Contents
Why is a non-uniform grid more accurate than a uniform grid?
The typical reason why a non-uniform can lead to higher accuracy is that the PDE to solve is not of the form ut(x, t) = uxx(x, t), but of the form ut(x, t) = (D(x)ux(x, t))x. If your non-uniform grid allows you to represent the real D(x) more accurately, you will get a more accurate solution.
What is the rationale for non-uniform meshes?
The rationale for non-uniform meshes goes like this (all equations understood to be qualitative, i.e., in general true but without the pretense to be provably so in all circumstances and for all equations or all possible discretizations):
Which is better a rectangular grid or a non-rectangular grid?
In contrast, a non-rectangular grid typically requires a coupling to all the surrounding elements in a 3x3x3=27 array surrounding the central element. As a general rule, numerical accuracy associated with finite difference equations is best when grid elements are uniform.
Which is the simplest definition of a grid?
The simplest kind of grid is one composed of rectangular elements defined by a set of planes perpendicular to each of the coordinate axes (x,y,z). The spacing between parallel planes may be constant or variable.
How does the non uniform mesh improve accuracy?
There are two ways that the non-uniform mesh improves accuracy: through reducing numerical dispersion and improving the resolution of interfaces. Numerical dispersion is an artifact resulting from the discrete spatial sampling of the FDTD mesh.
How is the non uniform mesh used in FDTD?
The automesh feature automatically configures the non-uniform mesh to minimize the effects of numerical dispersion. In the usual use case, the user simply chooses a setting on the accuracy slider, which ranges in value from 1 to 8.
What is the maximum error when interpolating on a mesh?
What is the maximum error when interpolating on a mesh in which the ith of n points is given by (i/n)^s, and s is a carefully chosen mesh grading parameter? The typical reason why a non-uniform can lead to higher accuracy is that the PDE to solve is not of the form ut(x, t) = uxx(x, t), but of the form ut(x, t) = (D(x)ux(x, t))x.