Understand the solve pipeline#

The solve pipeline is the internal call chain executed each time Solve() is called. Every _Simu in the EasyFEA.Simulations namespace runs the same pipeline, which lives in EasyFEA.Simulations._Simu. This guide traces it from the moment you call Solve() to the moment the solution is stored, aimed at advanced or curious users who want to understand the internals without reading the full source.

Note

The internals described here live in EasyFEA/Simulations/_simu.py, EasyFEA/Simulations/Solvers.py, and EasyFEA/FEM/_forms.py. The single-underscore methods (e.g. _Solver_Apply_Dirichlet) are advanced API; the double-underscore ones are private and should never be called directly.

Overview#

Every call to Solve() performs the same three high-level operations:

  1. Build — assemble the global sparse matrices (\(\Krm, \Crm, \Mrm, \Frm\)) from element integrals (skipped if nothing changed since the last solve).

  2. Apply BCs — add Neumann contributions to the right-hand side, then enforce Dirichlet constraints to constrain the system \(\Arm \, \xrm = \brm\).

  3. Solve — pass \(\Arm \, \xrm = \brm\) to the linear algebra backend (scipy, PETSc, pypardiso) and store the solution.

For non-linear problems (simu.isNonLinear = True), steps 1–3 are wrapped in a Newton–Raphson loop that repeats until the residual converges — see _Solver_Solve_Newton_Raphson() for more information.

Use EasyFEA with a Python debugger and an IDE#

To step through the solve pipeline with a debugger, install EasyFEA in editable mode so that the source files are used directly (no compiled copies):

git clone https://github.com/matnoel/EasyFEA.git
cd EasyFEA
python -m pip install -e .

With an editable install, breakpoints set inside EasyFEA/Simulations/_simu.py, EasyFEA/FEM/_forms.py, or any other source file will be hit normally.

Note

In editable mode, code-completion may stop working in some IDEs because the package is not placed in site-packages. To restore it:

  • VS Code / Pylance: add the repository root (the folder containing EasyFEA/) to Python › Analysis: Extra Paths in the Pylance extension settings, or add <repo>/EasyFEA/ to your PYTHONPATH.

  • PyCharm: mark the repository root as a Sources Root (right-click → Mark Directory as → Sources Root).

You could start by debugging the HelloWorld example.

EasyFEA beyond forward solves#

The FEM infrastructure — mesh.Get_* functions, FeArray arithmetic, Gauss-point integration — is not restricted to _Simu subclasses. You can use it directly to evaluate arbitrary integrals or construct custom operators over a mesh.

DIC (Digital Image Correlation) is the canonical example: it is a full analysis class built on the same mesh and integration machinery, but it never solves a linear system in the traditional sense. Instead it assembles correlation operators directly from mesh.Get_* functions and minimises a correlation functional. See Digital Image Correlation (DIC) analyses for worked examples.

This means EasyFEA can serve as a general-purpose FEM toolkit for any computation that benefits from structured Gauss-point integration over a mesh.