On 10/4/24 20:39, 'yy.wayne' via deal.II User Group wrote:
I'm solving a time-dependent wave equation, and dt is the time step. For
backward Euler
time integration, I get M+dt^2*K = (v,u) + (\delta T)^2*(\nabla v, \nabla u).
The time step
dt does not scale with mesh size h, so the condition number is not bounded.
I see. It's of course true that for an implicit discretization you don't
*have* to choose dt proportional to h. You can then get into a situation where
indeed the condition number grows.
But from a practical perspective, for accuracy (not stability) reasons, you
will want to choose dt \approx h/c where c is the wave speed. You just won't
get accurate solutions otherwise.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/dealii/a8bf0a9f-c08d-4e0b-b40c-bc84a726598c%40colostate.edu.
