COMSOL Multiphysics™

elinterp
Purpose
elinterp
Declare interpolation functions.
Syntax
Description
el.elem = 'elinterp'
el.name = fname
el.x = xgrid
el.y = ygrid
el.z = zgrid
el.data = fdata
el.method = 'nearest' | 'linear' | 'cubic' | 'spline'
The elinterp element declares an interpolation function based on a 1D, 2D or 3D
data set provided by the user. Interpolation functions take one, two or three
arguments, depending on the dimension of the data set.
The xgrid, ygrid and zgrid parameters are cell arrays of points, sorted in
increasing order, where the data is given. Depending on the dimensions, not all
fields are used. For 1D interpolation, the fdata parameter is a cell array of values
corresponding to the points in el.x. In the 2D case, the size of fdata is
length(xgrid)*length(ygrid), with x increasing fastest, and similarly in 3D.
There are four interpolation methods to choose from. Nearest neighbor and linear
interpolation are available in all dimensions, while 'cubic' and 'spline' can only
be used for interpolation in 1D data sets. The difference between the latter two is,
generally speaking, that 'cubic' preserves monotonicity and does not overshoot at
the cost of discontinuous second derivatives at the tying points.
Cautionary
Examples
Interpolation is provided only for real numbers. To interpolate complex numbers,
real and imaginary parts have to be treated separately.
Given the matrices x (1-by-m), y (1-by-n) and F (m-by-n), create a corresponding
interpolation element declaring a function f(x,y).
cellX = cell(1,m);
for i=1:m
cellX{i} = num2str(x(i));
end
cellY = cell(1,n);
for i=1:n
cellY{i} = num2str(y(i));
end
cellF = cell(1,m*n);
for i=1:m*n
cellF{i} = num2str(F(i));
end
84 | CHAPTER 1: COMMAND REFERENCE