Welcome to my first academic thought post! This is where I’ll share insights and reflections on my research.

Current Research Focus

My research centers on several key areas:

  1. Topology Optimization - Developing efficient algorithms for large-scale problems
  2. Reduced-Order Modeling - Creating adaptive models that balance accuracy and computational cost
  3. Thermal Systems - Applying optimization techniques to phase change materials

Recent Insights

Working on the primal-dual approach has revealed some interesting properties:

  • The on-the-fly nature allows for dynamic adaptation
  • Multi-fidelity strategies provide excellent computational savings
  • The framework extends naturally to various physics problems

Mathematical Framework

The core optimization problem can be expressed as:

minimize   J(u, ρ)
subject to  K(ρ)u = f
            0 ≤ ρ ≤ 1

Where ρ represents the design variables and u the state field.

Future Directions

I’m particularly excited about:

  • Integration with machine learning techniques
  • Applications to thermal energy storage systems
  • Handling non-linear contact problems like Kapitza resistance

Collaboration Opportunities

If you’re working on related topics, feel free to reach out! I’m always interested in discussing:

  • PDE-constrained optimization
  • Reduced-order modeling techniques
  • AI for scientific computing

More thoughts coming soon!