Abstract
This chapter describes the mathematical formulation for the implicit matrix-free structural dynamics solver on unstructured grids developed in this work. The elastic deformation of the structure is calculated with a matrix-free implicit dual-time-stepping scheme. A five-stage Runge–Kutta time-integration algorithm is used between each physical time-step to iterate the numerical solution in pseudo time until convergence is reached. The methods used to accelerate the convergence rate to steady-state in pseudo time, which are local time-stepping, implicit residual smoothing, and multigrid, are briefly described.
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