Multiple Time-Weighted Residual Methodology for Design and Synthesis of Time Integration Algorithms.
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| Title: | Multiple Time-Weighted Residual Methodology for Design and Synthesis of Time Integration Algorithms. |
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| Authors: | Wang, Yazhou1 (AUTHOR) yazhou.wang@tum.de, Maxam, Dean2 (AUTHOR) maxam010@umn.edu, Adams, Nikolaus1 (AUTHOR) nikolaus.adams@tum.de, Tamma, Kumar2 (AUTHOR) ktamma@umn.edu |
| Source: | Archives of Computational Methods in Engineering. Oct2025, Vol. 32 Issue 7, p4225-4264. 40p. |
| Subjects: | Time integration scheme, Computational mechanics, Multibody systems, Heat transfer, Numerical analysis, Structural dynamics, Algorithms |
| Abstract: | This paper proposes a novel multiple time-weighted residual methodology with new insights to enable the design of generalized linear multi-step algorithms in computational dynamics. Leveraging single, double, and triple time-weighted residuals in single, two, and three-field forms, respectively, we develop a new generation of Generalized Single-Step Single-Solve algorithms for second-order time-dependent systems. This approach yields the GS4-II p , GS4-II p , q , and GS4-II p , q , r computational frameworks, offering analysts a wide bandwidth of design options. Based on the proposed theory, we introduce the V0 TSS ∗ schemes, which exhibit numerical properties comparable to those of the existing V0 ∗ and traditional schemes, while offering the added benefit of the truly self-starting feature. The much coveted ZOO m schemes (zero-order overshooting with m roots) are also synthesized to achieve second-order time accuracy in all variables, unconditional stability, zero-order overshooting, controllable numerical dissipation/dispersion, and minimal computational complexity. The relationship between the newly proposed computational frameworks and existing methods is analyzed via a comprehensive overview to date, most of which are included as subsets in the newly proposed methodology. Therefore, the multiple time-weighted residual methodology provides a new insight and in-depth understanding of the advances in the literature, showcasing the significance of the proposed theory. Finally, numerical examples from multidisciplinary applications, encompassing multi-body dynamics, structural dynamics, and heat transfer, are presented to substantiate the proposed methodology. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | This paper proposes a novel multiple time-weighted residual methodology with new insights to enable the design of generalized linear multi-step algorithms in computational dynamics. Leveraging single, double, and triple time-weighted residuals in single, two, and three-field forms, respectively, we develop a new generation of Generalized Single-Step Single-Solve algorithms for second-order time-dependent systems. This approach yields the GS4-II p , GS4-II p , q , and GS4-II p , q , r computational frameworks, offering analysts a wide bandwidth of design options. Based on the proposed theory, we introduce the V0 TSS ∗ schemes, which exhibit numerical properties comparable to those of the existing V0 ∗ and traditional schemes, while offering the added benefit of the truly self-starting feature. The much coveted ZOO m schemes (zero-order overshooting with m roots) are also synthesized to achieve second-order time accuracy in all variables, unconditional stability, zero-order overshooting, controllable numerical dissipation/dispersion, and minimal computational complexity. The relationship between the newly proposed computational frameworks and existing methods is analyzed via a comprehensive overview to date, most of which are included as subsets in the newly proposed methodology. Therefore, the multiple time-weighted residual methodology provides a new insight and in-depth understanding of the advances in the literature, showcasing the significance of the proposed theory. Finally, numerical examples from multidisciplinary applications, encompassing multi-body dynamics, structural dynamics, and heat transfer, are presented to substantiate the proposed methodology. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 11343060 |
| DOI: | 10.1007/s11831-025-10262-3 |
