Numerical Solution Of Two Dimension Wave Equation With Galerkin Finite Element Method

Abstract

This thesis presents a finite element method, Galerkin finite element method that solves the 2D wave equation in (x,y) coordinates and time t. The Galerkin formulation is used to approximate the solution of the 2D wave equation along the x coordinate and y coordinate derivatives. The solution is based on considering wave motion in the direction normal to the boundary. The exact solution is described in terms of the boundary conditions for the values of pressure and eventually sufficient accuracy of the numerical solution. The results which are obtained by Mathematica 12 software is tested against the known analytical solution. The domain was discretized using linear rectan gular elements. The main advantage of this method is the ability to accurately represent the wave propagation in the free surface boundary with absorbing boundary condition at the edges of the grid. The resulting numerical algo rithm enables the evaluation of the 2D wave equati