Parallel-In-Time Spacetime Discontinuous Galerkin Method for Elastodynamics Via Hamilton's Principle
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We present a new multi-field formulation for linear elastodynamics via Hamilton's Principle of Stationary Action intended for use with causal Spacetime Discontinuous Galerkin methods for asynchronous (parallel-in-time) solutions. Three independent fields include the 0-form displacement u, and d-forms for stress, S, and linear momentum density, p, where d is the spatial dimension. The distributional exterior derivative includes an absolutely continuous part on element interiors and a jump part to accommodate jumps in the solution fields across element boundaries. The Stationary Action Principle weakly enforces the Equation of motion as well as compatibility of velocities due to u and p and strain rates induced by S and p. It also enforces suitable jump conditions for inter-element coupling and imposition of initial and boundary conditions. We demonstrate that all fields exhibit optimal convergence rates for equal-order discretization of u, S and p. We describe a parallel-adaptive implementation with new adaptive spacetime meshing capabilities in up to three spatial dimensions and time.
