
GPU-based Conjugated Gradient Solution for Phase Field ModelsGPU-based Conjugated Gradient Solution for Phase Field Models 115
it is clear that α should be chosen so that
and are orthogonal.
From Eqs. (5.2.5) and (5.2.6)
(5.2.12)
and replacing Eq. (5.2.12) in Eq. (5.2.11)
. (5.2.13)
Considering
, (5.2.14)
and substituting Eq. (5.2.7) in Eq. (5.2.14)
. (5.2.15)
Rearranging terms
(5.2.16)
and considering
. (5.2.17)
The equation for the step size is obtained by clearing α
(5.2.18)
Therefore, the SD method consists of a loop made of three fundamental
steps given an initial value : fi rst, the residual, i.e., the steepest descent
direction is calculated ...