Hi all,
I am using PETSc to solve a system of nonlinear equations arising from
Density Functional Theory. Depending on the actual problem setup the
residulas of the matrix-free linear solver (GMRES)
stagnate and the nonlinear system converges only slowly.
Besides preconditioning my second idea to improve the performance of the
linear solver was to use a higher order approximation of the
Jacobi-vector product. Therefore, I am trying to write a user defined
subroutine that calculates the approximation of the matrix-free
Jacobi-Vector product, i.e. I would like to have a routine which can
replace the default 1st order approximation
J(x)*v = (F(x+eps*v) - F(x) ) / eps
for instance by a 2nd order approximation such as
J(x)*v = (F(x+eps*v) - F(x-eps*v) ) / 2eps
So assuming that I have a subroutine which claculates the approximation
of J(x)*v, how do I get PETSc to use this result in the SNES solver?
Thank you very much,
Jonas
