[petsc-users] FW: Using TS IMEX for a mechanical problem with a fault

[Aagaard, Brad T]

From: Matthew Knepley <knepley at gmail.com>
Date: Friday, August 7, 2020 at 12:28 PM
To: PETSc <petsc-maint at mcs.anl.gov>
Cc: Brad Aagaard <baagaard at usgs.gov>
Subject: [EXTERNAL] Using TS IMEX for a mechanical problem with a fault

We are using ARKIMEX (tried many of the formulations) for a problem with elastodynamics. Thus we have, in first order form, 

  u_t - v = 0
  v_t - E(u) + C (v^+ - v^-) + f = 0
  C^T lambda = 0

Here u is the displacement, v is the velocity, E is the elastic operator, C are the compatibility condition across the fault (v^+ and v^- are velocity on opposite sides of the fault), and lambda is
the Lagrange multiplier enforcing the fault conditions.

We are running an example that breaks a bar in the middle and lets elastic waves travel outward and eventually fall off the end (absorbing boundary conditions). We are splitting this into a LHS and RHS for IMEX. The LHS operator looks like

 / M  0    0 \
|  0   M   C |
\  0 C^T  0 /

where M is the mass matrix and C is the operator from above. This gives the wrong solution, with the displacement being way too small and inconsistent with the velocity.

However, if I multiply the RHS by M^{-1}, then the solution "looks" right. Do the IMEX methods assume that the LHS Jacobian is the identity somewhere?

  Thanks,

     Matt

This is PyLith (https://github.com/geodynamics/pylith), so if someone wants to run it, we can help them out.


-- 
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

http://www.cse.buffalo.edu/~knepley/