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Accelerating the Computation of Density Functional Theory's Correlation Energy under Random Phase Approximations
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Accelerating the Computation of Density Functional Theory's Correlation Energy under Random Phase Approximations. |
| 개인저자 | Thicke, Kyle. |
| 단체저자명 | Duke University. Mathematics. |
| 발행사항 | [S.l.]: Duke University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 124 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088333891 |
| 학위논문주기 | Thesis (Ph.D.)--Duke University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Lu, Jianfeng. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | We propose novel algorithms for the fast computation of density functional theory's exchange-correlation energy in both the particle-hole and particle-particle random phase approximations (phRPA and ppRPA). For phRPA, we propose a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in the density response function by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the interpolative separable density fitting algorithm to further reduce the computational cost in a way analogous to that of the resolution of identity method.For ppRPA, we propose an algorithm based on stochastic trace estimation. A contour integral is used to break up the dependence between orbitals. The logarithm is expanded into a polynomial, and a variant of the Hutchinson algorithm is proposed to find the trace of the polynomial. This modification of the Hutchinson algorithm allows us to use the structure of the problem to compute each Hutchinson iteration in only quadratic time. This is a large asymptotic improvement over the previous state-of-the-art quartic-scaling method and over the naive sextic-scaling method. |
| 일반주제명 | Applied mathematics. Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
