A suite of second-order composite sub-step explicit algorithms with controllable numerical dissipation and maximal stability bounds
•This paper constructs and analyzes a composite s-sub-step explicit method.•Seven explicit schemes in the present method are developed and compared.•Each explicit scheme is second-order accurate and provides maximal stability bound.•Each explicit scheme (s>1) can control numerical dissipation at...
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| Published in: | Applied mathematical modelling Vol. 114; pp. 601 - 626 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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01.02.2023
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| ISSN: | 0307-904X |
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| Abstract | •This paper constructs and analyzes a composite s-sub-step explicit method.•Seven explicit schemes in the present method are developed and compared.•Each explicit scheme is second-order accurate and provides maximal stability bound.•Each explicit scheme (s>1) can control numerical dissipation at the bifurcation point.
This paper constructs a composite s-sub-step explicit method and analyzes second-order accuracy, conditional stability, and dissipation control at the bifurcation point. In the present s-sub-step method, each explicit scheme achieves identical second-order accuracy for analyzing general structures and provides maximal stability bound, that is 2×s where s denotes the number of sub-steps. Except for the single-sub-step case, each explicit scheme achieves dissipation control at the bifurcation point. After registering second-order accuracy and controllable numerical dissipation, the composite multi-sub-step explicit method should be well-designed to reach maximal stability bound. The analysis reveals that as the number of sub-steps increases, the developed explicit schemes can reduce numerical low-frequency dissipation and enlarge stability. Under the same computational cost, the advantage of reducing low-frequency dissipation and enlarging stability is gradually weakened with the increase of sub-steps, so the first seven explicit schemes are only developed and compared in this paper. Some typical experiments are provided to confirm the methods’ numerical performance. The proposed explicit schemes are more accurate and efficient for some models than existing second-order algorithms of that class. |
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| AbstractList | •This paper constructs and analyzes a composite s-sub-step explicit method.•Seven explicit schemes in the present method are developed and compared.•Each explicit scheme is second-order accurate and provides maximal stability bound.•Each explicit scheme (s>1) can control numerical dissipation at the bifurcation point.
This paper constructs a composite s-sub-step explicit method and analyzes second-order accuracy, conditional stability, and dissipation control at the bifurcation point. In the present s-sub-step method, each explicit scheme achieves identical second-order accuracy for analyzing general structures and provides maximal stability bound, that is 2×s where s denotes the number of sub-steps. Except for the single-sub-step case, each explicit scheme achieves dissipation control at the bifurcation point. After registering second-order accuracy and controllable numerical dissipation, the composite multi-sub-step explicit method should be well-designed to reach maximal stability bound. The analysis reveals that as the number of sub-steps increases, the developed explicit schemes can reduce numerical low-frequency dissipation and enlarge stability. Under the same computational cost, the advantage of reducing low-frequency dissipation and enlarging stability is gradually weakened with the increase of sub-steps, so the first seven explicit schemes are only developed and compared in this paper. Some typical experiments are provided to confirm the methods’ numerical performance. The proposed explicit schemes are more accurate and efficient for some models than existing second-order algorithms of that class. |
| Author | Li, Hua Li, Jinze Yu, Kaiping Lian, Yiwei Zhao, Rui |
| Author_xml | – sequence: 1 givenname: Jinze surname: Li fullname: Li, Jinze organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology, No. 92 West Dazhi Street, Harbin 150001, China – sequence: 2 givenname: Hua surname: Li fullname: Li, Hua organization: School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore – sequence: 3 givenname: Yiwei surname: Lian fullname: Lian, Yiwei organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology, No. 92 West Dazhi Street, Harbin 150001, China – sequence: 4 givenname: Rui surname: Zhao fullname: Zhao, Rui organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology, No. 92 West Dazhi Street, Harbin 150001, China – sequence: 5 givenname: Kaiping orcidid: 0000-0002-7722-0138 surname: Yu fullname: Yu, Kaiping email: kaipingyu1968@gmail.com organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology, No. 92 West Dazhi Street, Harbin 150001, China |
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| Keywords | Composite s-sub-step Second-order accuracy Explicit algorithms Self-starting Controllable dissipation |
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| SubjectTerms | Composite [formula omitted]-sub-step Controllable dissipation Explicit algorithms Second-order accuracy Self-starting |
| Title | A suite of second-order composite sub-step explicit algorithms with controllable numerical dissipation and maximal stability bounds |
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