Assumed Mode Methods for Structural Analysis and Simulation

A review of least‐squares methods for solving partial differential equations

“…The factor W 2 in equations (6) and (7) is the relative weight of the boundary residuals with respect to the interior residuals. A large W 2 would make boundary residuals more important than interior residuals.…”

“…A local weighting function may also be used, to force smaller residuals in part of the domain. For example, RZ in equation (6) may be replaced by w(x)Rt, or R i in equation (7) may be replaced by w(xi)Ri. Both W 2 and w(x) could be used in the same formulation.…”

“…In particular, promising results have been obtained by combining Powell's non-linear least-squares algorithm" and a mixed discrete f~r m u l a t i o n .~~ With this,approach, implementation requires only a subroutine that calculates values of &(a, xi) and WR,(a, xi) at each point when supplied a. Starting from an initial estimate of a, Powell's method then iteratively seeks the a that minimizes I d in equation (7).…”