F(X,Xdot) = 0
for steady state using the iteration
[G'] S = -F(X,0)
X += S
where
G(Y) = F(Y,(Y-X)/dt)
This is linearly-implicit Euler with the residual always evaluated "at steady state". See note below.
-ts_pseudo_increment <real> | - ratio of increase dt | |
-ts_pseudo_increment_dt_from_initial_dt <truth> | - Increase dt as a ratio from original dt | |
-ts_pseudo_fatol <atol> | - stop iterating when the function norm is less than atol | |
-ts_pseudo_frtol <rtol> | - stop iterating when the function norm divided by the initial function norm is less than rtol |
1. | - Todd S. Coffey and C. T. Kelley and David E. Keyes, Pseudotransient Continuation and Differential Algebraic Equations, 2003. | |
2. | - C. T. Kelley and David E. Keyes, Convergence analysis of Pseudotransient Continuation, 1998. |
Xdot = (Xpredicted - Xold)/dt = (Xold-Xold)/dt = 0
Therefore, the linear system solved by the first Newton iteration is equivalent to the one described above and in the papers. If the user chooses to perform multiple Newton iterations, the algorithm is no longer the one described in the referenced papers.