Denis Ridzal

Research

Computational and applied mathematics, numerical analysis, numerical optimization, partial differential equations (PDEs), scientific software development, high-performance computing (HPC), applications in physical science and engineering.

• Numerical optimization:
  Large-scale nonlinear programming; PDE-constrained optimization; stochastic optimization; matrix-free optimization; sequential quadratic programming (SQP); solvers and preconditioners for optimality systems.
• Numerical analysis and PDEs:
  Advanced compatible and high-order discretizations; finite element analysis; optimization-based property-preserving methods for hyperbolic problems.
• Scientific software development and HPC:
  Performance-portable and scalable implementations of numerical optimization algorithms through modern C++ programming; low-memory parallel computing through data compression; mixed-precision architectures for numerical optimization; extreme-scale PDE-constrained optimization.
• Applications:
  Optimal control, optimal design and inverse problems for solid mechanics, fluid dynamics, electromagnetics, semiconductor physics, electrical circuits, geophysics; additive manufacturing, shape optimization, topology optimization; sensing and image processing; trajectory optimization; analog computing; computational mesh optimization.