Research groups
Department of Applied Mathematics
Numerical analysis and HPC (High Performance Computing)
Numerical analysis deals with the search for approximate solutions to demanding mathematical tasks such as time-space partial differential equations describing the physical field. We focus on the development of methods whose computational complexity is directly proportional to the number of valid digits that we want to have in the solution. Tasks are discretized to a sequence of systems of linear equations, the size of which is billions of equations of a billion unknown. These systems must be addressed on a parallel computer (supercomputers) means HPC (High Performance Computing). Our research reflects the development of supercomputers. With regard to computer architecture, we change the computing paradigm, for example, to minimize access to memory. Research is mostly conducted by specific industrial applications. The development of new numerical methods also includes rigorous mathematical analysis in our group such as optimal convergence (constant number of iterations independent of the size of the task), numerical stability (methods in double, single and Half Precision) and parallel scalability of methods. We are currently developing open-source software library implementing parallel methods of final (FETI) and border (Beti) elements on graphic accelerators. We also develop real-time optimization methods in robotics. We are dealing with demanding molecular simulations.
Research topics:
- In parallel scalable methods for dealing with heat, acoustics, electromagnetism and contact tasks - feti, beti, parallel bem
- Development of software open-source libraries.
- Optimal algorithms of quadratic programming
- Using Methods of Dusty Optimization for Shape Optimization for Flow Eatures
- Use of optimization methods in robotics.
- Methods (non -adhesive) molecular dynamics
- Monte Carlo methods in molecular physics
- Motivation Industrial Problems eg Ultrasonic Aircraft Defects in cooperation with Honeywell
Group leader: doc. Ing. Dalibor Lukáš, Ph.D.
Laboratories
We are involved in the development of efficient algorithms to solve the tasks of quadratic programming, such as the tasks of contact mechanics or the tasks of machine learning SVM (Support Vector Machines) type. We implement these algorithms in our Permon Library (permon.vsb.cz), which builds on many scientific communities used by the PetSC library. We are also developing and implementing methods of feti distribution of the type of type, which today is one of the most effective massively parallel solutions of systems of linear equations. We are dealing with applications, modeling of hydromechanical processes in rocks or automated identification of forest fires from satellite images.
In the field of border element method, we are engaged in the implementation of border elements on GPU accelerators. We achieve 100 times the acceleration of the calculation already on common graphics cards on the PC. The key component of our software is the new operator pre-term border-element matrices. We also deal with time-space discretizations for the 3D equation of heat and wave equation.
In the use of optimization methods in robotics, we deal with robot guidance tasks to a prescribed position using an industrial camera calibration pattern. In the area of use of non -haired methods for solving the tasks of flow we use & i
Gallery of laboratories
