# PCS911 Engineering Computing

## Course description for academic year 2021/2022

### Contents and structure

Scientific and engineering computing is a rapidly developing field that brings together the three disciplines: applied mathematics (in particular numerical analysis), computer science, and engineering. This course introduces the fundamental topics of engineering computing, and provides a foundation for further studies and research in the field, and the knowledge necessary to be involved in industrial computing. The course provides an introduction to partial difference equations (PDEs), numerical methods for solving PDEs, and their applications to basic and practical engineering problems in areas such as computational fluid, computational medicine, and computational nanomaterials.

The course concentrates on the scientific and engineering computing pipeline: classification of mathematical models (discrete/continuous, deterministic/stochastic); modelling with partial differential equations (examples from fluid dynamics); numerical discretization of partial differential equations (grid generation; finite element method; time stepping; finite volume and discontinuous Galerkin method); numerical algorithms (iterative methods, preconditioning); analysis of the methods and results (stability, consistency, accuracy, convergence); implementation (matrix assembly, data storage and access, sequential and parallel implementation, visualization); applications (e.g. flow and transport in porous media, biomedical imaging, and thin-film modelling).

### Learning Outcome

Upon completion of the course the candidate should be able to:

Knowledge

• explain the engineering computing pipeline: modelling with PDE, discretization, numerical solution, and visualization.
• describe the techniques underlying grid generation, data storage, matrix assembly, parallelization, and visualization.
• define iterative methods for the system of equations and preconditioning techniques.
• summarise key application areas of engineering computing such as flow and transport in porous media.

Skills

• classify and derive models, apply discretization methods as well as explicit and implicit time stepping schemes to a given PDE model.
• generate grid, assemble matrices, solve, and then visualize using MATLAB or Python.
• analyze and interpret the results of the engineering computing pipeline.
• apply the basic approaches to analyze the adequacy and accuracy of numerical methods and underlying models.
• conduct convergence analysis of iterative methods.

General competence

• discuss and relate the roles of applied mathematics and computer science in solving large scale engineering problems.
• assess and reflect upon the applicability of the engineering computing pipeline to practically solve engineering problems.
• discuss research problems within engineering computing with peer researchers.

### Entry requirements

General admission criteria for the PhD programme.

### Recommended previous knowledge

Solid background in linear algebra, partial differential equations, algorithms, and programming experience in the context of programming environments such as Python and MATLAB.

### Teaching methods

The course consists of a combination of lectures and seminars. The lectures will be used for covering the core material of the course. Seminars permit participants to present and discuss recent research papers.

### Compulsory learning activities

There will be a number of smaller assignments and a larger project. The project work may be undertaken in groups but is required to have an individual component. The project will be on the modelling of an engineering problem focusing on the students ability to solve a full-fledged engineering problem, follow the computing pipeline as well as use the necessary computer tools for analysis. The larger project must be documented in a research paper and presented at a seminar.

### Assessment

The course is graded pass/fail based on the research paper and an oral exam. Each of the two components must result in a pass grade in order to obtain a pass grade for the entire course. Each participant must give one seminar, and present the larger project. The small assignments must have been approved in order to take the exam.