name: add-solver description: Add a new solver to the project user-invocable: true allowed-tools: Read, Write, Edit, Bash, Glob, Grep

Add Solver

Add a new numerical solver to the project.

Steps

1. Ask the user for the solver type/method (e.g., explicit FDM, MOL, FEM, etc.)
2. Read solvers/base.py to review the SolverBase interface
3. Create an appropriate subdirectory (e.g., solvers/fem/)
4. Implement the new solver inheriting from SolverBase:
   • Set the name class attribute
   • Implement solve(T0, r, dt, t_end, alpha) -> T_history
   • Handle r=0 singularity via L'Hopital's rule
   • Apply Neumann BC (r=0) and Dirichlet BC (r=1)
   • Use scipy.linalg.solve_banded for tridiagonal systems (performance)
5. Add tests in tests/test_solvers.py:
   • Basic operation test (temperature decreases via diffusion)
   • Boundary condition test
   • Nonlinear (alpha>0) test
6. Register the solver in app/run_benchmark.py SOLVERS list
7. Add stability constraints in policy/stability.py:
   • Determine if unconditionally stable or has CFL condition
   • Set temporal_order, spatial_order
   • Set alpha_max if there are nonlinearity limits
8. Verify all tests pass with python -m pytest tests/ -v
9. Run quick benchmark: python -m app.run_benchmark --alpha 0.5
10. Update HISTORY.md

Implementation Checklist

• Inherits from SolverBase
• name attribute set (lowercase, underscore-separated)
• solve() returns shape (nt+1, nr)
• r=0 singularity handled (L'Hopital)
• BC: T'(0)=0, T(1)=0
• Nonlinear chi computed correctly
• Registered in SOLVERS list
• Stability info in policy/stability.py
• Tests pass