Inverse nonlinear finite element problems with local and global constraints

A general one-step method for solving inverse finite-element (FE) field problems is described. Several inverse types are presented, indicating for each which parameters of the problem are specified and which remain to be determined. Mathematical steps are outlined, taking into account nonlinear material characteristics. Examples for some inverse field problems, using first-order triangular elements for the two-dimensional magnetostatic Maxwell equations, are included to illustrate the advantages of the method. The formulation preserves the requirement of a given local flux or a global constraint parameter while yielding the design, i.e. the geometry of the devices.<>