Applied mathematics and computer science & IT4Innovations

Department has research activities in development, analysis, implementation and application of models and numerical methods motivated by geo-applications. The focus is on elastic and elasto-plastic models, flow in porous media and heat transport including advanced topics as coupling these models (multiphysics), inverse analysis, limit load analysis and dealing with uncertainty including bayesian inverse. Special interest is in iterative solvers and high-performance computing methods for demanding applications.

Research directions

  • Setting of mathematical models
  • Flow problems in porous media with variable saturation
  • Formulation and numerical modeling of hydromechanical processes in continuum with failures
  • Application of THM models for description of saturation processes in sealing barriers of underground spent nuclear fuel storage
  • Analysis, discretization and solution of implicit constitutive problems
  • Numerical solution using the finite element method, semi-smooth Newton's method with damping, continuous and adaptive techniques
  • Analysis of limit load by convex optimization, duality and reliable númerical methods
  • Development of the Matlab library for solving elastic-plastic problems and limit analysis
  • Geotechnical stability assessment using limit analysis, shear strength reduction and with incorporation of porous media
  • Schwarz-type domain decomposition methods with applications for solving systems with symmetric positive definite matrix and saddle point systems
  • FETI domain decomposition methods
  • Preconditioning for saddle point matrices
  • Newton's methods, continuation
  • Iterative techniques for model coupling in multiphysics (especially in hydro-mechanics)
  • Methods for solving problems arising from the usage of stochastic Galerkin method
  • Algorithms enabling massive parallelization and high performance computing
  • Solving inverse problems for identification of material parameters and unknown loads
  • Solving optimal control problems with PDE (partial differential equations) constraints
  • Development of Bayesian inversion technique with construction and using a surrogate model; analysis of stochastic inversion with the aid of Metropolis-Hastings delayed algorithm
  • Simulation of processes described by partial differential equations with uncertain input data by stochastic Galerkin method
  • Determination of initial stress around tunnels using inverse analysis and elastic-plastic models
  • Numerical homogenization based on linear elasticity
  • Identification of material parameters based on inverse analysis
  • Creation of finite element meshes based on digital image processing of computational tomography
  • Determination of composite strength using perfect plasticity and limit load analysis
  • Development of experimental codes in Comsol for simulations of complex systems with multi-physical phenomena and their mutual coupling
  • Development of the PERMON library for solving quadratic programming problems
  • Program implementation of the in-house GEM software for modeling of thermo-mechanical processes
  • Development of in-house codes in Matlab for solving elasto-plastic problems and for geotechnical stability analysis