DAT521 Engineering Computing

Contents and structure

Scientific and engineering computing is a rapidly developing field that brings together the three disciplines: applied mathematics (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 introduces well-known important partial differential equations (PDEs), numerical methods for solving those PDEs, and their applications to basic and practical engineering problems in areas such as computational fluid dynamics, -structural mechanics, -image processing, -medicine, and -nanomaterials.

The course concentrates on the scientific and engineering computing pipeline: classification of mathematical models (deterministic or stochastic); modelling with partial differential equations (e.g. in fluid dynamics); numerical discretization of partial differential equations (e.g. grid generation, finite element, time stepping, finite volume, and discontinuous Galerkin); numerical algorithms (iterative methods and preconditioning); analysis of the methods and results (stability, consistency, accuracy, and 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

Knowledge

The student

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

Skills

The student

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

General competence

The student

• can discuss and relate the roles of applied mathematics and computer science in solving large scale engineering problems.
• Can assess and reflect upon the applicability of the engineering computing pipeline to practically solve engineering problems.

Entry requirements

ADA501 Mathematical modeling and simulation

Recommended previous knowledge

Solid background in linear algebra, vector calculus, 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 two smaller assignments and one larger assignment involving modelling of an engineering problem and application of the computing pipeline, including computer tools and analysis. Each of the assignments may be undertaken in groups.

In order to take the examinations, the assignments must be approved.

Assessment

The course is graded A-F based on an oral exam.

Examination support material

None

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