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The author considers two difficulties inherent to computational methodology of optimal magnet design for NMR (nuclear magnetic resonance): (a) spectral methods of magnetic field analysis that would be highly accurate, fast, and general, and (b) an optimization strategy that would eliminate physically as well as numerically unstable solutions. The least-squares approximation method of zonal harmonics with iterated accuracy improvement is shown to be an effective alternative for the highly accurate spectral analysis of magnetic field in NMR applications. The principle of stability, the averaging of perturbed solutions, and Monte Carlo evolution methods are recommended for optimal magnet design in NMR. Examples of real-world magnet designs are presented.>
Aleš Gottvald (1990) studied this question.