Based on your description, it appears that your model is correctly calculating the pressure distribution, but the resulting deformation is not as expected. Given that the influence coefficients are based on Love's equations and that you've verified your calculations, it's unlikely that the issue lies there.

Instead, it seems that the problem might be related to how the deformation field is being calculated or represented. Here are a few potential issues and solutions to consider:

Without the specific code and data, it's difficult to pinpoint the exact issue, but hopefully, these points can guide you towards a solution. If you continue to have issues, consider contacting colleagues or other researchers in your field, or posting your problem to a dedicated scientific computing forum. Good luck with your research!

Joshua Depiver Thank you for the reply, I really appreciate it. I think the problem is with my Influence Coefficients. I calculate the first row of the influence coefficient matrix with respect to x1 and y1 which is at the corner of the domain (picture attached). I then construct the entire matrix using toeplitz function. But the probelm is influence coefficient far from the corners are not what they should be (picture attached) this is because of the corner effect of the first row. Whereas if I calculate the first row with respect to xn/2 and yn/2 (center node) the influence coefficients near the edges of the domain are not correct and show 'continued influence' on the other edge of the domain (picture 3).

Influence coefficients are used in numerical simulations to determine how much influence a given node or point in the domain has on other nodes or points. These coefficients are often calculated based on the nodes' relative positions and the system's physical laws, such as the heat equation or Navier-Stokes equations for fluid dynamics.

As you've noticed, one common issue with influence coefficients is handling the boundaries or corners of the domain. In many cases, the influence coefficients near the boundaries will differ from those in the interior because the boundary conditions affect the system's behaviour.

One way to handle this is by using different formulas or methods to calculate the influence coefficients near the boundaries and interior. For example, you might calculate the first row of the influence coefficient matrix using x1 and y1 for the corners, and then use a different method for the interior points.

Another potential issue is that some numerical methods assume periodic boundary conditions, meaning that the system wraps around from one domain edge to the other. As you've described, this can result in 'continued influence' on the other edge of the domain. If your system doesn't have periodic boundary conditions, you might need to use a different method that properly handles the actual boundary conditions of your system.

It's hard to give more detailed advice without knowing the specifics of your system and the method you're using. However, I hope this gives you a starting point for understanding and resolving your issues.