Browsing by Author "Nguyen, Hoang"

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    Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials
    (PNAS, 2022) Zhang, Xu; Nguyen, Hoang; Zhang, Xiang; Ajayan, Pulickel M.; Wen, Jianguo; Espinosa, Horacio D.
    Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental–computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS 2 and MoSe 2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).
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    Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems
    (2003-12) Heinkenschloss, Matthias; Nguyen, Hoang
    We present Neumann-Neumann domain decomposition (DD) preconditioners for the solution of elliptic linear quadratic optimal control problems. The preconditioner is applied to the optimality system. A Schur complement formulation is derived that reformulates the original optimality system as a system in the state and adjoint variables restricted to the subdomain boundaries. The application of the Schur complement matrix requires the solution of subdomain optimal control problems with Dirichlet boundary conditions on the subdomain interfaces. The application of the inverses of the subdomain Schur complement matrices require the solution of subdomain optimal control problems with Neumann boundary conditions on the subdomain interfaces. Numerical tests show that the dependence of this preconditioner on mesh size and subdomain size is comparable to its counterpart applied to elliptic equations only.
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    Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems
    (2004-11) Heinkenschloss, Matthias; Nguyen, Hoang
    We develop and analyze a class of overlapping domain decomposition (DD) preconditioners for linear-quadratic elliptic optimal control problems. Our preconditioners utilize the structure of the optimal control problems. Their execution requires the parallel solution of subdomain linear-quadratic elliptic optimal control problems, which are essentially smaller subdomain copies of the original problem. This work extends to optimal control problems the application and analysis of overlapping DD preconditioners, which have been used successfully for the solution of single PDEs. We prove that the performance of the two-level versions of our preconditioners is independent of the mesh size and of the subdomain size. Our numerical studies indicate that the performance of our preconditioners for optimal control problems is comparable to the performance of their counterparts applied to single PDEs. Moreover, the performance of our preconditioners seems to be rather insensitive to the size of the control regularization parameter.
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    Hundred Digit Challenge Solutions
    (2002-05) Dussaud, Eric; Husband, Chris; Nguyen, Hoang; Reynolds, Daniel; Stolk, Christiaan
    This paper details our solutions to the "Hundred-dollar, Hundred-digit Challenge", which appeared in Volume 35, Number 1 of SIAM News.