Public case studies · private framework

Projects

These projects are designed as public technical case studies. The full source code may remain private when it is part of research, publication work, or the reusable FEM framework.

Core project

Reusable MATLAB FEM Framework

A general finite element research framework for implementing PDE models using reusable routines for mesh data, assembly, boundary conditions, time stepping, solver calls, verification, and plotting.

Sparse matrix assembly and model-dependent weak forms
Dirichlet/Neumann boundary-condition handling
Manufactured-solution verification workflow
Convergence tables and publication-style plots

Source code note: the framework is private because it is part of a reusable research and future company asset.

MATLABFEMPDEsSparse systems

Verification study

2D Poisson Equation FEM Verification

A clean elliptic PDE benchmark showing weak-form derivation, FEM discretization, manufactured solution, error computation, and convergence behavior.

Model problem on a two-dimensional computational domain
Linear finite element approximation
Exact solution used to verify accuracy
Solution/error plots and convergence table

PoissonMMSConvergence

Simulation study

Heat and Diffusion FEM Simulation

A parabolic PDE case study demonstrating transient simulation, time stepping, diffusion-dominated behavior, and visualization of evolving scalar fields.

Transient heat/diffusion equation
Implicit and semi-implicit numerical strategies
Field evolution plots
Verification-ready workflow

Heat transferDiffusionTime stepping

Research direction

Phase-Field Solidification Demo

A simplified public-facing demonstration of interface evolution and phase-field-type modeling, separated from unpublished research code.

Interface evolution and phase-field variables
Materials simulation direction
Parameter studies and scientific visualization
Connection to rapid solidification and multiphysics coupling

Source code note: public material should show figures, reports, and results only until publication/IP boundaries are clear.

Phase fieldMaterialsMultiphysics

Suggested case-study format

Section	What to show publicly
Problem	Governing PDE, domain, boundary conditions, and physical context.
Method	Weak form, finite element space, time discretization if needed, and solver strategy.
Verification	Manufactured solution, error norms, convergence table, and interpretation.
Results	Figures, plots, interface evolution, field visualization, and summary.
Code note	State that implementation is private when related to research/IP.