Engineering Computation

Overview of Course

This course can be carried out using either Octave or Python at the choice of the student. It contains the below content, however the delivery of this course is such that the student can choose the topics they wish to delve into.

General Numerical Methods

• Introduction
• Solution of Equations by Iteration
• Interpolation
• Spline Interpolation
• Numeric Integration and Differentiation

Numerical Linear Algebra

• Linear Systems: Gauss Elimination
• Linear Systems: LU-Factorization, Matrix Inversion
• Linear Systems: Solution by Iteration
• Linear Systems: Ill-Conditioning, Norms
• Least Squares Method
• Matrix Eigenvalue Problems: Introduction
• Inclusion of Matrix Eigenvalues
• Power Method for Eigenvalues
• Tridiagonalization and QR-Factorization

Numerical Methods for ODEs and PDEs

• Methods for First-Order ODEs
• Multistep Methods
• Methods for Systems and Higher Order ODEs
• Methods for Elliptic PDEs
• Neumann and Mixed Problems. Irregular Boundary
• Methods for Parabolic PDEs
• Method for Hyperbolic PDEs

Applications in Civil Engineering

DISCLAIMER
Due to the highly complex nature of some of the following topics, adequate notice must be provided (on a case-by-case basis) so that the proper competency can be secured on part of the tutor. If this time for preparation is cut-short due to immediate demand, then the quality of delivery cannot be guaranteed.

Conservation principles

• Conservation of mass (continuity law)
• Conservation of energy
• Conservation of momentum

Initial value problems (IVP)

Boundary value problems (BVP)

Constitutive laws

• Hooke's law
• Darcy's law
• Mohr–Coulomb failure criterion

Structural Engineering

• Mechanics of solids and structures
• Bars
• Torsion
• Beams
• Buckling of columns
• Plane stress, plane strain, and stress concentration

Geotechnical Engineering

• Seepage and Darcy's law
• Soil consolidation and settlement
• Groundwater flow in soil

Coastal Engineering

• Wave equations
• Modelling tsunamis
• Wave run-up
• Wave spectra and Fourier analysis

Water and Environmental Engineering

• Hydrological predictions through machine learning techniques
• Hydrological risk analysis
• Distribution and transport of pollutants

Transportation Engineering

• Queuing theory
• Optimization of transport networks
• Traffic flow predictions

Delivery of Content

Throughout the course, in-class exercises and tutorials will be used as well as homework.

In the case of real-world civil engineering applications of these computational methods, each project itself serves as practice, rendering tutorials and exercises unnecessary.