Spectral element method for the anisotropic wave equation

This report serves to mainly solve the anisotropic wave equation with the emphasis on utilising the Spectral Element Method to discretize space in favour of the Finite Element Method. We will introduce the former method in great detail, combining techniques utilised in the Finite Element Method but is improved by the accuracy from using high-degree Lagrange interpolants. In this method, the model volume is partitioned into several spectral elements which are then used to approximate the integration using the Gauss-Lobatto-Legendre integration rule. Next, we will discuss how we piece the spectral elements together to form a global mesh. Lastly, we will discretize time by using the Finite Difference Method to solve for the displacement at any Gauss-Lobatto-Legendre point at any given time. Based on the classification of the spectral elements, this report also investigates the various complexities to the anisotopic wave equation which is to be applied to each spectral element accordingly. Ultimately, the report aims to serve as a stepping stone for the construction of a code utilising the spectral element method in the future.Bachelor of Science in Mathematical Science