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In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. We compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.
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Adomian decomposition method reformulated using dimensionless nonlinear perturbation theory
The Adomian decomposition method (ADM) is a universal approach to solving governing equations in various engineering and technological applications. The applicability of the ADM is almost limitless due to its universal applicability, but its convergence rate and numerical accuracy are sensitive to the number of truncated terms in series solutions. More importantly, Adomian formalism still holds unresolved issues regarding the mismatch of the order of the expansion parameter. The current work provides an in-depth analysis of Adomian's decomposition method, Lyapunov's stability theory, and the nonlinear perturbation theory to resolve the fundamental mismatch with physical interpretation.
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- Award ID(s):
- 2034824
- PAR ID:
- 10581954
- Publisher / Repository:
- https://arxiv.org/abs/2501.10398
- Date Published:
- Format(s):
- Medium: X
- Institution:
- University of Hawaii at Manoa
- Sponsoring Org:
- National Science Foundation
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