Solving Coupled Cluster Equations by the Newton Krylov Method
| Autor: | Jiri Brabec, Libor Veis, Karol Kowalski, Chao Yang, David B. Williams-Young |
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| Rok vydání: | 2020 |
| Předmět: |
Iterative method
DIIS 010402 general chemistry Residual 01 natural sciences lcsh:Chemistry symbols.namesake couple cluster approximation 0103 physical sciences Convergence (routing) nonlinear solver Applied mathematics Original Research Mathematics 010304 chemical physics precondition Finite difference Newton-Krylov method General Chemistry Generalized minimal residual method 0104 chemical sciences Chemistry Coupled cluster lcsh:QD1-999 Jacobian matrix and determinant symbols |
| Zdroj: | Frontiers in Chemistry Frontiers in Chemistry, Vol 8 (2020) |
| ISSN: | 2296-2646 |
| DOI: | 10.3389/fchem.2020.590184 |
| Popis: | We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples. |
| Databáze: | OpenAIRE |
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