- Space mapping and defect correction
- Book title
- Model order reduction: theory, research aspects and applications
- Pages (from-to)
- Mathematics in industry. Subseries: The European Consortium for Mathematics in Industry
- Volume | Edition (Serie)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
In this chapter we present the principles of the space-mapping iteration techniques for the efficient solution of optimization problems. We also show how space-mapping optimization can be understood in the framework of defect correction.
We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the true solution.
In the last section we show a simple example from practice, comparing space-mapping
and manifold mapping and illustrating the efficiency of the technique.
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