FILE DESCRIPTIONS
pgrtwave.py
This Python module approximates a distributed optimal control for the wave equation
written in pressure-velocity formulation using mixed and hybrid PGRT FEM.
ocp_sample.py
An example of an optimal control problem for the wave equation using the PGRT FEM.
Output written in iterhist/ocp_sample.txt. (Example 1)
mfem_eoc.py
Computes the experimental orders of convergence in the mixed method. Output written
in iterhist/mfem_eoc.txt. (Example 2)
mfem_eoc_quasiunimesh.py
Computes the experimental orders of convergence in the mixed method with an initial
quasi-uniform mesh and successively refined by bisection. Output written
in iterhist/mfem_eoc_quasiunimesh.txt.
hfem_eoc.py
Computes the experimental orders of convergence in the hybrid method.
Output written in iterhist/hfem_eoc.txt.(Example 3)
hfem_condno.py
Prints the condition numbers of the system matrix in the hybrid formulation with
decreasing penalty parameters. Output written in iterhist/hfem_condno.txt.
hfem_eoc_penalty.py
Computes the experimental orders of convergence in the hybrid method with decreasing
penalty parameters. Output written in iterhist/hfem_eoc_penalty.txt.
strcolor.py
Module for output string coloring and highlighting.
mesh
Directory of npy files for the array of nodes and triangles. To be used in the script
mfem_eoc_quasiunimesh.py.
iterhist
Directory of iteration histories.
If you find these codes useful, you can cite the manuscript as:
G. Peralta and K. Kunisch, Mixed and hybrid Petrov–Galerkin finite element discretization for optimal control of the wave equation, Numerische Mathematik 150 (2), pp. 591-627, 2022. preprint.
Gilbert Peralta, Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, Baguio, Philippines 2600. Email: grperalta@up.edu.ph 31 March 2021