Tomáš Vejchodský

Grants
- Methods of higher order of accuracy for solution of multi-physics coupled problems (IAA100760702)
  from 01/01/2007 to 31/12/2011 investigator
- The design of efficient numerical methods for computer simulations of large nonlinear and associated transient problems belongs among the most recent topics in the sphere of technical and scientific computing. Examples include processing solid and liquid metals by electromagnetic field,
  problems of thermoelasticity and termoplasticity, fluid interaction with solid structures and others. The difficulty of coupled problems stems from the fact that various components of solutions exhibit specific characters, such as boundary layers in fluids or singularities in electromagnetic fields. Efficient and accurate solution of these problems requires the representation of various components by geometrically different meshes. From the mathematical point of view, various solution components belong to different Hilbert spaces and, therefore, their approximations require various types of finite elements. For each solution component we use the modern hp-adaptive version of the finite element method (hp-FEM), which is known for its exponential convergence.
- Advanced algorithms for solution of coupled problems in electromagnetism (102/07/0496)
  from 01/01/2007 to 31/12/2009 investigator
- The project resulted in internationally recognized results in the development and implementation of advanced algorithms for numerical modeling of coupled problems in the field of heavy current electrical engineering and electrotechnics. These tasks are characterized by an interaction of several physical fields. Characterization of such interactions is essential for reliable and economical design. Members of the research team focused primarily on advanced finite element method of higher order accuracy (hp-FEM) and the selected method of integral and integro-differential equations. The obtained were published in Dolezel, I., Karban, P. Solin, P.: Integral Methods in Low-Frequency Electromagnetics. Wiley, Hoboken, NJ, UA (2009), 388 pages.
- Mesh adaptivity for numerical solution of parabolic partial differential equations (201/04/P021)
  from 01/01/2003 to 31/12/2006 main investigator
- Mesh adaptivity for numerical solution of parabolic partial differential equations