https://github.com/piyueh/sem-toolbox
Python codes for exercises of spectral element methods
https://github.com/piyueh/sem-toolbox
Last synced: about 1 month ago
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Python codes for exercises of spectral element methods
- Host: GitHub
- URL: https://github.com/piyueh/sem-toolbox
- Owner: piyueh
- License: mit
- Created: 2016-09-14T17:27:02.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2016-12-20T16:14:22.000Z (over 8 years ago)
- Last Synced: 2025-04-14T03:06:41.715Z (about 1 month ago)
- Language: Jupyter Notebook
- Homepage:
- Size: 1.63 MB
- Stars: 4
- Watchers: 1
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
SEM Exercises
=============
This repo contains Python codes to the exercise problems in the book:
Spectral/hp Element Methods for Computational Fluid Dynamics,
2nd edition, by George Em Karniadakis & Spencer Sherwin.
The repository is divided into two parts:
1. a Python package -- **utils**: This package includes re-usable
components, such as Polynomial, quadrature, expansions, assembly, solvers, etc.
I use these components to write solutions to the exercises. These components
are in object-oriented style. Also, I try not to use math libraries.
Typically only numpy ndarray is used. This causes some performance problems and
some naive implementations. For example, fractional function is very naive.
2. a collection of Jupyter notebooks -- **solutions**:
This folder includes Jupyter notebooks to each exercises in the book. My
intention is not to provide a teaching material,
so normally there are only codes and answers to the
exercises. Normally no explainations or detailed derivations are provided.
And I don't really care how the codes in these notebooks look like,
so they are typically a mess. I care about the **utils** package more.
##Warning:
The intention of these codes are to check whether I really understand the
theory described in the book, not to develop a serious SEM solver
(though I hope these code can one day be used in real applications ...), so
1. the perfomance is not guaranteed;
2. the consistency of naming convention and coding style is not guaranteed; and
3. don't expect to see a good practice of software engineering here.
## Known issues:
1. Root-finding function is vary naieve, so it can not handle too many multiple
roots.
2. Jacobi polynomials with very high orders (P>=30, I think) cant not correctly
find their roots. It will return complex roots due to the root-finding method I
used. This means quadratures with very high orders may not work, either.