The numerical error associated with the simulation of linear wave phenomena using finite methods in both the frequency and time domain is considered. Both exact and numerically generated solutions of finite difference and finite element approximations to the scalar Helmholtz equation in one and two dimensions are used to demonstrate the dependence of the accuracy of the discrete solution on the number of nodes per wavelength, the electrical size of the computational domain, the order of the discretization, and the type of boundary conditions used. The results from these studies, as well as results from similar studies for finite difference approximations of Maxwell’s equations in the time domain, are used to generate simple expressions for selecting the nodal density to maintain a desirable accuracy.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Electrical and Electronic Engineering