Fast numerical method for calculation of electric and magnetic fields based on potential-flux duality

By discretising the field into slices and tubes, upper and lower bounds to the energy of a system are obtained. Each slice carries the same flux and each tube has the same potentials at its ends. This makes the best possible use of the input data and avoids the necessity for solving a set of simultaneous equations, which is a characteristic feature of the usual finite-element method. Savings of computer time of one order of magnitude can be achieved in small problems and several orders of magnitude are likely in large problems.