Partition of unity based data mappings

[davidscn]

Please describe the problem you are trying to solve. Our currently available mapping methods are either limited in terms of the convergence order (NN), limited in terms of computational cost (RBFs) or require additional information (NP and NNG). We would like to extend the available mapping concepts by a partition of unity concept, which is supposed to provide a scalable method for large systems with a higher convergence order.

Describe the solution you propose. The partition of unity method splits the domain up in several mildly overlapping regions (usually circles) and associates to each subregion a compactly supported weighting function. A mapping problem is solved in each subregion and the global solution is recovered by a weighted sum of all interpolated values in affected subregions. From the user perspective, the mapping should be easily configurable just as the currently available mapping methods. There might be new new configuration parameters for the size of the subregions and the overlap granularity (tbd).

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