Engineering 170A/B: Introduction to Modeling and Simulation I/II
Units: 2
Instructor: Dr. J. P. Verboncoeur
Prerequisites: Junior/Senior/Graduate standing, Engin. 77N, Math 53, Math 54
Catalog Description:
This course introduces the concepts of analytic modeling and computer simulation, using small projects drawn from the multidisciplinary areas of Computational Engineering Science. Those areas covered span biology, chemistry, applied mathematics, and physics, as well as all areas of engineering. Models will progress sequentially through problem statement, mathematical model, approximations and analytic solution, discrete model, object-oriented model, implementation and simulation, visualization, and comparison to analysis, experiment and observation. Part I stresses modeling, while Part II stresses simulation and visualization.
Course Objectives:
Computational modeling and simulation are increasingly important in modern science and engineering. This course provides an introduction to the concepts involved in starting from a physical problem in science and engineering, and developing a model as the basis for simulation; this initial treatment is designed to prepare students for the proposed senior capstone course in Computational Engineering Science on modeling and simulation. The successful student will become familiar with the basics of modeling, including the concepts of the physical, mathematical, discrete, and object models. The successful student will become familiar with the art of making approximations in order to make problems tractable for analysis and simulation. The successful student will also become familiar with means of implementing a discrete model using MatLab, and with basic means of visualizing and presenting results. Students will be exposed to basic linear algebra, spectral, finite difference, finite element, and Monte Carlo methods, and other numerical areas of contemporary interest at a survey level. The course will make considerable use of the built in functionality of MatLab to allow students to focus on the modeling and simulation without requiring detailed treatment of the implementation of the methods, a subject for courses in numerical analysis. The students will participate in a multidisciplinary group modeling and simulation project, and present the results in class.
Course Syllabus:
Engin. 170 A Introduction to Modeling and Simulation I
Week 1: Course overview; MatLab review.
Week 2: The physical model: how to restate real world problems and fill in missing information.
Week 3: The mathematical model: applying equations to the physical model.
Week 4: The art of approximation: making the equations analytically tractable
Week 5: The discrete model: restating the equations for the computer.
Week 6: Accuracy, and stability: when you can trust the computer.
Week 7: The object model: applying object oriented methods to computation.
Week 8: Simulation: Implementing and running the discrete or object model.
Week 9: Modeling case study.
Week 10: Modeling case study continued; simulation, visualization and comparison to theory.
Week 11: Group modeling exercise.
Week 12: Simplified model: comparison of theory and simulation
Week 13: Simulation of full model: demonstration of the power of simulation to solve analytically intractable problems.
Week 14: Visualization using MatLab.
Week 15: Review.
Engin. 170 B Introduction to Modeling and Simulation II
Week 1: Overview; review of modeling and simulation concepts.
Week 2: Modeling example: linear algebra.
Week 3: Simulation example: linear algebra.
Week 4: Modeling and simulation example: ordinary differential equations via MatLab’s Runge Kutta routine.
Week 5: Modeling and simulation example: coupled ordinary differential equations.
Week 6: Modeling and simulation example: spectral methods – using MatLab’s Fourier transforms.
Week 7: Modeling and simulation example: finite difference methods.
Week 8: Modeling and simulation example: determining accuracy and stability of methods.
Week 9: Multidisciplinary group project. Initial discussion of models.
Week 10: Modeling and simulation example: Monte Carlo methods.
Week 11: Multidisciplinary group project: Presentation of models.
Week 12: Survey of scientific data structures, optimization.
Week 13: Multidisciplinary group project: Presentation of simulation results.
Week 14: Modeling and simulation example: introduction to finite element methods.
Week 15: Review.
Texts: Course notes; recommended: Press et al., Numerical Recipes in C: the art of scientific computing, Cambridge Univ. Press (1992).
How Course Requirements Will be Met and Evaluated:
The requirements of the course will be met through 2 hours of weekly lecture, and 4 hours of weekly homework including course reading material and small projects designed to illustrate the material presented in lecture and stimulate critical thinking in the areas of modeling and simulation. The course will provide computer accounts with access to MatLab for use in simulation and visualization. A written final report based on individual modeling and simulation projects will demonstrate familiarity with the basic concepts of modeling and simulation. This course is a required component of the Computational Engineering Science Curriculum. Engin. 170 A (Part I) will be offered in the Fall, and Engin. 170 B (Part II) will be offered in the Spring.
Section Limit: 25
First Offered: 170 A: Fall 2001; 170 B: Spring 2002