Scientific Computing in Computational Mechanics: Some Recent Developments

  • Wick, Thomas (Leibniz University Hannover)

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In this plenary presentation, I summarize the developments of my group, collobarations, and myself over the last ten years. The work is in between scientific computing and computational mechanics. Both fields have large overlaps, but distinguish themselves towards real applications (and their type), rigorous mathematical analyses in functional frameworks, and solver developments. I discuss six topics in which similarities and differences become clear. The guiding principles are efficiency, robustness, and accuracy. First, nonlinear solvers, linear solvers, and preconditioners. Second, error-controlled goal-oriented space-time adaptivity. Third, multigoal-oriented error estimation and adaptivity. Fourth, goal-oriented reduced order modeling. Fifth, nonintrusive global-local multiscale in space. Sixth, two-phase crack flow in (phase-field) fracture porous media. These developments will be briefly underlined with respetive research software developments. Afterwards, numerical tests substantiate those six chosen topics. These include applications, convergence studies in time and space, error quantifications, and speed-ups in the computational cost.