Hi Ifechi,
To perform a 4D convolution of your node values with another similarly structured set of values without rearranging them into a 4D data-cube, you can use the following MATLAB example snippet:
% Define the size of the grid
N = 10; % Grid dimensions (N x N x N)
T = 1; % Number of time points
% Generate random test values for g and f
g_values = rand(N, N, N, T);
f_values = rand(N, N, N, T);
% Assuming g_values and f_values are N x T arrays for g(x,y,z,t) and f(x,y,z,t)
% Fourier transform of the response and source functions
G_fft = fftn(g_values);
F_fft = fftn(f_values);
% Element-wise multiplication in the Fourier domain (convolution theorem)
convolved_fft = G_fft .* F_fft;
% Inverse Fourier transform to get the convolved data
convolved_data = ifftn(convolved_fft);
% Display the size of the convolved data to verify
disp(size(convolved_data));
This code applies the convolution theorem using the Fast Fourier Transform (FFT) to efficiently compute the convolution across all dimensions. The “fftn” and “ifftn” functions handle the multi-dimensional aspect of your data.
Refer to the following documentation for more details:
- fftn: https://www.mathworks.com/help/matlab/ref/fftn.html.
- ifftn: https://www.mathworks.com/help/matlab/ref/ifftn.html.
Alternatively, if your mesh is sparse or you prefer not to use FFT, you can:
- Convolve your data iteratively over each dimension, one at a time.
- If your data is sparse, leverage MATLAB's sparse data structures to save memory and computation time.
- Create a custom convolution function tailored to your data structure, which could be more efficient for your specific application.
I hope this helps with your finite element (FE) modelling and Monte Carlo simulation comparison in MATLAB.
