W. Dai et R. Nassar, A GENERALIZED DOUGLAS ADI METHOD FOR SOLVING 3-DIMENSIONAL PARABOLIC DIFFERENTIAL-EQUATIONS ON MULTILAYERS, INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 7(7), 1997, pp. 659
Develops a generalized Douglas ADI method for solving three-dimensiona
l parabolic differential equations based on the idea of the regularize
d difference scheme. The method is simple, unconditionally stable and
well suited for either simulating fast transient phenomena or for comp
utations on fine spatial meshes. Numerical procedures that employ the
generalized Douglas ADI scheme were developed to solve three-dimension
al parabolic differential equations on multilayers. In these procedure
s, the generalized ''divide and conquer'' method for solving tridiagon
al linear systems is applied in order to overcome the problem with the
unknown value at the interface between layers. Numerical results show
that the procedure is accurate and efficient.