Fundamentals of Physical Modeling and Simulations

Abstract

Mathematical description of different physical phenomena and numerical methods for solving the obtained equations are discussed. The course presents the fundamentals of mathematical modeling including ordinary and partial differential equations along with boundary and initial conditions. Finite Difference Method and Finite Element Method for solving boundary value problems are shown in detail.

Objective

After completing this course a student will understand the main idea of representing physical phenomena with mathematical equations, will be able to apply an appropriate numerical method for solving the obtained equations, and will possess the knowledge to qualitatively evaluate the obtained results.

Content

a. Introduction to physical modeling and simulations b. Numerical methods for solving boundary (initial) value problems b.i. Finite difference method (FDM) b.ii. Finite element method (FEM) c. Boundary (initial) value problems of different physical phenomena c.i. Static and dynamic electric current distribution in solid conductors c.ii. Static und dynamic electric charge transport in semiconductors c.iii. Induced eddy currents in low frequency range (with numerous examples from the area of electrical energy technology) c.iv. Wave propagation in the RF-, microwave-, and optical frequency range (with numerous examples relevant for communication technology) c.v. Static and dynamic temperature distribution in solid bodies (with numerous examples relevant for electrical energy technology) c.vi. Static and dynamic mechanical structural analysis (with numerous examples from the area of MEMS technology)

Resources