Improving the efficiency of repmat and function with inputs of different sizes

I wrote a code that performs some calculation at each time step (Euler method). In the calculation I have groups of elements, which in principle can have different sizes. Some quantities need to be calculated per each element (X2_elements, Y_elements), other quantities in principle could be calculated only per each group (X, Z).

The code works correctly, but I identified two chockepoints that unreasonably reduce the computational speed. I believe the issue with both problems is that I am manipulating matrices and applying functions to them in an inefficient way.

Please find below the test code, where I highlighted the two Problems.

Additional notes:

-I do not really need the matrices X_elements and Z_matrices; I calculate them only to apply them together with Y_elements (which I do need) in myFunction.

-typically the number of elements in each group is 20 to 60 elements.

I'd like to find:

1. a more efficient way to calculate X_elements2, which at the moment uses repmat in a for-loop.

2. a more efficient to apply myFunction to the inputs, probably using the much smaller X and Z, instead of X_elements and Z_elements.

Thank you!

% Inputs
% nGroups: number of groups
% nElements: total number of elements
% nE: (1 x nGroups) vector indicating how many elements there are in each group
% elementToGroup: (1 x nElements) vector indicating to which group each element belongs
% Z: (1 x nGroups) vector with constant values (never updated during the calculation)
% fScalar: scalar parameter

% Initialization
X=zeros(nTime,nGroups);
X2=zeros(nTime,nGroups);
X_elements=zeros(nTime,nElements);
X_elements2=zeros(nTime,nElements);
Y_elements=zeros(nTime,nElements);
W_elements=zeros(nTime,nElements);
% Make cell structure containing indices of elements in each group
belongToG=cell(nGroups,1);
for g=1:nGroups
  belongToG{g}=find(elementToGroup==g);
end
% Calculate once Z_elements
Z_elements=zeros(1,nElements);
for g=1:nGroups
  Z_elements(belongToGroup{g})=Z(g);
end

% Main for-loop
for n=1:nTime
  % do stuff... and a new row of the X, X2, Y_elements matrices are calculated
  % Problem 1: Write values in all elements of each group
  for g=1:nGroups
    X_elements(n,belongToGroup{g})=repmat(X(n,g),1,nE(g)); % slow! :(
    X_elements2(n,belongToGroup{g})=repmat(X2(n,g),1,nE(g)); % slow! :(
  end
  % do more stuff...
  % Problem 2: Use the values in the new row of the matrices in a function
  W_elements(n,:)=myFunction(X_elements(n,:),Y_elements(n,:),Z_elements,fScalar); % slow :(
  % do more stuff...
end