论文标题
高阶准确的多sub-step隐式集成算法具有耗散控制的二阶双曲问题
High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems
论文作者
论文摘要
本文提出了一个基于显式单独的对角线runge-kutta（eSdirk）方法的子步骤集成算法的隐式家族。所提出的方法实现每个子步骤的三阶一致性，因此梯形规则始终在第一个子步骤中使用。本文首次证明了提议的$ s $ -sub-step隐式方法，$ s \ le6 $同时实现耗散控制和无条件稳定性时，可以达到$ s $ th级的精度。因此，本文使用三个，四个，五个子步骤和六个子步骤来开发，分析和比较当前$ s $ sub-step方法中四种成本优势的高阶隐式算法。每种高阶隐算算法都具有相同的有效刚度矩阵，以实现最佳的光谱特性。与已发布的算法不同，所提出的高阶方法不会降低解决强制振动的顺序。此外，这种新方法克服了作者以前的算法需要额外解决方案以获得准确加速的缺陷。线性和非线性示例被求解以确认四种新型高级算法的数值性能和优越性。
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.
