Multiscale Modeling

What it is about

In this module you will gain a systematic overview of models and methods of multiscale modeling from the continuum level down to the quantum- or atomistic level. You will learn fundamental principles, numerical techniques and multi-physical approaches, and you will be able to apply suitable simulation techniques for multiscale partial and ordinary differential equations as well as coarse-grained molecular dynamics models.

What you will be able to do

• Advanced knowledge of the fundamental challenges in multiscale problems
• Familiarity with physical models at different scales
• Basic understanding of molecular dynamics simulation and related software
• Basic knowledge of numerical, multi-resolution and multiscale techniques
• Ability to recognize connections between exemplary models and research/engineering problems
• Application of suitable simulation techniques to elliptic PDEs with multiscale coefficients
• Application of appropriate methods to ODEs with different time scales
• Creation of coarse-grained models for molecular dynamics simulations
• Recognizing the limits of existing models and open research questions

What the module consists of

• LectureConveying mathematical derivations and theoretical foundations; supplemented by animations and numerical examples
• ExercisesDeepening the lecture content: Matlab and Python scripts, implementation of missing building blocks for coarse-graining tasks
• Self-study / additional assignmentsFurther tasks to deepen understanding outside regular sessions; individual supervision by instructors

Teaching method

• Lecture with derivationsExplanation of theoretical foundations and mathematical concepts
• Animations and numerical examplesDemonstration of the capability and application of the methods to engineering problems
• Practical exercises in Matlab and PythonIndependent implementation and application of the discussed methods (e.g. coarse-graining)
• Consultation / office hoursClarification of individual questions and advising outside teaching sessions