Space Mapping and Defect Correction

D. Echeverrĭa, P. W. Hemker
2005 Computational Methods in Applied Mathematics  
In this paper we show that space-mapping optimization can be understood in the framework of defect correction. Then, space-mapping algorithms can be seen as special cases of defect correction iteration. In order to analyze the properties of space mapping and the space-mapping function, we introduce the new concept of flexibility of the underlying models. The best space-mapping results are obtained for so-called equally flexible models. By introducing an affine operator as a left preconditioner,
more » ... eft preconditioner, two models can be made equally flexible, at least in the neighborhood of a solution. This motivates an improved space-mapping (or manifold-mapping) algorithm. The left preconditioner complements traditional space mapping where only a right preconditioner is used. In the last section a few simple examples illustrate some of the phenomena analyzed in this paper. 2000 Mathematics Subject Classification: 65K05; 65B05.
doi:10.2478/cmam-2005-0006 fatcat:rigzjfbvbjapphdzxim645umzy