High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems
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...
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| Vydáno v: | Archive of applied mechanics (1991) Ročník 94; číslo 8; s. 2285 - 2334 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.08.2024
Springer Nature B.V |
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| ISSN: | 0939-1533, 1432-0681 |
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| Abstract | 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
≤
6
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. |
|---|---|
| AbstractList | 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
≤
6
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. 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≤6 can reach sth-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. |
| Author | Li, Hua Li, Jinze Yu, Kaiping Zhao, Rui |
| Author_xml | – sequence: 1 givenname: Jinze surname: Li fullname: Li, Jinze organization: School of Astronautics, Harbin Institute of Technology – sequence: 2 givenname: Hua surname: Li fullname: Li, Hua organization: School of Mechanical and Aerospace Engineering, Nanyang Technological University – sequence: 3 givenname: Kaiping surname: Yu fullname: Yu, Kaiping email: kaipingyu1968@gmail.com organization: School of Astronautics, Harbin Institute of Technology – sequence: 4 givenname: Rui surname: Zhao fullname: Zhao, Rui organization: School of Astronautics, Harbin Institute of Technology |
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| Keywords | Optimal spectral features Dissipation control High-order accuracy ESDIRK Implicit time integration |
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| SubjectTerms | Accuracy Algorithms Classical Mechanics Dissipation Engineering Forced vibration Implicit methods Load Original Runge-Kutta method Stiffness matrix Theoretical and Applied Mechanics Velocity |
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| Title | High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems |
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