Scholarly Works, Mathematics
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Browsing Scholarly Works, Mathematics by Content Type "Conference proceeding"
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- An Adaptive Zolotarev Upper-Bound for the Singular Values of Loewner MatricesGarcia Hilares, Nilton; Embree, Mark (2021-11-12)
- Application of Interpolatory Methods of Model Reduction to an Elevated Railway PierBertero, S.; Gugercin, Serkan; Sarlo, R. (2023-01-01)Be it due to time constraints or insufficient processing power - or a combination of both - the use of models with large numbers of degrees of freedom (DoF) may be unsuitable to provide a client with results in a timely manner. The use of physics-based reduced models - or proxy structures - are popular among practitioners to solve this issue, as they keep intact all the underlying properties of the second order problems at a fraction of the cost. In this paper, interpolatory methods of model reduction are explored as an alternative, and applied to a 3D Space Frame. The methods chosen allow for structure-preserving reduced models and differ mainly on the selection of interpolation points. A comparison between the response of these reduced models and a proxy structure against two different types of inputs show that interpolatory methods are a viable, more flexible option when it comes to reducing the internal DoF's of a structural model, though engineering judgement helps to ensure it adequately captures the most relevant aspects of the response for the specific application.
- Collaborative Multi-Robot Multi-Human Teams in Search and RescueWilliams, Ryan K.; Abaid, Nicole; McClure, James; Lau, Nathan; Heintzman, Larkin; Hashimoto, Amanda; Wang, Tianzi; Patnayak, Chinmaya; Kumar, Akshay (2022-04-30)Robots such as unmanned aerial vehicles (UAVs) deployed for search and rescue (SAR) can explore areas where human searchers cannot easily go and gather information on scales that can transform SAR strategy. Multi-UAV teams therefore have the potential to transform SAR by augmenting the capabilities of human teams and providing information that would otherwise be inaccessible. Our research aims to develop new theory and technologies for field deploying autonomous UAVs and managing multi-UAV teams working in concert with multi-human teams for SAR. Specifically, in this paper we summarize our work in progress towards these goals, including: (1) a multi-UAV search path planner that adapts to human behavior; (2) an in-field distributed computing prototype that supports multi-UAV computation and communication; (3) behavioral modeling that yields spatially localized predictions of lost person location; and (4) an interface between human searchers and UAVs that facilitates human-UAV interaction over a wide range of autonomy.
- Dynamical Mode Decomposition (DMD) for Power NetworksGarcia Hilares, Nilton (2022-12-02)
- Image segmentation by graph partitioningGarcia Hilares, Nilton (2021-10-07)
- Lyapunov Bounds on Transient Growth for Dynamical SystemsGarcia Hilares, Nilton; Embree, Mark (2021-04-30)
- A Parallel Aggregation Algorithm in Algebraic MultigridGarcia Hilares, Nilton (2019-10-09)
- A partially extending strand convection model with Newtonian solvent for modeling thixotropic yield stress fluids: stability of shear-banded flowRenardy, Yuriko Y.; Renardy, Michael J. (2017-06-15)
- Resilient s-ACD for Asynchronous Collaborative Solutions of Systems of Linear EquationsErlandson, Lucas; Atkins, Zachary; Fox, Alyson; Vogl, Christopher; Miedlar, Agnieszka; Ponce, Colin (IEEE, 2023-09-26)Solving systems of linear equations is a critical component of nearly all scientific computing methods. Traditional algorithms that rely on synchronization become prohibitively expensive in computing paradigms where communication is costly, such as heterogeneous hardware, edge computing, and unreliable environments. In this paper, we introduce an s-step Approximate Conjugate Directions (s-ACD) method and develop resiliency measures that can address a variety of different data error scenarios. This method leverages a Conjugate Gradient (CG) approach locally while using Conjugate Directions (CD) globally to achieve asynchronicity. We demonstrate with numerical experiments that s-ACD admits scaling with respect to the condition number that is comparable with CG on the tested 2D Poisson problem. Furthermore, through the addition of resiliency measures, our method is able to cope with data errors, allowing it to be used effectively in unreliable environments.
- Spectral analysis of implicit 2 stage block Runge-Kutta preconditionersGander, Martin J.; Outrata, Michal (Elsevier, 2023-01-01)We analyze the recently introduced family of preconditioners in [15] for the stage equations of implicit Runge-Kutta methods for two stage methods. We give explicit formulas for the eigenvalues and eigenvectors of the preconditioned systems for a general method and use these to give explicit convergence estimates of preconditioned GMRES for some common choices of the implicit Runge-Kutta methods. This analysis also allows us to qualitatively predict and explain the main observed features of the GMRES convergence behavior, not only bound it. We illustrate our analysis with numerical experiments. We also consider the direction of numerical optimization for improving the preconditioners performance, as suggested in [15]. We consider two different ways – both distinct to the one introduced in [15] – and numerically optimize these, using the explicit bounds obtained beforehand.
- Topology Optimization with Adaptive Mesh RefinementDe Sturler, Eric; Paulino, Glaucio H.; Wang, Shun (2008)
- Zolotarev bounds for the singular values of Loewner matricesGarcia Hilares, Nilton; Embree, Mark (2020-11-20)