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.
от партнера
Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python
Мюнхенский университет Людвига-Максимилиана (LMU)Об этом курсе
Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.
Чему вы научитесь
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.
Программа курса: что вы изучите
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
Рецензии
- 5 stars80,06 %
- 4 stars16,07 %
- 3 stars1,92 %
- 2 stars1,60 %
- 1 star0,32 %
Лучшие отзывы о курсе COMPUTERS, WAVES, SIMULATIONS: A PRACTICAL INTRODUCTION TO NUMERICAL METHODS USING PYTHON
Truly useful and challenging due to the mixture of concepts. Really made me integrate knowledge I had before about numerical methods and mathematics.
Great insight for the application of numerical approximation and improving the capability in programming
This is a great course for intro to numerical course with additional bonus on python code, although a little bit too fast pace.
A great course for anyone interested in numerical methods applied to the wave equation. Clear and engaging lectures.
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