0543166 20240103225916.620210614235959.9 2 s. E cav_un_epca*054316561-62SozopolInstitute of Information and Communication Technologies, Bulgarian Academy of Sciences2021 cav_un_auth*0100790 Matonoha Ctirad UIVT-O Oddělení výpočetní matematiky Department of Computational Mathematics Department of Computational Mathematics Ústav informatiky AV ČR, v. v. i. cav_un_auth*0410335 Moskovka A. CZ K cav_un_auth*0292941 Valdman Jan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://parallel.bas.bg/Conferences/SciCom21/lssc21.pdf Many problems in science and engineering have their mathematical formulation which leads to solving an operator equation Au = f , u ∈ M , f ∈ H , (1) where H is a Hilbert (or Banach) space, M is a subspace of H, u is a solution of (1) and A is an operator on M. In particular, we will focus on differential operators. There are a lot of methods for solving (1) and one of them is the so called variational approach which is based on finding the minimum of corresponding energy functional. In our text we represent the variational principle for solving some particular problems using a finite elements method (FEM) for discretization of energy functionals. Minimization procedures of energy functionals require the knowledge of a gradient. If an exact gradient form is not available or difficult to compute, a numerical approximation can be assembled locally. The key feature is the sparsity of Hessian matrix which significantly affects the time and memory demands of evaluations cav_un_auth*0410336 LSSC 2021: International Conference on Large-Scale Scientific Computations /13./ 20210607 20210611 Sozopol BG 2022 4 O 4o 20231122145756.9 RVO:67985807 http://hdl.handle.net/11104/0320442 cav_un_auth*0295079 Západočeská univerzita v Plzni ZČU CZ S 2021 Soubory v repozitáři: 0543166-aw.pdf SCOPUS PUBMED WOS cav_un_epca*0543165 Large-Scale Scientific Computations LSSC’21. Scientific Program, Abstracts, List of Participants 61 62 Sozopol Institute of Information and Communication Technologies, Bulgarian Academy of Sciences 2021