Research areas

Numerical Analysis, Scientific Computing, High Performance Computing, Numerical Simulation of Partial Differential Equations
Topology Optimization, Conjugate Heat Transfer
Optimization Techniques

Research areas

My research develops predictable and efficient algorithms for time-dependent partial differential equations (PDEs), with a strong emphasis on advanced discretizations methods and high-performance computing scalability. I work at the intersection of numerical analysis, numerical linear algebra, and PDE-constrained optimization, designing fast and reliable solvers using tailored preconditioners and parallel-in-time techniques. My contributions include space–time spectral methods that possess superior convergence properties, ideal for fluids and materials science applications. I have also worked on the convergence theory of optimization methods that underlie machine-learning algorithms.

I collaborate with academia and industry on provably stable algorithms for fluid–thermal coupling, developing stable space-time partitioned and monolithic schemes for conjugate heat transfer problems and topology optimization of transient heat conduction. These tools support energy-sustainable engineering by enabling thermal designs that improve heat-exchange efficiency and cut cooling and computation costs in large-scale structural design.