Development of Serial and Parallel Algorithms forComputing the Electronic Structure of MaterialsUsing the Charge Patching Method

U tezi je predstavljena implementacija metode teorija funkcionala gustine (DFT) bazirana na metodi za sklapanje naelektrisanja (CPM) koja koristi bazise gausijanskih funkcija. Metod je baziran na pretpostavci da se elektronska gustina naelektrisanja velikih sistema, može predstaviti kao suma doprinosa pojedinačnih atoma, takozvanih motiva gustine naelektrisanja, koji se dobijaju računanjem malog prototip sistema. Talasna funkcija, kao i gustina naelektrisanja, se u našoj implementaciji reprezentuju uz pomoć bazise gausijanskih funkcija, dok se motivi opisuju korišćenjem prostornih koordinata. Uz pomoć procedure za minimizaciju se iz motiva opisanih koordinatama, dobija gustina naelektrisanja predstavljena u bazisu Gausijana. Implementacija serijskog programa pokazuje značajno poboljšanje u performansama u odnosu na prethodne implementacije bazirane na ravnim talasima. Ova implementacija rešava sistem od približno 1000 atoma na jednom procesorskom jezgru za svega nekoliko sati. Paralelna implementacija uz pomoć naprednih metoda paralelizacije i distribucije podataka omogućava rešavanje sistema od više desetina hiljada atoma. Najveći testirani sistem ima približno 20000 atoma i testiran je na 256 paralelnih procesa.We present the implementation of the density functional theory (DFT) based charge patching method (CPM) using the basis of Gaussian functions. The method is based on the assumption that the electronic charge density of a large system is the sum of contributions of individual atoms, so called charge density motifs, that are obtained from calculations of small prototype systems.In our implementation wave functions and electronic charge density are represented using the basis of Gaussian functions, while charge density motifs are represented using a real space grid. A constrained minimization procedure is used to obtain Gaussian basis representation of charge density from real space representation of motifs. The code based on this  implementation exhibits superior performance in comparison to previous implementation of the charge patching method using the basis of plane waves. It enables calculations of electronic structure of systems with around 1000 atoms on a single CPU core with computational time of just several hours. The parallel implementation enables calculations for the system with more than ten thousand atoms. The largest system tested has around 20000 atoms and was computed on 256 parallel processes