Research Interests

 Numerical analysis, scientific computing, variational problems and optimization   

  • Computational fluid dynamics, Navier-Stokes equations, free surface flows. Finite element methods, Immersed boundary methods. Applications to hydraulic engineering, glaciers, sedimentation, casting, and particle flows.
  • Non-smooth optimization, variational problems, calculus of variations, non-smooth generalized eigenvalue problems. Finite element methods.
  • Numerical methods for fully nonlinear elliptic equations. Least-squares methods, augmented Lagrangian algorithms, Monge-Ampère equation, Eikonal equation.
  • Computational methods for nonlinear dynamical systems coupled to global optimization. Numerical methods for ordinary differential equations, fast-slow decompositions.
  • Industrial applications.
  • Computational economics, Financial mathematics and applications.

Research activities

  • CFD and Free Surface Flows
    • Numerical Simulation of incompressible free surface flows surrounded by compressible gas with surface tension effects. Applications to mold casting, droplet dynamics, bubbles. Simulations of the evolution of alpine glaciers. Prediction of flooding in dam breaks. Simulation of viscoelatic flows and Bingham flows. Modeling of multiphase flows. Sedimentation processes, dam break flows and impulse waves. Industrial applications.
  • Computational Economics and Finance
    • Optimal portfolio investment strategies using Monge-Ampère approaches. Numerical methods. Nonlinear dynamics.
  • Non-Smooth Optimization, Fully/Implicitly Nonlinear Elliptic Equations and Generalized Eigenvalues Problems
    • Numerical methods for fully and implicitly nonlinear elliptic equations in two and three space dimensions, such as the Monge-Ampère equation, Eikonal equations, prescribed Jacobian equation, or the Sigma-2 problem.
    • Numerical methods for non-smooth eigenvalue problems and non-smooth problems from the Calculus of variations.
    • Numerical methods for eigenvalues problems arising in the determination of the best constants in Strauss and Nirenberg inequalities, as well as Korn inequalities, in the scalar and vectorial cases. Application to Bingham flows.
    • Augmented Lagrangian methods for determination of load capacity ratio in stress analysis.
    • Augmented Lagrangian methods and over-relaxation methods for smoothing and denoising of signals. Application to free surface flows and image denoising with PDE-based techniques.
    • Determination of the best constants in Sobolev injections.
    • Numerical simulation of non-smooth advection-diffusion problems. Application to sand mechanics and water deposition.
  • Optimization and Numerical ODEs
    • Computational methods for thermodynamical equilibrium problems. Primal-dual interior-point or active sets techniques. Sequential quadratic programming methods.
    • Numerical methods for the computation of the convex hull/convex envelope of the Gibbs free energy.
    • Numerical solution of differential-algebraic equations. Numerical methods for event detections in discontinuous ODEs arising in optimization-constrained systems of ODEs. Coupling of numerical methods for ODes with optimization methods.
    • Numerical linear algebra techniques for the solution of large structured systems of DAEs. Development of decomposition techniques for weakly coupled subsystems. Reduction methods into fast and slow subsystems.
    • Time splitting algorithms for chemical kinetics problems.
Sand cones, Silver temple, Kyoto, 2009
Orthogonal maps and origamis (w. D. Gourzoulidis), 2019