Numerical solution of a two-dimensional Helmholtz equation with Dirichlet boundary conditions

2021 ◽  
pp. 1-12
Author(s):  
Saja J. Kahlaf ◽  
Ali A. Mhassin
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional

scholarly journals Accuracy Investigation of FDM, FEM and MoM for a Numerical Solution of the 2D Laplace’s Differential Equation for Electrostatic Problems

2021 ◽  
Vol 1 (2) ◽  
pp. 26-30
Author(s):  
Bojan Glushica ◽  
Andrijana Kuhar ◽  
Vesna Arnautovski Toseva
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Advantages And Disadvantages ◽  
Electrostatic Problems ◽  
Dimensional Domain

Laplace’s differential equation is one of the most important equations which describe the continuity of a system in various fields of engineering. As a system gets more complex, the need for solving this equation numerically rises. In this paper we present an accuracy investigation of three of the most significant numerical methods used in computational electromagnetics by applying them to solve Laplace’s differential equation in a two-dimensional domain with Dirichlet boundary conditions. We investigate the influence of discretization on the relative error obtained by applying each method. We point out advantages and disadvantages of the investigated computational methods with emphasis on the hardware requirements for achieving certain accuracy.

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