space-time Galerkin POD
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.
Space-time Galerkin POD (Python)
Implementation of space-time generalized POD and space-time Galerkin for solving Burgers' equation.
Setup
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.
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
andfenics
, a timer function, and caching of intermediate results - mat-lib-plots -- routines for plotting
- sadptprj_riclyap_adi -- linear algebra helper routines
- dolfin_navier_scipy -- interface between
- this repo already contains the home-brew modules and -- for the default parameters -- the factorized mass matrices
Classical POD and BFGS (Matlab)
Implementation of classical POD for the space reduction and BFGS for the optimization.
Setup
Change directory to pod-bfgs-matlab/
. To rerun the numerical tests, run driver_tab9.m
, driver_tab10.m
, or driver_tab11.m
.
Dependencies
- Matlab (v 8.0.0.783 (R2012b))
- Matlab (v 9.1.0.441655 (R2016b))
Hardware documentation
See logs_editha
for the logfiles of the numerical tests and the hardware specifications.