Computational Physics Group

Asynchronous Space-Time Algorithm based on a Domain Decomposition Method for Structural Dynamics Problems on Non-Matching Meshes

W. Subber² and K. Matous<sup>1,2

1</sup>Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, 46556, USA.

²Center for Shock Wave-processing of Advanced Reactive Materials (C-SWARM)
University of Notre Dame
Notre Dame, IN, 46556, USA.

Abstract

    Large-scale practical engineering problems featuring localized phenomena often benefit from local control of mesh and time resolutions to efficiently capture the spatial and temporal scales of interest. To this end, we propose an Asynchronous Space-Time Algorithm based on a Domain Decomposition Method for structural dynamics problems on non-matching meshes. The three-field algorithm is based on the dual-primal like domain decomposition approach utilizing the localized Lagrange multipliers along the space and time common-refinement-based interface. The proposed algorithm is parallel in nature and well suited for a heterogeneous computing environment. Moreover, two-levels of parallelism are embedded in this novel scheme. For linear dynamical problems, the algorithm is unconditionally stable, shows an optimal order of convergence with respect to space and time discretizations as well as ensures conservation of mass, momentum and energy across the non-matching grid interfaces. The method of manufactured solutions is used to verify the implementation, and an engineering application is considered, where a sandwich plate is impacted by a projectile.
        

Conclusions

    We develop the Asynchronous Space-Time Algorithm based on the Domain Decomposition Method for structural dynamics problems on non-matching meshes. The methodology is based on the dual-primal like domain decomposition technique utilizing the localized Lagrange multipliers. For optimal accuracy and preserving physical quantities, the interface between the non-matching meshes is discretized using the common-refinement-based technique. Moreover, we extend the idea of common refinement to the temporal dimension and introduce a generalized  method for the local Lagrange multiplier field. The algorithm offers two-levels of parallelism and is well suited for a heterogeneous computing environment. For linear dynamical problems, PASTA-DDM is an unconditionally stable scheme and preserves mass, momentum and energy along the common interface. Furthermore, PASTA-DDM maintains the optimal rate of convergence with respect to mesh size and time increment for displacement, velocity and acceleration. The computer implementation is verified using the method of manufactured solutions, and rigorous assessment of mass, momentum and energy jump conditions across the common refinement is performed. A projectile impact problem shows potential of PASTA-DDM for a variety of engineering applications.

Acknowledgment

     This work has been supported by the Department of Energy, National Nuclear Security Administration, under Award No. DE-NA0002377.

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