Fundamentals Of Numerical Methods (SUT, year 1)

Module description

Course objectives:

The aim of the course is to introduce students to the fundamentals of numerical techniques.

Content of the course:

The course consists of lectures, computer lab and individual projects. Lectures cover: Limitations of numerical methods. Elements of differential geometry. Discretization of conservation, variation and reciprocity principles, as a basis of numerical methods. Weighted residuals, choice of weighting functions. Collocation, Galerkin and other formulations (least squares, sub-region collocation, moments). Application of weighted residuals for the solution of sets of algebraic equations, differential and integral equations. Trial functions for weighted residual solutions of differential equations. Functions satisfying boundary conditions (Ritz method), functions satisfying differential equation (Trefftz method), functions satisfying neither boundary conditions nor differential equation. Finite element method. Functions of finite support, local coordinates. Transformation of coordinates systems. Weak Galerkin formulation. Matrix assembly. Neumann and Robin boundary conditions. Dirichlet boundary conditions and their direct and penalty function implementation.

During computer lab, the students will program simple examples using MatLab and write a short project to solve heat conduction using Finite Elements.

Lectures are conducted in an interactive way with use of audiovisual tools. During the lecture problem questions/topics are raised, students take part in the discussion and brainstorms, trying to find solution/answers, assess existing solutions as well as develop critical thinking. Students are encouraged to participate in discussions which are  moderated by the tutor. Students will be able to explain and discuss the dynamic nature of complex systems and change over time. They will be able to apply the tools and concepts of system dynamics and systems thinking in their present lives.

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