Optimal design method by using the boundary element analysis for plural permanent magnets

An optimal design method for plural permanent magnets is described. When the sizes of the magnets are unknown variables, the equation that optimizes the size in the desired flux distribution becomes nonlinear. From this point of view, a novel domain element called a size modification element is conceived. The proposed technique is based on the specific element and the least squares method to determine the optimum size or position of the plural permanent magnets. The method has been applied to the optimum design of plural magnets in an undulator