# Numerical Modelling of Physical Phenomena in Engineering, Biology and Medicine

Higher education teachers: Maček-Lebar Alenka
Credits: 6
Semester: winter
Subject code: 64252

## Subject description

Prerequisits:

• The condition for inclusion in the study process is the knowledge of higher mathematics and the basics of programming.
• In order to fulfil academic requirements, students must complete the prescribed laboratory exercises and oral examination.

Content (Syllabus outline):

Lectures:

• A brief overview of the basic procedures of modelling in engineering and biology; determination of the system and its surroundings, the selection and mathematical description of variables that describe the system and the observation time.
• Numerical methods for solving systems of linear algebraic equations and nonlinear algebraic equations.
• The optimization procedures.
• Numerical methods for solving ordinary differential equations.
• Formulation of partial differential equations with appropriate initial and boundary conditions.
• Numerical solution of partial differential equations; basics of finite difference method and finite element method.
• The basics of cellular automata and Monte Carlo methods.
• Laboratory work:
• Solving of various problems in biology and medicine using Matlab, its toolboxes (Partial Differential Equation Toolbox) and Comsol Multiphysics program.

Objectives and competences:

During this course students will gain knowledge about the modeling and the use of numerical methods for solving problems in engineering, biology and medicine. They will learn the basic procedures of mathematical model construction on the basis of typical examples from technique, medicine and biology. They will learn the basics of cellular automata modeling, Monte Carlo methods and optimization procedures.

Mostly, the course deals with numerical methods for solving partial differential equations. Students learn the theoretical basis of the finite difference and finite element method. On the basis of solving simple problems at the beginning and more complex problems during the course the students familiarize with the advantages and limitations of numerical methods. An important part of the learning process is an analysis of the calculated values and their comparison with the experimentally obtained values in cases where the results of the corresponding measurements are available. The diversity of cases offers students an useful knowledge in the wider field of engineering and science.

Intended learning outcomes:

Understanding the concepts of modelling and the basics of solving mathematical formulations by numerical methods. Knowledge of the theory of finite difference and finite element methods as the main methods for the numerical solution of partial differential equations. The ability to use these methods on simple and complex cases; correct determination of the boundary conditions, the choice of the type and number of elements, analysis of the results. Understanding the strengths and weaknesses of numerical methods. Supplementing the knowledge of Matlab and familiarization with the software Comsol Multiphysics. Ability to independently design the model of selected phenomenon, to select an appropriate method for solving the problem and to analyse the results.

Solving the problems from different areas of engineering, biology and medicine offers the students use of the knowledge at many scientific fields. Knowledge of the methods for numerical solving the systems of algebraic equations, ordinary differential equations and partial differential equations in various fields. Knowledge of appropriate software tools.

Learning and teaching methods:

Lectures; solving typical problems in the context of laboratory work; solving complex tasks in the context of laboratory work and independent work at home.

## Study materials

1. Dunn SM, Constantinides A, Moghe PV. Numerical methods in biomedical engineering, Elsevier 2006
2. Reddy J.N. Introduction to the Finite Element Method, McGraw-Hill 1993
3. Fagan MJ. Finite Element Analysis - Theory and Practice, Longman 1992
4. Kwon YW, Bang H. The finite element method using Matlab, CRC Press 2000
5. Comsol Multiphysics - User's Guidebook, Comsol AB., 2004
6. Schiff JL. Cellular Automata: A Discrete View of the World, Wiley-Interscience 2008

# Study in which the course is carried out

• 1 year - 2nd cycle - Electrical Engineering - Information and Communication Technologies
• 1 year - 2nd cycle - Electrical Engineering - Electronics
• 1 year - 2nd cycle - Electrical Engineering - Electrical Power Engineering
• 1 year - 2nd cycle - Electrical Engineering - Biomedical Engineering
• 1 year - 2nd cycle - Electrical Engineering - Control Systems and Computer Engineering
• 1 year - 2nd cycle - Electrical Engineering - Mechatronics
• 1 year - 2nd cycle - Electrical Engineering - Robotics