https://github.com/bueler/fas-intro
Paper and Python program to make the full approximation storage (FAS) scheme blindingly clear
Science Score: 20.0%
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Last synced: 10 months ago
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Paper and Python program to make the full approximation storage (FAS) scheme blindingly clear
Basic Info
- Host: GitHub
- Owner: bueler
- License: mit
- Language: Python
- Default Branch: master
- Homepage: https://arxiv.org/abs/2101.05408
- Size: 1.62 MB
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- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
- Releases: 0
Created over 4 years ago
· Last pushed almost 4 years ago
https://github.com/bueler/fas-intro/blob/master/
# fas-intro
This little project is finished. I posted the preprint to [arxiv.org/abs/2101.05408](https://arxiv.org/abs/2101.05408). I do not plan to pursue publication.
The program `fas1.py` in directory `py/` demonstrates by example how the _full approximation storage_ (FAS) multigrid scheme works. It solves an easy nonlinear ODE BVP using piecewise-linear finite elements and a nonlinear Gauss-Seidel smoother.
## Documentation (the preprint)
Read `fas.pdf` in `doc/` after generating it:
$ cd doc/
$ make
Clean up the LaTeX clutter in `doc/` with
$ make clean
## Run the program
To get started do
$ cd py/
$ ./fas1.py -h
Do the following simple run using FAS V-cycles on a mesh of 2^6=64 subintervals:
$ ./fas1.py -K 6 -monitor -show
The following solves to discretization error on fine meshes in a single F-cycle using 9 WU:
$ for KK in 2 4 6 8 10 12 14 16; do ./fas1.py -mms -fcycle -K $KK -cyclemax 1; done
See also the convergence study, using a version of the problem with a known exact solution (method of manufactured solutions), in `py/study/converge.sh`. Solver complexity (optimality), namely runtime and work units, is studied in in `py/study/optimal.sh` and `py/study/slow.sh`. These are described in section 6 of `doc/fas.pdf`.
Run software tests:
$ make test
Owner
- Name: Ed Bueler
- Login: bueler
- Kind: user
- Location: Fairbanks, Alaska, USA
- Company: University of Alaska Fairbanks
- Website: http://bueler.github.io
- Repositories: 56
- Profile: https://github.com/bueler
Professor of Mathematics (Applied)
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| Name | Commits | |
|---|---|---|
| Ed Bueler | e****r@a****u | 637 |
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