Numerical Quadratures of First-Order Partial Derivatives Given on Discrete Points. Least Squares Method Utilizing FEM Shape Function or Finite Difference Approximation.

Abstract

With regard to inverse design problems, numerical integration of the first-order partial derivatives given on discrete points in n-dimensional spaces is demanded occasionally, for example, to obtain a velocity field satisfying the velocity gradients given in the field. In this paper, such numerical quadratures are proposed by the use of the shape function for finite element methods or the finite difference approximation, based on a least squares method. Applicability of these methods is confirmed by applying them to a two-dimensional problem, and the characteristics of computational accuracy and the CPU time necessitated are discussed.