Convergence acceleration of the Newton-Raphson method using successive quadratic function approximation of residual

This paper presents new methods for determining a proper relaxation factor of the Newton-Raphson method to accelerate the convergence characteristics of a nonlinear finite-element analysis. In the methods, the squared residual of the Galerkin's approximation is successively approximated to a quadratic function using the gradients or Brent's method, and a relaxation factor is determined by minimizing the quadratic function until a quasioptimum relaxation factor is obtained. The presented methods are applied to the TEAM Workshop problem 13, and the results are compared with a conventional method.