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<div class="">On Mar 27, 2019, at 8:07 PM, Sajid Ali via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>> wrote:</div>
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<div class=""><span class="gmail-pl-c">Hi, <br class="">
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I'm able to solve the following equation using complex numbers (with ts_type cn and pc_type gamg) :<br class="">
u_t = A*u'' + F_t*u; </span><br class="">
<span class="gmail-pl-c">(where A = -1j/(2k) amd u'' refers to u_xx+u_yy implemented with the familiar 5-point stencil)</span><br class="">
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Now, I want to solve the same problem using real numbers. The equivalent equations are:
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u_t_real = 1/(2k) * u''_imag + F_real*u_real - F_imag*u_imag<br class="">
u_t_imag = -1/(2k) * u''_real + F_imag*u_real - F_real*u_imag
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<div class="">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.
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<div class="">I tried doing this and the gamg preconditioner complains about an unsymmetric matrix. If i use the default preconditioner, I get DIVERGED_NONLINEAR_SOLVE.
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Is there a way to better organize the matrix ? <br class="">
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<div class="">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 ?</div>
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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.</div>
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<div>Thanks,</div>
<div>Hong (Mr.) </div>
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<div class="">Thank You,<br class="">
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<div style="font-size:12.8px" class="">Sajid Ali<br class="">
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<div style="font-size:12.8px" class="">Applied Physics<br class="">
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<div style="font-size:12.8px" class="">Northwestern University</div>
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