Ementorhub

What you'll 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.

Skills you'll gain

Simulations

Engineering Analysis

Linear Algebra

Mechanics

Applied Mathematics

NumPy

Distributed Computing

Jupyter

Finite Element Methods

Python Programming

Numerical Analysis

Vibrations

Mathematical Modeling

Differential Equations

There are 9 modules in this course

The course targets anyone who aims at developing or using numerical methods applied to partial differential equations and is seeking a practical introduction at a basic level. The methodologies discussed are widely used in natural sciences, engineering, as well as economics and other fields.

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

Week 05 The Pseudospectral Method, Function Interpolation

Week 06 The Linear Finite-Element Method - Static Elasticity

Week 07 The Linear Finite-Element Method - Dynamic Elasticity

Week 08 The Spectral-Element Method - Lagrange Interpolation, Numerical Integration

Week 09 The Spectral Element Method - 1D Elastic Wave Equation, Convergence Test