Recently, the novel designs and developments encompassing isochronous integrators [iIntegrators] for systems of ordinary differential equations (ODE-iIntegrators) have been invented that entail most of the research to-date developed over the past 50 years or so including new and novel optimal schemes for both second-order and first-order transient systems. This present thesis next takes upon the daunting challenges for the extensions of the ODE iIntegrators to systems of differential-algebraic equations (DAEs). The iIntegrators for DAEs (DAE-iIntegrators) is an extremely powerful time integration toolkit with new and contemporary schemes that are novel and suitable to DAEs of any index which can be applied both for second- and first-order systems; and it includes most single step single solve implicit/semi-explicit schemes which preserve second-order time accuracies in all the variables (this is the novelty and it is not trivial and is not readily achievable with current state of the art for the differential and algebraic quantities to-date due to lack of fundamental understanding, poor or improper designs and implementation). Sub-cases include the classical algorithms in second-order systems such as Newmark, HHT-alpha, WBZ methods and many others, including mechanical integrators, and more new and optimal algorithms and designs for second-order systems; and this very same computational framework (hence, the name isochronous integration) readily adapts to the simulation of first-order systems as well as an added bonus and includes most of the classical developments such as Crank-Nicholson method, Gear's method, MacCormack's method and so on including more new and optimal designs encompassing both implicit and explicit schemes for first-order systems as well under the umbrella of a single unified toolkit. The new and novel DAE-iIntegration architecture is envisioned as the next generation toolkit, and can also be widely used, for example, as an added bonus for applicability to multi-physics problems such as fluid-structure, thermal-structure interaction problems. Additional studies on the multiple subdomain DAE simulations and model order reduction by the proper orthogonal decomposition (POD) for ODE systems are also investigated.
University of Minnesota Ph.D. dissertation.December 2014. Major: Mechanical Engineering. Advisor: Kumar Tamma. 1 computer file (PDF); xiii, 416 pages.
Novel Design and Development of Isochronous Time Integration Architectures for Ordinary Differential Equations and Differential-Algebraic Equations: Computational Science and Engineering Applications.
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