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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| Cites_doi | 10.1007/s00366-014-0390-x 10.1007/s00419-022-02286-z 10.1007/s11071-020-06020-8 10.1016/S0045-7825(00)00189-4 10.1007/s11071-020-06101-8 10.1002/nme.7291 10.1016/S0045-7825(02)00264-5 10.1007/BF00363983 10.1016/0045-7825(94)90061-2 10.1002/nme.1620151011 10.1002/eqe.4290020208 10.1002/(SICI)1097-0207(19961030)39:20<3475::AID-NME10>3.0.CO;2-H 10.1007/s00366-020-01129-1 10.1002/eqe.4290060111 10.1016/j.apm.2018.12.027 10.1016/j.cja.2020.05.005 10.1061/JMCEA3.0000098 10.1002/(SICI)1097-0207(19960630)39:12<2131::AID-NME947>3.0.CO;2-Z 10.1142/S0219455421500735 10.1016/j.compstruc.2022.106814 10.1016/0045-7825(92)90115-Z 10.1016/j.compstruc.2005.08.001 10.1142/S0219455415500546 10.1243/09544062JMES2093 10.1016/j.cma.2015.06.016 10.1016/S0045-7825(96)01191-7 10.1108/02644400810891544 10.1007/s00419-019-01637-7 10.1016/j.compstruc.2013.06.007 10.1016/j.apm.2022.10.012 10.1007/s11831-021-09536-3 10.1016/j.compstruc.2018.11.001 10.1016/j.compstruc.2012.01.009 10.1115/1.4036821 10.1002/(SICI)1097-0207(19980115)41:1<65::AID-NME270>3.0.CO;2-F 10.1002/(SICI)1097-0207(19990620)45:5<569::AID-NME595>3.0.CO;2-A 10.1016/j.compstruc.2006.09.004 10.1016/j.compstruc.2018.10.008 10.1007/s11071-019-04936-4 10.1142/S0219455421501066 10.1115/1.2900803 10.1002/nme.6574 10.1002/eqe.4290150710 10.1016/j.cma.2021.114436 10.1002/eqe.4290050306 10.2140/jomms.2017.12.57 10.1016/S0045-7825(99)00024-9 10.1061/(ASCE)0733-9445(2008)134:6(973) 10.1007/s00466-003-0469-5 10.1007/BF00913408 10.1016/0021-9991(92)90331-R 10.1002/(SICI)1097-0207(19990720)45:8<971::AID-NME613>3.0.CO;2-M 10.1002/nme.637 10.1016/S0045-7825(96)01243-1 |
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| Keywords | Optimal spectral features Dissipation control High-order accuracy ESDIRK Implicit time integration |
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| References | WangYTammaKMaxamDXueTQinGAn overview of high-order implicit algorithms for first-/second-order systems and novel explicit algorithm designs for first-order system representationsArch. Comput. Methods Eng.20212835933619 MalakiyehMMShojaeeSBatheK-JThe Bathe time integration method revisited for prescribing desired numerical dissipationComput. Struct.2019212289298 HilberHMHughesTJRTaylorRLImproved numerical dissipation for time integration algorithms in structural dynamicsEarthq. Eng. Struct. Dyn.19775283292 FanSCFungTCShengGA comprehensive unified set of single-step algorithms with controllable dissipation for dynamics Part IFormulation. Comput. Methods Appl. Mech. Eng.19971458798 Fung, T.C.: Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms. Part 2 — Second-order equations. Int. J. Num. Methods Eng. 45, 971–1006 (1999) Rezaiee-PajandMEsfehaniSAHEhsanmaneshHAn efficient weighted residual time integration familyInt. J. Struct. Stab. Dyn.20212121501064280931 LiJYuKA novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamicsArch. Appl. Mech.202090737772 FungTCComplex-time-step Newmark methods with controllable numerical dissipationInt. J. Num. Methods Eng.19984165931601316 KrenkSConservative fourth-order time integration of non-linear dynamic systemsComput. Methods Appl. Mech. Eng.201529539553388824 KimWReddyJNA new family of higher-order time integration algorithms for the analysis of structural dynamicsJ. Appl. Mech.20178407100817 SimoJCTarnowNWongKExact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamicsComput. Methods Appl. Mech. Eng.1992100631161187632 HulbertGMHughesTJRAn error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamicsEarthq. Eng. Struct. Dyn.198715901910 LiJLiHLianYZhaoRYuKA suite of second-order composite sub-step explicit algorithms with controllable numerical dissipation and maximal stability boundsAppl. Math. Model.20231146016264498706 MancusoMUbertiniFThe Nørsett time integration methodology for finite element transient analysisComput. Methods Appl. Mech. Eng.200219132973327 TarnowNSimoJCHow to render second order accurate time-stepping algorithms fourth order accurate while retaining the stability and conservation propertiesComput. Methods Appl. Mech. Eng.19941152332521285020 SoaresDA straightforward high-order accurate time-marching procedure for dynamic analysesEng. Comput.20223816591677 ArgyrisJHDunnePCAngelopoulosTDynamic response by large step integrationEarthq. Eng. Struct. Dyn.19732185203 WoodWBossakMZienkiewiczOAn alpha modification of Newmark’s methodInt. J. Num. Methods Eng.19801515621566595373 BatheKJBaigMMIOn a composite implicit time integration procedure for nonlinear dynamicsComput. Struct.200583251325242174999 GonzalezOExact energy and momentum conserving algorithms for general models in nonlinear elasticityComput. Methods Appl. Mech. Eng.2000190176317831807477 LiJYuKLiXA novel family of controllably dissipative composite integration algorithms for structural dynamic analysisNonlinear Dyn.20199624752507 BankRECoughranWMGrosseEHRoseDJKentsmithRTransient simulation of silicon devices and circuitsIEEE Trans. Electron Dev.19853216 KwonS-BBatheK-JNohGSelecting the load at the intermediate time point of the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe time integration schemeComput. Struct.2021254 BatheKJConserving energy and momentum in nonlinear dynamics: a simple implicit time integration schemeComput. Struct.2007854374452303506 ZhangHZhangRXingYMasaratiPOn the optimization of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-sub-step composite time integration methodsNonlinear Dyn.202010219391962 MancusoMUbertiniFA methodology for the generation of low-cost higher-order methods for linear dynamicsInt. J. Num. Methods Eng.200356188319121965017 SimoJCTarnowNThe discrete energy-momentum method - Conserving algorithms for nonlinear elastodynamicsZeitschrift Fur Angewandte Mathematik Und Physik1992437577921182782 FungTCUnconditionally stable higher-order accurate Hermitian time finite elementsInt. J. Num. Methods Eng.19963934753495 LiJLiHZhaoRYuKOn second-order s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s$$\end{document}-sub-step explicit algorithms with controllable dissipation and adjustable bifurcation point for second-order hyperbolic problemsEuropean J. Mech. - A/Solids2023974505447 Rezaiee-PajandMAlamatianJNumerical time integration for dynamic analysis using a new higher order predictor-corrector methodEng. Comput.200825541568 ChoiBBatheK-JNohGTime splitting ratio in the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe time integration method for higher-order accuracy in structural dynamics and heat transferComput. Struct.2022270 LiJYuKA truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamicsNonlinear Dyn.202010225032530 MancusoMUbertiniFAn efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulationComput. Mech.2003321541682020163 Rezaiee-PajandMKarimi-RadMA new explicit time integration scheme for nonlinear dynamic analysisInt. J. Struct. Stab. Dyn.20161615500543567746 BatheK-JNohGInsight into an implicit time integration scheme for structural dynamicsComput. Struct.201298–9916 de FrutosJSanz-SernaJMAn easily implementable fourth-order method for the time integration of wave problemsJ. Comput. Phys.19921031601681188091 Rezaiee-PajandMKarimi-RadMMore accurate and stable time integration schemeEng. Comput.201531791812 LiJYuKTangHFurther assessment of three Bathe algorithms and implementations for wave propagation problemsInt. J. Struct. Stab. Dyn.20212121500734255742 NohGBatheK-JThe Bathe time integration method with controllable spectral radius: the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe methodComput. Struct.2019212299310 HilberHMHughesTJRCollocation, dissipation and ‘overshoot’ for time integration schemes in structural dynamicsEarthq. Eng. Struct. Dyn.1978699117 ChungJHulbertGMA time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} methodJ. Appl. Mech.1993603713751223971 KuhlDRammEGeneralized energy-momentum method for non-linear adaptive shell dynamicsComput. Methods Appl. Mech. Eng.19991783433661711044 LiJZhaoRYuKLiXDirectly self-starting higher-order implicit integration algorithms with flexible dissipation control for structural dynamicsComput. Methods Appl. Mech. Eng.20223894348274 LiJYuKA simple truly self-starting and L-stable integration algorithm for structural dynamicsInt. J. Appl. Mech.202012129 Hughes, T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis Dover Civil and Mechanical Engineering (Dover Publications, 2000) LiJYuKZhaoRFangYThree optimal families of three-sub-step dissipative implicit integration algorithms with either second, third, or fourth-order accuracy for second-order nonlinear dynamicsInt. J. Num. Methods Eng.2023124373337664631843 GrafenhorstMRangJHartmannSTime-adaptive finite element simulations of dynamical problems for temperature-dependent materialsJ. Mech. Mater. Struct.20171257913576124 NewmarkNMA method of computation for structural dynamicsJ. Eng. Mech. Div.1959856794 Rezaiee-PajandMAlamatianJImplicit higher-order accuracy method for numerical integration in dynamic analysisJ. Struct. Eng.2008134973985 NohGBatheK-JAn explicit time integration scheme for the analysis of wave propagationsComput. Struct.2013129178193 ZhaoRLiJYuKA self-starting dissipative alternative to the central difference methodsArch. Appl. Mech.202393571603 ShaoHCaiCA three parameters algorithm for numerical integration of structural dynamic equationsChinese J. Appl. Mech.198857681 FungTCUnconditionally stable higher-order Newmark methods by sub-stepping procedureComput. Methods Appl. Mech. Eng.199714761841470541 Rezaiee-Pajand, M., Sarafrazi, S.R.: A mixed and multi-step higher-order implicit time integration family. Arch. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224, 2097–2108 (2010) SongCEisenträgerSZhangXHigh-order implicit time integration scheme based on Padé expansionsComput. Methods Appl. Mech. Eng.2022390 HeHNonlinear aeroelastic analysis of the folding fin with freeplay under thermal environmentChinese J. Aeronaut.20203323572371 LiJYuKAn alternative to the Bathe algorithmAppl. Math. Modell.2019692552723895060 Rezaiee-PajandMEsfehaniSAHKarimi-RadMHighly accurate family of time integration methodStruct. Eng. Mech.201867603616 LiJYuKLiXAn identical second-order single step explicit integration algorithm with dissipation control for structural dynamicsInt. J N Tarnow (2637_CR27) 1994; 115 M Rezaiee-Pajand (2637_CR7) 2016; 16 HM Hilber (2637_CR52) 1978; 6 R Zhao (2637_CR4) 2023; 93 M Rezaiee-Pajand (2637_CR40) 2008; 25 S Krenk (2637_CR33) 2015; 295 J Li (2637_CR17) 2023; 124 2637_CR42 J Li (2637_CR6) 2022; 395 B Choi (2637_CR51) 2022; 270 JC Simo (2637_CR62) 1992; 43 W Kim (2637_CR38) 2017; 84 MM Malakiyeh (2637_CR24) 2019; 212 RE Bank (2637_CR16) 1985; 32 KJ Bathe (2637_CR15) 2007; 85 W Wood (2637_CR10) 1980; 15 JH Argyris (2637_CR43) 1973; 2 M Rezaiee-Pajand (2637_CR35) 2008; 134 J Li (2637_CR14) 2021; 21 J de Frutos (2637_CR46) 1992; 103 JC Simo (2637_CR59) 1992; 100 TC Fung (2637_CR31) 1998; 41 TC Fung (2637_CR65) 1996; 39 J Li (2637_CR22) 2020; 102 D Soares (2637_CR49) 2022; 38 M Rezaiee-Pajand (2637_CR2) 2015; 31 NM Newmark (2637_CR8) 1959; 85 J Li (2637_CR37) 2022; 389 O Gonzalez (2637_CR61) 2000; 190 KJ Bathe (2637_CR13) 2005; 83 M Rezaiee-Pajand (2637_CR57) 2021; 21 J Chung (2637_CR12) 1993; 60 H He (2637_CR64) 2020; 33 J Li (2637_CR53) 2023; 97 GM Hulbert (2637_CR56) 1987; 15 G Noh (2637_CR18) 2019; 212 K-J Bathe (2637_CR63) 2012; 98–99 M Grafenhorst (2637_CR39) 2017; 12 J Li (2637_CR3) 2021; 122 2637_CR20 J Li (2637_CR54) 2023; 114 H Shao (2637_CR11) 1988; 5 2637_CR1 Y Wang (2637_CR41) 2021; 28 D Kuhl (2637_CR58) 1999; 45 M Mancuso (2637_CR32) 2003; 32 C Song (2637_CR47) 2022; 390 H Zhang (2637_CR34) 2020; 102 J Li (2637_CR21) 2019; 69 TC Fung (2637_CR26) 1996; 17 TC Fung (2637_CR29) 1997; 147 D Kuhl (2637_CR60) 1999; 178 J Li (2637_CR23) 2020; 12 J Li (2637_CR19) 2019; 96 J Li (2637_CR25) 2020; 90 W Kim (2637_CR28) 2017; 84 M Mancuso (2637_CR45) 2003; 56 X Li (2637_CR44) 1996; 39 M Rezaiee-Pajand (2637_CR36) 2018; 67 2637_CR55 SC Fan (2637_CR30) 1997; 145 S-B Kwon (2637_CR50) 2021; 254 G Noh (2637_CR5) 2013; 129 M Mancuso (2637_CR48) 2002; 191 HM Hilber (2637_CR9) 1977; 5 |
| References_xml | – reference: Rezaiee-PajandMEsfehaniSAHKarimi-RadMHighly accurate family of time integration methodStruct. Eng. Mech.201867603616 – reference: NohGBatheK-JAn explicit time integration scheme for the analysis of wave propagationsComput. Struct.2013129178193 – reference: ArgyrisJHDunnePCAngelopoulosTDynamic response by large step integrationEarthq. Eng. Struct. Dyn.19732185203 – reference: SoaresDA straightforward high-order accurate time-marching procedure for dynamic analysesEng. Comput.20223816591677 – reference: LiJYuKTangHFurther assessment of three Bathe algorithms and implementations for wave propagation problemsInt. J. Struct. Stab. Dyn.20212121500734255742 – reference: ZhangHZhangRXingYMasaratiPOn the optimization of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-sub-step composite time integration methodsNonlinear Dyn.202010219391962 – reference: HeHNonlinear aeroelastic analysis of the folding fin with freeplay under thermal environmentChinese J. Aeronaut.20203323572371 – reference: GonzalezOExact energy and momentum conserving algorithms for general models in nonlinear elasticityComput. Methods Appl. Mech. Eng.2000190176317831807477 – reference: Rezaiee-PajandMEsfehaniSAHEhsanmaneshHAn efficient weighted residual time integration familyInt. J. Struct. Stab. Dyn.20212121501064280931 – reference: LiXWibergNStructural dynamic analysis by a time-discontinuous Galerkin finite element methodInt. J. Num. Methods Eng.199639213121521396393 – reference: WoodWBossakMZienkiewiczOAn alpha modification of Newmark’s methodInt. J. Num. Methods Eng.19801515621566595373 – reference: Rezaiee-Pajand, M., Sarafrazi, S.R.: A mixed and multi-step higher-order implicit time integration family. Arch. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224, 2097–2108 (2010) – reference: NewmarkNMA method of computation for structural dynamicsJ. Eng. Mech. Div.1959856794 – reference: de FrutosJSanz-SernaJMAn easily implementable fourth-order method for the time integration of wave problemsJ. Comput. Phys.19921031601681188091 – reference: Rezaiee-PajandMKarimi-RadMA new explicit time integration scheme for nonlinear dynamic analysisInt. J. Struct. Stab. Dyn.20161615500543567746 – reference: MancusoMUbertiniFA methodology for the generation of low-cost higher-order methods for linear dynamicsInt. J. Num. Methods Eng.200356188319121965017 – reference: NohGBatheK-JThe Bathe time integration method with controllable spectral radius: the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe methodComput. Struct.2019212299310 – reference: BatheKJBaigMMIOn a composite implicit time integration procedure for nonlinear dynamicsComput. Struct.200583251325242174999 – reference: KuhlDRammEGeneralized energy-momentum method for non-linear adaptive shell dynamicsComput. Methods Appl. Mech. Eng.19991783433661711044 – reference: KimWReddyJNEffective higher-order time integration algorithms for the analysis of linear structural dynamicsJ. Appl. Mech.201784 – reference: Rezaiee-PajandMAlamatianJImplicit higher-order accuracy method for numerical integration in dynamic analysisJ. Struct. Eng.2008134973985 – reference: SongCEisenträgerSZhangXHigh-order implicit time integration scheme based on Padé expansionsComput. Methods Appl. Mech. Eng.2022390 – reference: ChungJHulbertGMA time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} methodJ. Appl. Mech.1993603713751223971 – reference: GrafenhorstMRangJHartmannSTime-adaptive finite element simulations of dynamical problems for temperature-dependent materialsJ. Mech. Mater. Struct.20171257913576124 – reference: MancusoMUbertiniFAn efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulationComput. Mech.2003321541682020163 – reference: ChoiBBatheK-JNohGTime splitting ratio in the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe time integration method for higher-order accuracy in structural dynamics and heat transferComput. Struct.2022270 – reference: Hughes, T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis Dover Civil and Mechanical Engineering (Dover Publications, 2000) – reference: LiJYuKZhaoRFangYThree optimal families of three-sub-step dissipative implicit integration algorithms with either second, third, or fourth-order accuracy for second-order nonlinear dynamicsInt. J. Num. Methods Eng.2023124373337664631843 – reference: HilberHMHughesTJRCollocation, dissipation and ‘overshoot’ for time integration schemes in structural dynamicsEarthq. Eng. Struct. Dyn.1978699117 – reference: LiJYuKA simple truly self-starting and L-stable integration algorithm for structural dynamicsInt. J. Appl. Mech.202012129 – reference: SimoJCTarnowNThe discrete energy-momentum method - Conserving algorithms for nonlinear elastodynamicsZeitschrift Fur Angewandte Mathematik Und Physik1992437577921182782 – reference: ZhaoRLiJYuKA self-starting dissipative alternative to the central difference methodsArch. Appl. Mech.202393571603 – reference: LiJYuKAn alternative to the Bathe algorithmAppl. Math. Modell.2019692552723895060 – reference: LiJLiHLianYZhaoRYuKA suite of second-order composite sub-step explicit algorithms with controllable numerical dissipation and maximal stability boundsAppl. Math. Model.20231146016264498706 – reference: Butcher, J.C.: Num. Methods Ord. Diff. Equ., 3rd edn. Wiley, New York (2016) – reference: LiJLiHZhaoRYuKOn second-order s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s$$\end{document}-sub-step explicit algorithms with controllable dissipation and adjustable bifurcation point for second-order hyperbolic problemsEuropean J. Mech. - A/Solids2023974505447 – reference: HulbertGMHughesTJRAn error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamicsEarthq. Eng. Struct. Dyn.198715901910 – reference: LiJZhaoRYuKLiXDirectly self-starting higher-order implicit integration algorithms with flexible dissipation control for structural dynamicsComput. Methods Appl. Mech. Eng.20223894348274 – reference: MancusoMUbertiniFThe Nørsett time integration methodology for finite element transient analysisComput. Methods Appl. Mech. Eng.200219132973327 – reference: WangYTammaKMaxamDXueTQinGAn overview of high-order implicit algorithms for first-/second-order systems and novel explicit algorithm designs for first-order system representationsArch. Comput. Methods Eng.20212835933619 – reference: LiJYuKLiXAn identical second-order single step explicit integration algorithm with dissipation control for structural dynamicsInt. J. Num. Methods Eng.2021122108911324202425 – reference: FungTCUnconditionally stable higher-order Newmark methods by sub-stepping procedureComput. Methods Appl. Mech. Eng.199714761841470541 – reference: LiJYuKA truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamicsNonlinear Dyn.202010225032530 – reference: MalakiyehMMShojaeeSBatheK-JThe Bathe time integration method revisited for prescribing desired numerical dissipationComput. Struct.2019212289298 – reference: ShaoHCaiCA three parameters algorithm for numerical integration of structural dynamic equationsChinese J. Appl. Mech.198857681 – reference: Rezaiee-PajandMKarimi-RadMMore accurate and stable time integration schemeEng. Comput.201531791812 – reference: HilberHMHughesTJRTaylorRLImproved numerical dissipation for time integration algorithms in structural dynamicsEarthq. Eng. Struct. Dyn.19775283292 – reference: KrenkSConservative fourth-order time integration of non-linear dynamic systemsComput. Methods Appl. Mech. Eng.201529539553388824 – reference: FanSCFungTCShengGA comprehensive unified set of single-step algorithms with controllable dissipation for dynamics Part IFormulation. Comput. Methods Appl. Mech. Eng.19971458798 – reference: Rezaiee-PajandMAlamatianJNumerical time integration for dynamic analysis using a new higher order predictor-corrector methodEng. Comput.200825541568 – reference: LiJYuKZhaoRTwo third-order explicit integration algorithms with controllable numerical dissipation for second-order nonlinear dynamicsComput. Methods Appl. Mech. Eng.20223954412694 – reference: BankRECoughranWMGrosseEHRoseDJKentsmithRTransient simulation of silicon devices and circuitsIEEE Trans. Electron Dev.19853216 – reference: LiJYuKA novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamicsArch. Appl. Mech.202090737772 – reference: TarnowNSimoJCHow to render second order accurate time-stepping algorithms fourth order accurate while retaining the stability and conservation propertiesComput. Methods Appl. Mech. Eng.19941152332521285020 – reference: BatheK-JNohGInsight into an implicit time integration scheme for structural dynamicsComput. Struct.201298–9916 – reference: KimWReddyJNA new family of higher-order time integration algorithms for the analysis of structural dynamicsJ. Appl. Mech.20178407100817 – reference: LiJYuKLiXA novel family of controllably dissipative composite integration algorithms for structural dynamic analysisNonlinear Dyn.20199624752507 – reference: KuhlDCrisfieldMEnergy-conserving and decaying algorithms in non-linear structural dynamicsInt. J. Num. Methods Eng.1999455695991687371 – reference: BatheKJConserving energy and momentum in nonlinear dynamics: a simple implicit time integration schemeComput. Struct.2007854374452303506 – reference: FungTCUnconditionally stable higher-order accurate Hermitian time finite elementsInt. J. Num. Methods Eng.19963934753495 – reference: FungTCComplex-time-step Newmark methods with controllable numerical dissipationInt. J. Num. Methods Eng.19984165931601316 – reference: SimoJCTarnowNWongKExact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamicsComput. Methods Appl. Mech. Eng.1992100631161187632 – reference: KwonS-BBatheK-JNohGSelecting the load at the intermediate time point of the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe time integration schemeComput. Struct.2021254 – reference: FungTCFanSCShengGExtrapolated Galerkin time finite elementsComput. Mech.1996173984051395441 – reference: Fung, T.C.: Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms. Part 2 — Second-order equations. Int. J. Num. Methods Eng. 45, 971–1006 (1999) – volume: 31 start-page: 791 year: 2015 ident: 2637_CR2 publication-title: Eng. Comput. doi: 10.1007/s00366-014-0390-x – volume: 93 start-page: 571 year: 2023 ident: 2637_CR4 publication-title: Arch. Appl. Mech. doi: 10.1007/s00419-022-02286-z – volume: 5 start-page: 76 year: 1988 ident: 2637_CR11 publication-title: Chinese J. Appl. Mech. – volume: 102 start-page: 1939 year: 2020 ident: 2637_CR34 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-020-06020-8 – volume: 389 year: 2022 ident: 2637_CR37 publication-title: Comput. Methods Appl. Mech. Eng. – volume: 190 start-page: 1763 year: 2000 ident: 2637_CR61 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(00)00189-4 – volume: 102 start-page: 2503 year: 2020 ident: 2637_CR22 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-020-06101-8 – volume: 124 start-page: 3733 year: 2023 ident: 2637_CR17 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/nme.7291 – volume: 191 start-page: 3297 year: 2002 ident: 2637_CR48 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(02)00264-5 – ident: 2637_CR1 – volume: 17 start-page: 398 year: 1996 ident: 2637_CR26 publication-title: Comput. Mech. doi: 10.1007/BF00363983 – volume: 115 start-page: 233 year: 1994 ident: 2637_CR27 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/0045-7825(94)90061-2 – volume: 15 start-page: 1562 year: 1980 ident: 2637_CR10 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/nme.1620151011 – volume: 2 start-page: 185 year: 1973 ident: 2637_CR43 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290020208 – ident: 2637_CR55 – volume: 39 start-page: 3475 year: 1996 ident: 2637_CR65 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/(SICI)1097-0207(19961030)39:20<3475::AID-NME10>3.0.CO;2-H – volume: 38 start-page: 1659 year: 2022 ident: 2637_CR49 publication-title: Eng. Comput. doi: 10.1007/s00366-020-01129-1 – volume: 6 start-page: 99 year: 1978 ident: 2637_CR52 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290060111 – volume: 69 start-page: 255 year: 2019 ident: 2637_CR21 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2018.12.027 – volume: 33 start-page: 2357 year: 2020 ident: 2637_CR64 publication-title: Chinese J. Aeronaut. doi: 10.1016/j.cja.2020.05.005 – volume: 85 start-page: 67 year: 1959 ident: 2637_CR8 publication-title: J. Eng. Mech. Div. doi: 10.1061/JMCEA3.0000098 – volume: 39 start-page: 2131 year: 1996 ident: 2637_CR44 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/(SICI)1097-0207(19960630)39:12<2131::AID-NME947>3.0.CO;2-Z – volume: 21 start-page: 2150073 year: 2021 ident: 2637_CR14 publication-title: Int. J. Struct. Stab. Dyn. doi: 10.1142/S0219455421500735 – volume: 270 year: 2022 ident: 2637_CR51 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2022.106814 – volume: 100 start-page: 63 year: 1992 ident: 2637_CR59 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/0045-7825(92)90115-Z – volume: 395 year: 2022 ident: 2637_CR6 publication-title: Comput. Methods Appl. Mech. Eng. – volume: 83 start-page: 2513 year: 2005 ident: 2637_CR13 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2005.08.001 – volume: 16 start-page: 1550054 year: 2016 ident: 2637_CR7 publication-title: Int. J. Struct. Stab. Dyn. doi: 10.1142/S0219455415500546 – ident: 2637_CR20 doi: 10.1243/09544062JMES2093 – volume: 295 start-page: 39 year: 2015 ident: 2637_CR33 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2015.06.016 – volume: 145 start-page: 87 year: 1997 ident: 2637_CR30 publication-title: Formulation. Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(96)01191-7 – volume: 25 start-page: 541 year: 2008 ident: 2637_CR40 publication-title: Eng. Comput. doi: 10.1108/02644400810891544 – volume: 90 start-page: 737 year: 2020 ident: 2637_CR25 publication-title: Arch. Appl. Mech. doi: 10.1007/s00419-019-01637-7 – volume: 129 start-page: 178 year: 2013 ident: 2637_CR5 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2013.06.007 – volume: 114 start-page: 601 year: 2023 ident: 2637_CR54 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2022.10.012 – volume: 84 year: 2017 ident: 2637_CR28 publication-title: J. Appl. Mech. – volume: 28 start-page: 3593 year: 2021 ident: 2637_CR41 publication-title: Arch. Comput. Methods Eng. doi: 10.1007/s11831-021-09536-3 – volume: 212 start-page: 299 year: 2019 ident: 2637_CR18 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.11.001 – volume: 98–99 start-page: 1 year: 2012 ident: 2637_CR63 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2012.01.009 – volume: 97 year: 2023 ident: 2637_CR53 publication-title: European J. Mech. - A/Solids – volume: 67 start-page: 603 year: 2018 ident: 2637_CR36 publication-title: Struct. Eng. Mech. – volume: 254 year: 2021 ident: 2637_CR50 publication-title: Comput. Struct. – volume: 84 start-page: 071008 year: 2017 ident: 2637_CR38 publication-title: J. Appl. Mech. doi: 10.1115/1.4036821 – volume: 41 start-page: 65 year: 1998 ident: 2637_CR31 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/(SICI)1097-0207(19980115)41:1<65::AID-NME270>3.0.CO;2-F – volume: 45 start-page: 569 year: 1999 ident: 2637_CR58 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/(SICI)1097-0207(19990620)45:5<569::AID-NME595>3.0.CO;2-A – volume: 85 start-page: 437 year: 2007 ident: 2637_CR15 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2006.09.004 – volume: 212 start-page: 289 year: 2019 ident: 2637_CR24 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.10.008 – volume: 96 start-page: 2475 year: 2019 ident: 2637_CR19 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-019-04936-4 – volume: 21 start-page: 2150106 year: 2021 ident: 2637_CR57 publication-title: Int. J. Struct. Stab. Dyn. doi: 10.1142/S0219455421501066 – volume: 60 start-page: 371 year: 1993 ident: 2637_CR12 publication-title: J. Appl. Mech. doi: 10.1115/1.2900803 – volume: 122 start-page: 1089 year: 2021 ident: 2637_CR3 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/nme.6574 – volume: 32 start-page: 16 year: 1985 ident: 2637_CR16 publication-title: IEEE Trans. Electron Dev. – volume: 15 start-page: 901 year: 1987 ident: 2637_CR56 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290150710 – volume: 390 year: 2022 ident: 2637_CR47 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2021.114436 – volume: 5 start-page: 283 year: 1977 ident: 2637_CR9 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290050306 – volume: 12 start-page: 57 year: 2017 ident: 2637_CR39 publication-title: J. Mech. Mater. Struct. doi: 10.2140/jomms.2017.12.57 – volume: 178 start-page: 343 year: 1999 ident: 2637_CR60 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(99)00024-9 – volume: 134 start-page: 973 year: 2008 ident: 2637_CR35 publication-title: J. Struct. Eng. doi: 10.1061/(ASCE)0733-9445(2008)134:6(973) – volume: 32 start-page: 154 year: 2003 ident: 2637_CR32 publication-title: Comput. Mech. doi: 10.1007/s00466-003-0469-5 – volume: 43 start-page: 757 year: 1992 ident: 2637_CR62 publication-title: Zeitschrift Fur Angewandte Mathematik Und Physik doi: 10.1007/BF00913408 – volume: 103 start-page: 160 year: 1992 ident: 2637_CR46 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(92)90331-R – ident: 2637_CR42 doi: 10.1002/(SICI)1097-0207(19990720)45:8<971::AID-NME613>3.0.CO;2-M – volume: 56 start-page: 1883 year: 2003 ident: 2637_CR45 publication-title: Int. J. Num. Methods Eng. doi: 10.1002/nme.637 – volume: 12 start-page: 1 year: 2020 ident: 2637_CR23 publication-title: Int. J. Appl. Mech. – volume: 147 start-page: 61 year: 1997 ident: 2637_CR29 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(96)01243-1 |
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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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