An Efficient Two-Level Preconditioner for Multi-Frequency Wave Propagation Problems: Numerical Examples and MAPLE derivations

This repository contains additional material to [BvG18]:

• complete the proof of Lemma 4.1 with two Maple scripts (files in subfolder /maple),
• visualization of Lemma 4.1: https://manuelmbaumann.github.io/optimal-tau/,
• numerical experiments as presented in Section 6 (subfolder /num_exper).

Numerical experiments:

Our numerical experiments are done in Python3 and are stored in the subfolder /num_exper. The experiments can be reproduced with the scripts exp1.sh - exp5.sh, respectively. An example run from the command line looks like:

python3 elast_wedge.py --ndims=2 --freq=[1.0,10.0] --Nom=5 --damping=0.7

(extreme frequencies displayed in red)

Dependencies:

For the proof of Lemma 4.1:

• Maple [v 18.02]

For the visualization:

• Bokeh [v 0.12.4]

For the numerics:

• nutils: pip install git+https://github.com/joostvanzwieten/nutils@955bc67d219496e26b037f47855709a222850d7c
• NumPy [v 1.8.2], SciPy [v 0.14.0], matplotlib [v 1.4.2]

Hardware info:

All numerical examples presented in Section 6 of [BvG17] have been implemented in Python-3 running over GNU/Debian Linux, and executed on a computer with 4 CPUs Intel I5 with 32 GB of RAM.

References:

• [BvG18]: M. Baumann and M.B. van Gijzen (2018). An Efficient Two-Level Preconditioner for Multi-Frequency Wave Propagation Problems. Appl. Numer. Meth., doi: 10.1016/j.apnum.2018.08.020.