An adaptive time integration procedure for automated extended-explicit/implicit hybrid analyses

This paper introduces a new explicit-implicit time-marching formulation, presenting a novel hybrid approach for wave propagation analysis. The proposed solution algorithm employs a set of simple, single-step, single-solver, truly self-starting recurrence relationships, which incorporate three time-i...

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Veröffentlicht in:Engineering with computers Jg. 41; H. 1; S. 535 - 564
1. Verfasser: Soares, Delfim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Springer London 01.02.2025
Springer Nature B.V
Schlagworte:
Accuracy
Algorithms
Automation
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Dissipation
Engineering
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Methods
Original Article
Parameters
Propagation
Solvers
Systems Theory
Time integration
Wave propagation
Wave propagation models
Enhanced performance
Controllable numerical dissipation
Locally-defined parameters
Adaptive time integration
Explicit/implicit analysis
ISSN:0177-0667, 1435-5663
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Zusammenfassung:This paper introduces a new explicit-implicit time-marching formulation, presenting a novel hybrid approach for wave propagation analysis. The proposed solution algorithm employs a set of simple, single-step, single-solver, truly self-starting recurrence relationships, which incorporate three time-integration parameters. These parameters are adaptively evaluated for each element of the adopted spatial discretization, taking into account the local characteristics of the model and a user defined parameter. They enable automated extended-explicit/implicit and non-dissipative/dissipative elements to be established, allowing enhanced hybrid analyses to be straightforwardly performed. The proposed formulation is highly accurate, efficient, and very simple to implement and to apply, avoiding complex coupling procedures and interface treatments that are typically considered for mixed explicit/implicit analyses. The new technique is also very versatile, allowing the user to locally control the numerical properties of the adopted time-integration procedure and, consequently, to elaborate very sophisticated solution strategies. Numerical results are presented at the end of the paper, illustrating the good performance and the effectiveness of the proposed novel approach, which combines the best features (such as stability, reduced solver efforts etc.) of both implicit and explicit formulations.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-024-02025-8