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All talks will be online, on Fridays from 11 a.m. to noon, followed by a 30-minutes interaction with the speaker on zoom. The Zoom room will be available from 10:30 a.m., and requires a passcode to access. The passcode will be sent in the weekly seminar announcement. If you are interested, but do not have access to the passcode, please contact Dr. Qiu, jingqiu@udel.edu​​.
Want to suggest a speaker? Send email to the organizer, Jingmei Qiu.
Information about the Courtyard Newark - University of Delaware Hotel.​
| Yongtao Zhang, Notre Dame University | 146 | Yongtao Zhang, Notre Dame University | Zoom | <p><span class="wrap-text"><strong>Title:</strong> Fast sparse grid simulations of high order WENO schemes <br><strong>Speaker: </strong>Yongtao Zhang, University of Notre Dame<br><strong>Abstract:</strong>Â Mathematical
models arising from applications are often PDE problems defined on
multidimensional spatial domains. However, when the spatial dimension
increases, the number of spatial grid points increases significantly. It
leads to large amount of operations and computational costs in the
numerical simulations, especially for high order accuracy schemes. In
the literature, sparse-grid technique has been developed as a very
efficient approximation tool for high dimensional problems. In this
talk, I will present our recent results on designing sparse grid
weighted essentially non-oscillatory (WENO) schemes for solving
hyperbolic PDEs. Our goal is to apply sparse grid techniques in high
order WENO schemes to achieve more efficient computations than that in
their regular performance in solving multidimensional PDEs. A challenge
is how to design the schemes on sparse grids such that comparable high
order accuracy of the WENO schemes in smooth regions of the solutions
can still be achieved as that for computations on regular single grids.
Additional challenge is that nonlinear stability of WENO simulations
needs to be preserved. We apply sparse-grid combination approach to
overcome these difficulties. WENO interpolations are applied for the
prolongation part in sparse-grid combination technique. The approach is
applied to both classical WENO scheme and the fifth order
multiresolution WENO scheme which is much simpler in computing linear
weights. Numerical examples defined on domains with up to four spatial
dimensions are presented to show that significant computational times
are saved, while both accuracy and stability of the original schemes are
maintained for numerical simulations on sparse grids. The methods are
also applied to some multidimensional Vlasov based PDEs to further
demonstrate large savings of computational costs by comparing with
simulations on regular single grids. This is joint work with graduate
students Ernie Tsybulnik and Xiaozhi Zhu at Notre Dame.</span><br></p> | 10/22/2021 3:00:00 PM | 10/22/2021 4:00:00 PM | | |
| Dr. Xue Hong, University of Delaware | 149 | Dr. Xue Hong, University of Delaware | | | 10/29/2021 3:00:00 PM | 10/29/2021 4:00:00 PM | | |
| Mark Gockenbach, University of Delaware | 147 | Mark Gockenbach, University of Delaware | Zoom | | 11/12/2021 4:00:00 PM | 11/12/2021 5:00:00 PM | | |
| Yangwen Zhang, Carnegie Mellon University | 145 | Yangwen Zhang, Carnegie Mellon University | Zoom | <p>​<span class="wrap-text"><strong>Title:</strong> Sharp $L^\infty$ estimates of HDG methods for Poisson equation II: 3D<br><strong>Abstract:</strong>
In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal
$L^\infty$ estimates (up to logarithmic factors) for the solution of
Poisson's equation by a hybridizable discontinuous Galerkin (HDG)
method. However, the estimates \emph{only} work in 2D. In this paper,
we use the approach in [Numer. Math., 131 (2015), pp. 771–822] and
obtain \emph{sharp} (without logarithmic factors) $L^\infty$ estimates
for the HDG method in both 2D and 3D. Numerical experiments are
presented to confirm our theoretical result.</span><br></p> | 11/19/2021 4:00:00 PM | 11/19/2021 5:00:00 PM | | |
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