A complex contour based perfectly matched layer applied to a pattern generating model equation.

Abstract

The observable universe consists of several non equilibrium systems that generate spatiotemporal behaviour in the form of various patterns. As the elementary laws of physics and chemistry are unable to explain the pattern forming behaviour of such systems, scientists have turned to desktop experiments and model equations to gain further insight. The model equations that generate numerical solutions similar to real world systems are computationally intensive, and this thesis discusses the possibility of designing a numerical scheme which are to reduce the computation time for a specific model equation.

The design is based on the perfectly matched layer (PML), a mathematical-numerical technique that works as an artificial absorbing layer within the discretized grid boundaries.

The thesis discuss how to impose a PML version of the model equation into the numerical method of lines(MOL) procedure, and various numerical and mathematical techniques are discussed in order to build this scheme.

The numerical simulations for the PML-equation fail to produce the correct spatiotemporal behaviour, and the discussed analysis states that a PML does not apply to the model equation discussed in the thesis.