space-time Galerkin POD

Code and hardware documentation of the numerical tests reported in our first submission of Space-time Galerkin POD with application in optimal control of semi-linear parabolic partial differential equations.

Space-time Galerkin POD (Python)

Implementation of space-time generalized POD and space-time Galerkin for solving Burgers' equation. This is a snapshot of the repo spacetime-genpod-burgers that is under continuous development.

Setup

Change directory to spacetime-pod-python/. To rerun the numerical examples run

python2.7 run_numtests_genpod.py
python2.7 run_numtests_bfgspod_step.py
python2.7 run_numtests_bfgspod_heartshape.py

The script run_numtests_genpod.py has a switch for the two testcases inival and heartshape.

To get the timings, set timingsonly = True in the scripts.

Dependencies:

• dolfin (FEniCS) (v 1.3.0; 1.5.0; 2016.2.0)
• scipy (v 0.13.3; 0.17.0)
• numpy (v 1.8.2; 1.11.0)
• scikit-sparse (v 0.3)
  • used for factorization of the mass matrices
  • critical for critical parameters (like small nu)
  • scipy's, numpy's built-in Cholesky routines can be used instead but the algorithm may fail at critical parameters
• and my home-brew python modules
  • dolfin_navier_scipy -- interface between scipy and fenics, a timer function, and caching of intermediate results
  • mat-lib-plots -- routines for plotting
  • sadptprj_riclyap_adi -- linear algebra helper routines
• this repo already contains the home-brew modules and -- for the default parameters -- the factorized mass matrices

Hardware documentation

See logs_pc764 for the logfiles of the numerical tests and the hardware specification of the PC used for the tests reported in the manuscript.