General structure for PDE model implementation using finite element assembly, boundary conditions, sparse solvers, time stepping, and verification workflows.
Clean benchmark direction for verifying elliptic and parabolic PDE solvers using exact solutions, error norms, and convergence tables.
Research direction involving interface evolution, heat/solute coupling, phase-field variables, and stability-aware numerical schemes.
Selected demo work can show how MATLAB research workflows translate into Python/SciPy sparse-matrix implementations.
Implementation direction for semi-implicit time stepping, stabilized schemes, and coupled PDE model workflows.
Use of diagrams, 3D reasoning, vector calculus, and structured explanations to communicate mathematical ideas clearly.