Title :
New absorbing boundary conditions for the finite difference method based on discrete solutions of Laplace equation
Author :
Da Silva, Franklin C. ; Soares, Antònio M. ; De Menezes, Leonardo R A X
Author_Institution :
Faculdade de Tecnologia, Brasilia Univ., Brazil
Abstract :
This work investigates the use of discrete solutions of Laplace equation to generate new absorbing boundary conditions for the Finite Difference Method.. The study is performed by solving the numerical difference equation analytically. These solutions show some useful characteristics that prove to be useful for the design of special boundaries. A particular use of special boundaries is the simulation of infinite size meshes. In this work, the behavior of the common four-point finite difference scheme for the Laplace equation is studied. Another interesting result is a parameter that can define the amount of iterations necessary to achieve a given error. The work is validated by comparison between the discrete solutions and numerical results.
Keywords :
Laplace equations; boundary-value problems; computational electromagnetics; convergence of numerical methods; difference equations; finite difference methods; Laplace equation; absorbing boundary conditions; convergence behavior; discrete solutions; electromagnetic problems; finite difference method; infinite size meshes; iterations; numerical difference equation; Boundary conditions; Convergence of numerical methods; Difference equations; Discrete transforms; Extrapolation; Finite difference methods; Helium; Laplace equations; Numerical analysis; Polynomials;
Conference_Titel :
Microwave and Optoelectronics Conference, 2003. IMOC 2003. Proceedings of the 2003 SBMO/IEEE MTT-S International
Print_ISBN :
0-7803-7824-5
DOI :
10.1109/IMOC.2003.1242865