Define fields with x and y coordinates and perform analysis combining these fields.

I have solution of 2 Fields defined by 1a and 1b in matrix. For each component x and y i have a matrix. To obtain final equation 5a as a combination of 1a and 1b i have been separately adding x components of 1a and 1b and y components of 1a and 1b to form the x and y components of 5a. Is there a way to define these equations in matlab so that matlab understands the x and y cordinates and i dont have to do the operations separately for each cordinates x and y ?

Answer 1

[Arnav]

Hi,

Assuming that the two fields are already represented as vectors, a simpler way to add these two fields is to simply use the + operator between them. MATLAB vectorizes the operation such that it is more efficient than individually adding the components. Vectorization also makes the resulting code more readable.

This can be done as shown below:

syms l phi beta z F_lm; 
x_hat = [1;0] ; y_hat = [0;1]; 
HE_odd = F_lm*(x_hat*sin(l*phi) + y_hat*cos(l*phi))*exp(1i*beta*z); 
HE_even = F_lm*(x_hat*cos(l*phi)  -y_hat*sin(l*phi))*exp(1i*beta*z); 
OAM_lm = HE_even + HE_odd % This operation is vectorized 

OAM_lm = 

Refer to the below documentation link to understand more about vectorization

https://www.mathworks.com/help/releases/R2019a/matlab/matlab_prog/vectorization.html