On Mar 27, 2019, at 8:07 PM, Sajid Ali via petsc-users
<petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>> wrote:
Hi,
I'm able to solve the following equation using complex numbers (with ts_type cn
and pc_type gamg) :
u_t = A*u'' + F_t*u;
(where A = -1j/(2k) amd u'' refers to u_xx+u_yy implemented with the familiar
5-point stencil)
Now, I want to solve the same problem using real numbers. The equivalent
equations are:
u_t_real = 1/(2k) * u''_imag + F_real*u_real - F_imag*u_imag
u_t_imag = -1/(2k) * u''_real + F_imag*u_real - F_real*u_imag
Thus, if we now take our new u vector to have twice the length of the problem
we're solving, keeping the first half as real and the second half as imaginary,
we'd get a matrix that had matrices computing the laplacian via the 5-point
stencil in the top-right and bottom-left corners and a diagonal [F_real+F_imag,
F_real-F_imag] term.
I tried doing this and the gamg preconditioner complains about an unsymmetric
matrix. If i use the default preconditioner, I get DIVERGED_NONLINEAR_SOLVE.
Is there a way to better organize the matrix ?
PS: I'm trying to do this using only real numbers because I realized that the
optimized avx-512 kernels for KNL are not implemented for complex numbers.
Would that be implemented soon ?
Can you provide a PETSc log for your code using complex numbers with -ts_type
cn and -pc_type gamg? I am doubtful that it could benefit much from AVX
optimizations on KNL.
Thanks,
Hong (Mr.)
Thank You,
Sajid Ali
Applied Physics
Northwestern University
