NUMERICAL DIFFERENTIATION IN MAGNETIC-FIELD POSTPROCESSING

Postprocessing encompasses graphic display and numerical computation. The critical process in this work is numerical differentiation. Method s of numerical differentiation of approximate solutions may be divided into three groups: direct numerical differentiation, smoothing method s based on superconvergence properties, and methods that exploit prope rties the solution is known to possess though the numerical approximat ion does not. The choice of method is determined by the problem, as we ll as the use to which derivatives are put: graphical display, local f ield calculation, mesh refinement or a a posteriori error estimation. The paper compares current derivative extraction methods and reviews p rogress in this field, with particular attention to superconvergent pa tch recovery and methods based on Green's second identity. A new modif ication of the method based on Green's second identity is presented, t o include inhomogeneous and discontinuous materials.