A Nonlinear Parallel Algorithm with Application to the Stefan Problem
R. E. White · SIAM Journal on Numerical Analysis · 1986
The algebraic problem $B\gamma (E) + A\beta (E) = \eta $, which may evolve from elliptic or parabolic partial differential equations, is studied. Conditions are given so that a parallel algorithm of a nonlinear Gauss–Seidel type converges to the unique solution. An application is given to the solidification of a channel in which the continuum problem is discretized by the finite element method. These computations show a significant decrease in computing times as compared to serial algorithms.