High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915322423934976 |
|---|---|
| author | Li, Jinze Li, Hua Yu, Kaiping Zhao, Rui |
| author_facet | Li, Jinze Li, Hua Yu, Kaiping Zhao, Rui |
| contents | This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed $ s $-sub-step implicit method with $ s\le6 $ can reach $ s $th-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present $ s $-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors' previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13820 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems Li, Jinze Li, Hua Yu, Kaiping Zhao, Rui Numerical Analysis 34-04, 74-10, 74H15 This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed $ s $-sub-step implicit method with $ s\le6 $ can reach $ s $th-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present $ s $-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors' previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms. |
| title | High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems |
| topic | Numerical Analysis 34-04, 74-10, 74H15 |
| url | https://arxiv.org/abs/2209.13820 |