes running even 100,000 iterations did not produce optimal results. The best recorded convergence curve for the uniform selection was also much worse than that for the proportional selection (Fig.

The recommended index sets and their estimated benefits were similar, but not exactly the same in both solutions. The observed differences were presumably caused by the query plan cost models that did not exactly match. Materializing the indexes recommended by our tool for the storage size limit of 40%, applied for the DB/2 database, improved the estimated workload cost by over 55%, but obviously not as much as the original DB/2 recommendation. The same situation was observed when applied the DB/2 recommendation to our cost model — the value of the objective function was better for our solution than for the DB/2 advisor’s one.

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