The Time Dimension and Integrators: Isochronous Integrators and Implicit/Explicit Framework for Computational Dynamics and Science and Engineering Problems

Abstract eng:
This presentation highlights the next generation computational technology and framework dealing with the time dimension that is envisioned for transient dynamic simulations in the general areas as related to computational dynamics of particles, materials and structures. In particular, the spectrum of applications are in general, applicable to a wide variety of computational science and engineering problems to include, elasto-dynamics, particle and rigid body dynamics, molecular dynamics, multi-body dynamics, contact-impact dynamics and the like, to name a few. More importantly, the novelty and scientific contributions underlying this next general computational framework lies in its general applicability to both second-order and first-order transient systems via use of the “same computational framework” which can be readily switched/adapted between first/second order transient systems, thence the name “isochronous integrators” or “iIntegrators” framework; consequently, its applicability to also multi-scale and multi-physics problems such as fluid/structure, thermal/structure problems and the like are an added dimension. Under the umbrella of Algorithms by Design and a unified methodology and framework, we design a generalized methodology of computation which encompasses most of the integration schemes that have been developed over the past fifty years or so, plus new avenues and new and novel schemes which inherit improved and optimal features for the selected simulation at hand for computational dynamics and science and engineering applications. A wide variety of both implicit methods of time integration and explicit counterparts are inherent in this framework. Furthermore the same computational framework is ideally suitable/adaptable for both second/first order transient systems through the use of simply changing very few parameters; which is a novel feature of the framework. We describe the theory and underlying basis of designing computational algorithms for transient/dynamic systems; identify the pros and cons and selection features of how to pick a particular algorithm for particular applications; show the improved physics, and how to go about and extend the linear algorithms by design for nonlinear transient/dynamics applications through rigorous mathematical treatments to foster the effective computation of computational science and engineering applications. Numerous simulations will be presented to enable a good grasp of the theoretical basis and practical use of integrators for computational dynamics of particles, materials and structures for the purposes of illustration.

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