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Temporal and Spatial Coupling Methods for the Efficient Modelling of Dynamic Solids.

Kin Fung Chan1, Nicola Bombace2, Indrajeet Sahu1

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Summary
This summary is machine-generated.

This study introduces efficient finite element methods for dynamic solid modeling, significantly reducing computational costs. The new approach enables faster simulations by using multiple time steps and non-conforming meshes.

Keywords:
dynamic modellingexplicit finite elementsheterogeneous discretisationsmulti-time steppingnon-matching meshes

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Area of Science:

  • Computational mechanics
  • Solid mechanics
  • Numerical analysis

Background:

  • Dynamic solid modeling with finite elements is computationally intensive.
  • Existing methods often require conforming meshes and single time steps, limiting efficiency.

Purpose of the Study:

  • To develop efficient coupling methods for dynamic finite element analysis of solids.
  • To reduce the computational cost associated with complex solid dynamics simulations.

Main Methods:

  • A multi-time-step integration algorithm is proposed to utilize varying time steps across the domain.
  • Explicit resolution of interfaces between subdomains ensures continuity of acceleration and tractions.
  • A spatial coupling method is integrated with multi-time-stepping, accommodating non-conforming meshes at interfaces.

Main Results:

  • The developed methods achieve significant speedups, exceeding 12x compared to traditional single-time-step approaches.
  • Parameter-free coupling operators are defined, eliminating the need for additional degrees of freedom at interfaces.
  • The approach successfully models solids dynamically with finite elements efficiently.

Conclusions:

  • The proposed efficient coupling methods substantially reduce computational cost in finite element analysis of dynamic solids.
  • The multi-time-step and spatial coupling approach offers a robust and efficient alternative for complex simulations.
  • This work paves the way for faster and more accessible dynamic solid modeling.