What algorithm does Matlab use to solve an FEM structural model in the PDE toolbox?

I'm solving a FEM (structural static) using Matlab's PDE Toolbox, and I'm trying to figure out how it actually solves for the displacements in the mesh (just for my own learning purposes). The object model.SolverOptions has properties for an ODE solver, a nonlinear solver, and a lanczos solver, but I believe that my model is a linear PDE, which would fall under none of those categories. I tried printing out statistics to just see if the algorithm is iterative or not, but it won't display any. The solver options documentation even says just that: "For linear stationary problems, there is no statistics and convergence report to display." Does this imply that the solver is non-iterative? I’ve looked through the Partial Differential Equation Toolbox User’s guide here: Partial Differential Equation Toolbox User's Guide (mathworks.com) but can only find information on the nonlinear solver. Are there any other sources I can look to to figure out what algorithm is being used, or is the algorithm proprietary?

Answer 1

[Ayush]

Hey Grace,

I understand that you are using PDE toolbox and solving a FEM. You want to learn how it solves for the displacements in the mesh.

For linear problems, the PDE Toolbox uses the direct sparse solver by default which is non-iterative in nature. This solver can handle large and sparse systems of equations efficiently and accurately.

For more help on solving a PDE, you can also refer to this MathWorks documentation link : https://in.mathworks.com/help/pde/ug/pde.pdemodel.solvepde.html

I hope this information helps!