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

Implementation of space-time generalized POD and space-time Galerkin for solving Burgers' equation.

Change directory to spacetime-pod-python/. To rerun the numerical examples run python run_numtests.py. Set timingsonly = True there, to only get the timings.

• 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

Implementation of classical POD for the space reduction and BFGS for the optimization.

Change directory to pod-bfgs-matlab/. To rerun the numerical tests, run driver_tab9.m, driver_tab10.m, or driver_tab11.m.

• Matlab (v 8.0.0.783 (R2012b))
• Matlab (v 9.1.0.441655 (R2016b))

See logs_editha for the logfiles of the numerical tests and the hardware specifications.