High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems

被引:1
|
作者
Li, Jinze [1 ]
Li, Hua [2 ]
Yu, Kaiping [1 ]
Zhao, Rui [1 ]
机构
[1] Harbin Inst Technol, Sch Astronaut, 92 West Dazhi St, Harbin 150001, Peoples R China
[2] Nanyang Technol Univ, Sch Mech & Aerosp Engn, 50 Nanyang Ave, Singapore 639798, Singapore
基金
中国国家自然科学基金;
关键词
Implicit time integration; ESDIRK; Dissipation control; Optimal spectral features; High-order accuracy; MOMENTUM CONSERVING ALGORITHMS; IMPROVED NUMERICAL DISSIPATION; TIME INTEGRATION; DYNAMIC-ANALYSIS; NEWMARK METHODS; EXACT ENERGY; METHODOLOGY; STABILITY; SCHEMES; FAMILY;
D O I
10.1007/s00419-024-02637-y
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ s\le 6 $$\end{document} 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.
引用
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页码:2285 / 2334
页数:50
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