Dynamic ADI Methods for Elliptic Equations
Said K. Doss, Keith Miller · SIAM Journal on Numerical Analysis · 1979
This paper develops “dynamic” ADI methods involving a computerized strategy for completely automatic change of the iteration parameter $\Delta t$ in alternating direction implicit methods for linear or nonlinear elliptic equations. Computational results are presented for many large scale trial runs, corresponding to the finite difference equations for the divergence equation $ abla \cdot a abla u = \phi $ on various regions, with various linear $(a(x,y))$ or nonlinear $(a(x,y,u))$ coefficient choices. Our experience is that DADI has always worked, and worked extremely well.