Introduction to numerical methods using Jupyter Notebooks

A set of Jupyter Notebooks demonstrating various numerical methods in Python. Among those are:

Single-step time integration: Euler forward and backward, Crank-Nicolson.
Finite difference, finite element, collocation, subdomain, least-squares methods
Iterative Picard and Newton-Raphsons solution methods
Stabilization methods: Mass lumping and finite increment calculus
First aspects of localization of softening material models
Concepts of staggered and monolithic coupling schemes

Illustrative examples chosen include first order models, beam bending theories and Terzaghi consolidation.

The notebooks mainly make use of

numpy
scipy
matplotlib
ipywidgets
sympy

The latter allows an interactive adaptation of parameters to immediatly illustrate their effect, e.g. the time-step size.

The notebooks can be viewed with nbviewer, see https://jupyter.org/, or can now also be run interactively using binder (available through nbviewer).

See https://nagelt.github.io

Comments and contributions are welcome.

Related publication:

Kern, D., & Nagel, T. (2022). An experimental numerics approach to the terrestrial brachistochrone. GAMM Archive for Students, 4(1), 29–35. https://doi.org/10.14464/gammas.v4i1.512

Name		Name	Last commit message	Last commit date
Latest commit History 123 Commits
Beams		Beams
Data		Data
Images		Images
avalanche		avalanche
plot_functions		plot_functions
.gitignore		.gitignore
00_ODEs.ipynb		00_ODEs.ipynb
01_Forward_Euler.ipynb		01_Forward_Euler.ipynb
02_Backward_Euler_Picard.ipynb		02_Backward_Euler_Picard.ipynb
03_Generalized_Midpoint_Picard.ipynb		03_Generalized_Midpoint_Picard.ipynb
03b_Generalized_Midpoint_Picard_Nonlin.ipynb		03b_Generalized_Midpoint_Picard_Nonlin.ipynb
04_Generalized_Midpoint_Newton.ipynb		04_Generalized_Midpoint_Newton.ipynb
04a_Newton_Picard.ipynb		04a_Newton_Picard.ipynb
04b_Generalized_Midpoint_Newton_Nonlinear.ipynb		04b_Generalized_Midpoint_Newton_Nonlinear.ipynb
04c_Erddruck_Newton.ipynb		04c_Erddruck_Newton.ipynb
04d_Newton_arclength.ipynb		04d_Newton_arclength.ipynb
05_soil_column_Ritz_Galerkin_Collocation.ipynb		05_soil_column_Ritz_Galerkin_Collocation.ipynb
05a_CPT_Least_Squares.ipynb		05a_CPT_Least_Squares.ipynb
06_soil_column_FEM.ipynb		06_soil_column_FEM.ipynb
06_soil_column_FEM_LD.ipynb		06_soil_column_FEM_LD.ipynb
06a_discretization_and_integration.ipynb		06a_discretization_and_integration.ipynb
06aa_soil_column_FDM.ipynb		06aa_soil_column_FDM.ipynb
07_Terzaghi_1D_consolidation.ipynb		07_Terzaghi_1D_consolidation.ipynb
07b_Terzaghi_1D_consolidation_explicit.ipynb		07b_Terzaghi_1D_consolidation_explicit.ipynb
07c_Terzaghi_1D_consolidation_CN.ipynb		07c_Terzaghi_1D_consolidation_CN.ipynb
07d_Terzaghi_1D_consolidation_mass_lumping.ipynb		07d_Terzaghi_1D_consolidation_mass_lumping.ipynb
07e_Terzaghi_1D_consolidation_mass_lumping_FIC_stabilization.ipynb		07e_Terzaghi_1D_consolidation_mass_lumping_FIC_stabilization.ipynb
08_coupled_problems.ipynb		08_coupled_problems.ipynb
09_localization_1d.ipynb		09_localization_1d.ipynb
10_freeze_thaw.ipynb		10_freeze_thaw.ipynb
2D_Adv_Diff.ipynb		2D_Adv_Diff.ipynb
2D_FEM_2.ipynb		2D_FEM_2.ipynb
LICENSE		LICENSE
Lagrange_constraints.ipynb		Lagrange_constraints.ipynb
Least_Squares_Exercise.ipynb		Least_Squares_Exercise.ipynb
Periodic_BC.ipynb		Periodic_BC.ipynb
README.md		README.md
SOC_sand_pile.ipynb		SOC_sand_pile.ipynb
TUBAF_header.ipynb		TUBAF_header.ipynb
constrained_minimum.ipynb		constrained_minimum.ipynb
heat_conduction_symmetries.ipynb		heat_conduction_symmetries.ipynb
permafrost.ipynb		permafrost.ipynb
requirements.txt		requirements.txt

License

nagelt/Numerical_Methods_Introduction

Folders and files

Latest commit

History

Repository files navigation

Introduction to numerical methods using Jupyter Notebooks

About

Resources

License

Stars

Watchers

Forks

Languages