Ballooning and infinitesimal scaling for unbounded field problems

Computer-aided design of electromagnetic devices often involves solving an unbounded elliptic boundary-value problem. Ballooning and infinitesimal scaling, two methods for dealing with the exterior of elliptic boundary-value problems, are shown to be sufficiently closely related for either method to be considered a generalisation of the other. They are shown to differ in their computational complexity, however, so there may be clear practical advantages in favour of either method even though the results obtained may not differ at all.