Yes, I'm solving a transient wave equation. Should the behavior
between M + dt*K and M + dt^2*K be similar when solving the linear
system? I can only understand them as positive helmholtz equation,
the latter more dominated by mass matrix.
The condition number of K is h^{-2}, so if you choose dt=h, for the wave
equation you should generally obtain a matrix
M + dt^2 K
whose condition number is bounded as you refine the mesh. For the heat
equation, you get
M + dt K
which will (if you choose dt=h) have a condition number that grows like
h^{-1}.
As a consequence, I'm a *bit* surprised that your iterations grow by so
much, but it's been a long time since I've solved the wave equation and
so I don't recall whether what you see is expected or not.
Best
W.
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