An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation
Source abstract
Abstract
Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.
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Research context
OpenAlex topics: Numerical methods for differential equations · Electromagnetic Simulation and Numerical Methods · Differential Equations and Numerical Methods
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
Funding
National Natural Science Foundation of China
References (38)
Show source-provided references
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