Course content

This is numerical methods for engineers, with a focus on research-applicable methodologies and the underlying theory.The scope is engineering broadly, but is motivated by research needs within energy process engineering.

Topics include:

1. General principles used throughout (degrees of freedom, computational complexity - big O notation, truncation errors and error propagation, convergence, iterative refinement)
2. Linear Algebraic Equations (Gaussian elimination, LU decomposition, Gauss-Siedel, matrix inversion, matrix conditioning)
3. Nonlinear Algebraic Equations (Newton methods, secant methods, single and multiple variable DAE equation sets)
4. Curve fitting (linear regression, multivariate models, polynomial interpolation, splines)
5. Numerical Differentiation (finite difference methods)
6. Numerical Integration (first and higher order explicit and explicit methods - Euler, Adams-Bashforth, Richardson Extrapolation etc)
7. Ordinary Differential Equations (ODEs, DAE + ODE systems. Multistep methods, stepsize adaptation)
8. Partial Differential Equations (finite element and difference methods, Galerkin method)
9. Computational Fluid Dynamics (solving, meshing, tools, etc)
10. Other timely topics relevant for research, such as surrogate modelling, and sequential modular flowsheet solving

Learning outcome

Students will be able to understand and apply numerical methods theory by creating, implementing, and usingalgorithms to solve engineering problems common in energy engineering research. Students can then advance thefrontiers of numerical methods by expanding, adapting, and innovating the state of the art as they encounter new andmore difficult engineering research problems.

Learning methods and activities

Lecture style. Students will work on assignments or small projects, potentially personalized to the research needs and goals of the student.

Recommended previous knowledge

Experience in solving systems of equations, and using open or commercial software that solves them (e.g. any commercial equation solvers, Python or Matlab-based solvers, fluid dynamics simulators, etc.)

Required previous knowledge

Programming skills in at least one programming language.Theory in the relevant areas of mathematics for science and engineering (especially linear algebra, differential and integral calculus, ordinary and partial differential equations)

Course materials

Course notes and recommended texts and video.