# Computational Science and Engineering

## Important note: |

Confusingly this minor has two codes, TW-Mi-195-17 (in Coursebase) and TI-Mi-195-17 (in OSIRIS).This is a mathematical minor! |

### Introduction

CSE is a multidisciplinary application-driven field that deals with the development and application of computational models and simulations. Often coupled with high-performance computing to solve complex physical problems arising in engineering analysis and design (computational engineering) as well as natural phenomena (computational science). CSE has been described as the "third mode of discovery" (next to theory and experimentation). In many fields, computer simulation, development of problem-solving methodologies and robust numerical tools are integral and therefore essential to business and research.

The CSE minor offers an excellent opportunity to deepen your knowledge and broaden your horizon.

The minor programme in CSE spans several dozen departments and research areas within the TU Delft. This minor is designed for a coupling to science and engineering majors. It should attract students who have an interest in numerical and computational aspects and in applying computational techniques to address problems in their own major. The CSE minor offers the students a platform to learn and apply modelling and computational knowledge in various research areas within the different faculties. It can also be used for self-assessing their potential to do a CSE related Masterâ€™s programme.

*Intended for*

*Intended for*

The minor is reserved for Bachelor Students with the following background: Aerospace Engineering (AE), Applied Sciences (AS), Civil Engineering and Geosciences (CEG), Electrical Engineering, Mathematics and Computer Science (EEMCS) and Mechanical, Maritime and Materials Engineering (3mE) at the TU Delft who would like to broaden and deepen their knowledge on computer simulations for science and engineering problems. And also for students from other universities as long as they meet the expected prior knowledge.

*Study goal of the CSE Minor*

*Study goal of the CSE Minor*

The minor gives a coherent introduction to Computational Science and Engineering. A priority concern of the CSE minor is the development of a coordinated curriculum that follows a multidisciplinary approach and serves computationally-oriented graduate students throughout science and engineering.

The undergraduate student is able to:

- Understand and apply numerical methods to partial and stochastic differential equations.
- Make a computer program for a given numerical algorithm including: testing, debugging, profiling and adding comments.
- Make a computer program in an object oriented computer language.
- Obtain knowledge of future trends in science/engineering/computing.
- Synthesize their knowledge and competences in a final project (enhance oral and written communication competences).

*Courses*

*Courses*

The CSE minor consists of an integrated set of courses combined with an integrating project applying the attained skills in a domain specific application. The final project is split up into two phases. In the first phase the students will formulate their project by discussing relevant articles amongst each other and also with their domain-specific supervisor. After a literature study the project should be defined with a properly posed research questions and a feasible time schedule. In the second phase the group of students will perform the actual research with a strong CSE emphasis. And finally, at the end of the project, every group should deliver a final report.

**The minor offers the following courses and projects:**

**Numerical Methods for Differential Equations ***TW3730TU, 6 ECTS*Finite differences, finite volumes in R^2, error analysis, discrete and continuous maximum principles, processing of boundary conditions, time integration.

**Scientific Programming ***TW3710TU, 3 ECTS*The course will bring the students to a level where they are able to change algorithms from e.g. numerical analysis into efficient and robust programs that run on a simple computer.

**Object oriented scientific programming C++ ***TW3720TU, 3 ECTS*Introduction to C++ programming (C++11 standard). Object-oriented scientific/parallel programming. Programming in team: source version control, build/testing systems.

**Numerical methods for Stochastic Differential Equations ***TW3750TU, 6 ECTS*Introduction to Ito and Stratonovitz calculus for stochastic integrals, Stratonovitz calculus, modelling uncertainty using stochastic differential equations, Numerical schemes for stochastic differential equations, strong order of convergence, weak order of convergence. Applications in financial mathematics (option pricing) and environmental modelling (pollution transport).

**Parallel Computing ***TW3740TU, 4 ECTS*Principle and basic techniques of parallel computing. Concepts of the interplay between parallel algorithmic and architecture and programming of parallel computers. Parallel algorithms and parallel programming models (such as shared-variable, message-passing, etc.) are discussed. Basic concepts of problem decomposition, scheduling and mapping for parallel computation in large scale computational science & engineering problems are considered. The lab exercise comprises the solution of a problem on a parallel computer.

**Final project: Two components**

**Part A: Literature study (project definition and pre-study) ***TW3715TU, 2 ECTS*In the first phase the students will formulate their project by discussing relevant articles amongst each other and also with their domain-specific supervisor. After a literature study the project should be defined with a properly posed research questions and a feasible time schedule.

**Part B: Main project work (implementation and writing report) ***TW3725TU, 6 ECTS*In the second phase the group of students will perform the actual research with a strong CSE emphasis. And finally, at the end of the project, every group should deliver a final report.

*More information*

*More information*

Ms. Ir. B. (Berna) Torun

Faculty of Electrical Engineering, Mathematics and Computer Science

Numerical Analysis

B.Torun@tudelft.nl

+31 15 27 86290