Title:
Block Iterative Methods with Applications to Density Functional Theory
Block Iterative Methods with Applications to Density Functional Theory
Author(s)
Shah, Shikhar
Advisor(s)
Chow, Edmond
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Abstract
A novel, cubic-scaling algorithm for computing the electronic correlation energy in density functional theory via the random phase approximation was proposed. The key computational kernel involves solving a family of large, sparse, and complex block linear systems. A short-term recurrence block Krylov subspace method was proposed to solve this family of linear systems and yields both a short time-to-solution and good parallel efficiency. Efficiency losses arising from an emergent load imbalance vanish when a shifted Laplacian preconditioner was introduced. A second novel algorithm was also proposed by leveraging block Krylov subspace methods to perform a functional trace approximation. This alternative algorithm is also cubic-scaling and most viable when higher levels of parallelism are available or required. Additionally, two adjacent topics were investigated. First, a method for choosing a robust low degree polynomial preconditioner was proposed. In situations where a random right-hand side vector produces a poor preconditioner, such as for highly non-normal matrices, this novel method is preferable. Second, a method for avoiding exact diagonalization in nonlinear polynomial-filtered subspace iteration was proposed. This approximate diagonalization was significantly faster than exact counterparts while not adversely impacting the convergence of the nonlinear subspace iteration procedure.
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Date Issued
2024-07-27
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Text
Resource Subtype
Dissertation