Since Fall 2008, the seminar provides a venue for researchers and students to present and discuss mathematical approaches for the investigation of challenging real-life problems. Topics range from pure mathematical subjects to applications. The seminar also aims to encourage students to develop their own research projects. We welcome all those who want to broaden their perspective on the mathematical methods used in contemporary research...

Send an e-mail to igtomas@ttu.edu if:

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| The Dictator EquationVakhtang Putkaradze Mathematical and Statistical Sciences, University of Alberta |

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| Recent developments on convex integration applied to surface quasi-geostrophic equationsKazuo Yamazaki Department of Mathematics and Statistics, Texas Tech University |

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| Chaos in the stochastic Galerkin-Navier-Stokes equationsSam Punshon-Smith Department of Mathematics, Tulane University |

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| A random selection of mathematical and computational challenges in pulsed power and plasma scienceJacob Stephens Department of Electrical Engineering, Texas Tech University |

Naturally, the pulsed power community faces a number of mathematical and computational challenges. These range from molecular dynamics models of gas, electron, and ion emission from solids and dielectrics, various plasma models (fluid, particle, magnetohydrodynamic, and more), electromagnetic models, and often multi-physics combinations of these models and more. More recently, these models have been combined with modern optimization and machine learning techniques to develop next generation pulsed power systems with state-of-the-art capabilities. This talk will discuss a few of the mathematical and computational challenges in the pulsed power community.

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| Structure-preserving approximation techniques for computational fluid dynamicsEric Tovar Los Alamos National Laboratories, XCP-2 |

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| Learning Turbulence Models from Data - A Unified Perspective of Data Assimilation and Machine LearningHeng Xiao University of Stuttgart, Cluster of Excellence SimTech |

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| A New Theory of Fractional Differential Calculus and Fractional Sobolev Spaces and ApplicationsXiaobing Feng University of Tennessee, Department of Mathematics |

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- To be notified about TTU's Applied Mathematics Seminar on a weekly basis please send e-mail to igtomas@ttu.edu

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| Low-rank Methods for Radiation Transport CalculationsRyan McClarren University of Notre Dame, Aerospace and Mechanical Engineering |

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| Pseudo-spectral methods for incompressible flows with variable densityLoic Cappanera University of Houston, Department of Mathematics |

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| Approximate Eigenvalues via the Landscape Function in Disordered MediaShiwen Zhang University of Massachusetts Lowell, Department of Mathematics |

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| Hidden symmetries in quantum mechanics revealed by the trajectory-based formulationBill Poirier Texas Tech University, Department of Chemistry |

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| Development of a coupled Trefftz and finite element method for approximating Maxwell's equationsPeter Monk University of Delaware, Department of Mathematics |

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| Scalable Multiphysics Block Preconditioning for Solution of Implicit Continuum Models for Challenging Plasma Physics Systems with Application to Magnetic Confinement FusionJohn Shadid Sandia National Laboratories, Department of Mathematics and Statistics University of UNM |

This talk will discuss the structure of the implicit continuum fluid models that we are employing for MFC type applications. These include resistive magnetohydrodynamics (MHD), and a partially ionized multifluid electromagnetic (EM) plasma formulation. After discretization by stabilized finite element type methods the strongly coupled highly nonlinear algebraic system is achieved with a fully-coupled Newton nonlinear iterative method. The resulting large-scale sparse linear systems are iteratively solved by a GMRES Krylov method, preconditioned by approximate block factorization (ABF) and physics-based preconditioning approaches. These methods reduce the coupled multiphysics system to a set of simplified sub-systems to which scalable algebraic multilevel methods (AMG) can be applied. A critical aspect of these preconditioners is the development of approximate Schur complement operators that encode the critical cross-coupling physics of the system. To demonstrate the flexibility and performance of these methods we consider application of these techniques to various challenging prototype plasma problems. These include computational results relevant to aspects of magnetic confinement fusion applications. Results are presented on robustness, efficiency, and the parallel and algorithmic scaling of the solution methods. This work is collaborative with Jesus Bonilla, Edward Phillips, Peter Ohm, Michael Crockatt, Ignacio Tomas, Roger P. Pawlowski, R. Tuminaro, Jonathan Hu, Xinazhu-Tang, and Luis Chacon.

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