About this Course

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Intermediate Level

Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.

Approx. 35 hours to complete
English
Subtitles: English

What you will learn

  • 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.

Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level

Basic knowledge of calculus and analysis, series, partial differential equations, and linear algebra.

Approx. 35 hours to complete
English
Subtitles: English

Instructor

Offered by

Ludwig-Maximilians-Universität München (LMU) logo

Ludwig-Maximilians-Universität München (LMU)

Syllabus - What you will learn from this course

Week
1

Week 1

3 hours to complete

Week 01 - Discrete World, Wave Physics, Computers

3 hours to complete
6 videos (Total 63 min), 1 reading, 1 quiz
6 videos
W1V2 Spatial scales and meshing12m
W1V3 Waves in a discrete world6m
W1V4 Parallel Simulations10m
W1V5 A bit of wave physics16m
W1V6 Python and Jupyter notebooks10m
1 reading
Jupiter Notebooks and Python10m
1 practice exercise
Discretization, Waves, Computers45m
Week
2

Week 2

4 hours to complete

Week 02 The Finite-Difference Method - Taylor Operators

4 hours to complete
8 videos (Total 41 min)
8 videos
W2V2 Definitions3m
W2V3 Taylor Series5m
W2V4 Python: First Derivative10m
W2V5 Operators5m
W2V6 High Order3m
W2V7 Python: High Order7m
W2V8 Summary1m
1 practice exercise
Taylor Series and Finite Differences20m
Week
3

Week 3

3 hours to complete

Week 03 The Finite-Difference Method - 1D Wave Equation - von Neumann Analysis

3 hours to complete
9 videos (Total 50 min)
9 videos
W3V2 Algorithm4m
W3V3 Boundaries, Sources4m
W3V4 Initialization4m
W3V5 Python: Waves in 1D5m
W3V6 Analytical Solutions4m
W3V7 Python: Waves in 1D3m
W3V8 Von Neumann Analysis19m
W3V9 Summary1m
1 practice exercise
Acoustic Wave Equation with Finite Differences in 1D - CFL criterion
Week
4

Week 4

7 hours to complete

Week 04 The Finite-Difference Method in 2D - Numerical Anisotropy, Heterogeneous Media

7 hours to complete
10 videos (Total 83 min)
10 videos
W4V2 Acoustic Waves 2D – Finite-Difference Algorithm6m
W4V3 Python: Acoustic Waves 2D8m
W4V4 Acoustic Waves 2D – von Neumann Analysis5m
W4V5 Acoustic Waves 2D – Waves in a Fault Zone8m
W4V6 Python: Waves in a Fault Zone9m
W4V7 Elastic Wave Equation – Staggered Grids16m
W4V8 Python: Staggered Grids5m
W4V9 Improving numerical accuracy11m
W4V10 Wrap up3m
1 practice exercise
Acoustic Wave Equation in 2D - Numerical Anisotropy - Staggered Grids45m

Reviews

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