Constrained functional similarity by minimizing the H1 seminorm and applications to engineering problems

Abstract

Often in engineering problems a function and a set of constraints are given and a new function is sought that is the “closest” to the original one and also satisfies the constraints. Typically functional closeness is sought using criteria such as the well-known least-squares criterion. In this paper a shape similarity is defined that may be preferable to use in certain situations. The problem is solved for the discrete case when the original function is given as a set of values and the constraints are linear. The similarity criterion is based on minimizing the discretized H1 seminorm of the difference between the original and the sought functions. Engineering examples are presented.