PDE static solution fails with singular Jacobian error

Hello,

My colleague and I have been using Matlab's PDE solver to model cooling issues for a sample in our homebuilt cryostat. Recently, we discovered that depending on the initial guess given, our static solution will give various nonphysical results. This has been solved by reducing the residual tolerance, but we want to make sure we understand why this is happening. I have a simplified version of the code attached to help clarify the issues.

My questions are:

1. The solution is sensitive to the choice of initial guess. How important it is for the initial guess to satisfy the boundary conditions? If we use "ta" as the initial condition on line 29, the program fails with singular Jacobian error at the first iteration in solvepde, but if we use "tf" as the initial condition on line 29, then the program runs without error.

2. The function pdenonlin allows one to use a "lumped" approximation for the Jacobian. The option is available from the GUI pde modeler app. However, only full Jacobian is available in solvepde through PDEModel objects. What are the advantages of full Jacobian over "lumped" approximation? Is it still possible to request a "lumped" Jacobian through solvepde?

Thanks,

Ryan