For example, if all the heat sources are clumped at one end of the material, they cannot adequately control the area at the other end of the material. Based on this insight, the design objective considered here is that of decomposing a domain so that controls in different regions minimally interfere with each other. The exact control value in one region has little effect on results in other regions. The exact control placement in one region has little effect on results in other regions. We encode these criteria in terms of structures in fields, encapsulated in influence graphs.
Probes serve as representatives for the effects of arbitrarily-placed controls.
In particular, the probes that most strongly affect a location serve as the basis for an approximation of the effects that would be produced by a control placed at that location. We now overview how to satisfy the decomposition criteria enumerated above. Evaluate the effect of control value by distinguishing near field from far field . In a good decomposition, the total energy in the far field is small. Evaluate the effect of control placement by comparing heat flows.