Numerical differentiation in magnetic field postprocessing

Abstract

Postprocessing encompasses graphic display and numerical computation. The critical process in this work is numerical differentiation. Methods of numerical differentiation of approximate solutions may be divided into three groups: direct numerical differentiation, smoothing methods based on superconvergence properties, and methods that exploit properties the solution is known to possess though the numerical approximation does not. The choice of method is determined by the problem, as well as the use to which derivatives are put: graphical display, local field calculation, mesh refinement or a a posteriori error estimation. The paper compares current derivative extraction methods and reviews progress in this field, with particular attention to superconvergent patch recovery and methods based on Green's second identity. A new modification of the method based on Green's second identity is presented, to include inhomogeneous and discontinuous materials.