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dc.contributor.advisorTemizer, İlker
dc.contributor.authorKaraca, Kaan
dc.date.accessioned2021-09-13T11:04:39Z
dc.date.available2021-09-13T11:04:39Z
dc.date.copyright2021-09
dc.date.issued2021-09
dc.date.submitted2021-09-10
dc.identifier.urihttp://hdl.handle.net/11693/76508
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Master's): Bilkent University, Mechanical Engineering, İhsan Doğramacı Bilkent University, 2021.en_US
dc.descriptionIncludes bibliographical references (leaves 61-66).en_US
dc.description.abstractVariationally consistent atomic forces are computed for Kohn-Sham density func-tional theory (DFT) solved via a higher order finite element (FEM) framework. Force expressions are derived for pseudopotential and all-electron settings in a unified structure. Generalized gradient approximations are additionally ad-dressed together with nonlinear core correction in the same pseudopotential set-ting. Classical Lagrange basis functions are used as well as non-uniform rational B-spline (NURBS) basis in isogeometric analysis concept. Calculated forces have been shown to be variationally consistent with energies. Reference force values have been generated through Kohn-Sham DFT software packages and accuracy of forces is verified. Finally, geometry optimizations have been conducted. For this purpose, several optimization algorithms are tested for their robustness, compu-tational cost and ease of implementation. Fast inertial relaxation engine (FIRE) algorithm is eventually chosen as the optimization algorithm. Variationally con-sistent forces allow conducting geometry optimization even at coarse meshes, finding the energy minima of any particular setup. Optimized ground state ge-ometries have also been compared with those obtained from reference software packages, showing very close agreement with values reported in literature.en_US
dc.description.statementofresponsibilityby Kaan Karacaen_US
dc.format.extentxii, 67 leaves : illustrations, charts ; 30 cm.en_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectKohn-Sham density functional theoryen_US
dc.subjectFinite element methoden_US
dc.subjectIsogeo-metric analysisen_US
dc.subjectForce calculationen_US
dc.subjectGeometry optimizationen_US
dc.titleGeometry optimization with variationally consistent forces using higher-order finite element methods in Kohn-Sham density functional theory calculationsen_US
dc.title.alternativeYüksek dereceli sonlu elemanlar yöntemi tabanlı Kohn-Sham yoğunluk fonksiyonel kuramı çerçevesinde varyasyonel tutarlı kuvvetlerle geometri eniyilemesien_US
dc.typeThesisen_US
dc.departmentDepartment of Mechanical Engineeringen_US
dc.publisherBilkent Universityen_US
dc.description.degreeM.S.en_US
dc.identifier.itemidB130945


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