Interested in learning how to solve partial differential equations with numerical methods and how to turn them into python codes? This course provides you with a basic introduction how to apply methods like the finite-difference method, the pseudospectral method, the linear and spectral element method to the 1D (or 2D) scalar wave equation. The mathematical derivation of the computational algorithm is accompanied by python codes embedded in Jupyter notebooks. In a unique setup you can see how the mathematical equations are transformed to a computer code and the results visualized. The emphasis is on illustrating the fundamental mathematical ingredients of the various numerical methods (e.g., Taylor series, Fourier series, differentiation, function interpolation, numerical integration) and how they compare. You will be provided with strategies how to ensure your solutions are correct, for example benchmarking with analytical solutions or convergence tests. The mathematical aspects are complemented by a basic introduction to wave physics, discretization, meshes, parallel programming, computing models.
von
Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python
Ludwig-Maximilians-Universität München (LMU)Über diesen Kurs
Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.
Was Sie lernen werden
How to solve a partial differential equation using the finite-difference, the pseudospectral, or the linear (spectral) finite-element method.
Understanding the limits of explicit space-time simulations due to the stability criterion and spatial and temporal sampling requirements.
Strategies how to plan and setup sophisticated simulation tasks.
Strategies how to avoid errors in simulation results.
Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.
Lehrplan - Was Sie in diesem Kurs lernen werden
Week 01 - Discrete World, Wave Physics, Computers
Week 02 The Finite-Difference Method - Taylor Operators
Week 03 The Finite-Difference Method - 1D Wave Equation - von Neumann Analysis
Week 04 The Finite-Difference Method in 2D - Numerical Anisotropy, Heterogeneous Media
Bewertungen
- 5 stars80,06 %
- 4 stars16,07 %
- 3 stars1,92 %
- 2 stars1,60 %
- 1 star0,32 %
Top-Bewertungen von COMPUTERS, WAVES, SIMULATIONS: A PRACTICAL INTRODUCTION TO NUMERICAL METHODS USING PYTHON
Would have like more "empty" cells in notebooks for trying to establish loop one self and then having a "correct" output to aim for. Maybe followed by a solution cell with a correct implementation.
Great course, I hope there will be a followup covering all the parts Prof. Igel mentioned in the final lecture. Amazing balance theory/practice and fantastic Jupyter Notebooks
Excellent coverage of the fundamentals. Would love to see another course like this developed that covers more advanced material.
Great experience. Really came to know about the theory of simulation techniques coupled with the introductory knowledge of python language.
Häufig gestellte Fragen
Wann erhalte ich Zugang zu den Vorträgen und Aufgaben?
Was bekomme ich, wenn ich das Zertifikat erwerbe?
Ist finanzielle Unterstützung möglich?
Haben Sie weitere Fragen? Besuchen Sie das Learner Help Center.