An Analytic and Numerical Study of Helmholtz Equation Using Finite Element Method.

Herein, analyzed is a symmetric finite element method (FEM) formulation that can be used to calculate time-harmonic acoustic waves in external domains by using finite elements. The dispersion study shows how mesh refining affects the discrete representation of the FEM parameters. In the Helmholtz area, stabilization through coefficient modification is used in conjunction with conventionally stabilized finite elements to enhance FEM performance. Numerical evidence backs up the robust performance of this finite element perfectly matched layer (PML) approach. We suggest and evaluate a quick technique for calculating the answer to the Helmholtz equation in a confined region using a changing wave speed function. Wave splitting is the method's foundation. To solve iteratively for a specified tolerance, the Helmholtz equation is first divided into one-way wave equations. The wave speed function and the previously solved one-way wave equations are both necessary for the source functions to function. Then, using the sum of one-way solutions for each iteration, the Helmholtz equation's solution is roughly determined. to decrease computational expenses. The findings show that each model under consideration has significant variances in density and speed. The findings show the effective application of MATLAB R2021 software and the finite element method to solve both first and second-order Helmholtz equations. [ABSTRACT FROM AUTHOR]