| Dr. Hong Zhang, Argonne National Lab | 152 | Dr. Hong Zhang, Argonne National Lab | | | 4/22/2022 3:00:00 PM | 4/22/2022 4:00:00 PM | | |
| Professor Peter Monk, University of Delaware | 148 | Professor Peter Monk, University of Delaware | | <p>​<span class="wrap-text"><strong>Title:</strong> Development of a coupled Trefftz and finite element method for approximating Maxwell's equations<br><strong>Abstract:</strong>
The talk focuses on a discontinuous Galerkin method for the time
harmonic Maxwell system. This method is based on the use of a finite
element grid, but uses plane wave solutions of Maxwell's equations on
each element to approximate the global field. Because each basis
function satisfies Maxwell's equations, the problem can be reduced to a
coupled linear system on the faces of the grid. Arbitrarily high order
of convergence can be achieved by taking more planes waves in suitable
directions element by element, although ill-conditioning must be
carefully controlled. Unfortunately this method has severe deficiencies
when applied to some resonant problems. To remedy this, we have tried
to couple polynomial finite element methods with the plane wave scheme.
I shall report on the current state of this effort.</span><br></p> | 2/18/2022 4:00:00 PM | 2/18/2022 5:00:00 PM | | |
| Dr. William Taitano, Air Force Research Lab | 151 | Dr. William Taitano, Air Force Research Lab | | | 2/11/2022 4:00:00 PM | 2/11/2022 5:00:00 PM | | |
| Dr. Jingmei Qiu, University of Delaware | 150 | Dr. Jingmei Qiu, University of Delaware | | <p>​Title: A Conservative Low Rank Tensor Representation of Nonlinear Vlasov-Poisson and Vlasov-Maxwell Solutions</p><p><br>Abstract:
We propose a low-rank tensor approach to approximate nonlinear Vlasov
solutions and their associated flow maps. The approach takes advantage
of the fact that the differential operators in the Vlasov equation is
tensor friendly, based on which we propose to dynamically and
adaptively build up low-rank solution basis by adding new basis
functions from discretization of the PDE, and removing basis from an
SVD-type truncation procedure. For the discretization, we adopt a high
order finite difference spatial discretization and a second order strong
stability preserving multi-step time discretization. We apply the same
procedure to evolve the dynamics of the flow map in a low-rank fashion,
which proves to be advantageous when the flow map enjoys the low rank
structure, while the solution suffers from high rank or displays
filamentation structures. Local conservation properties are built in by a
set of special projections. Hierarchical Tucker decomposition is
adopted for high dimensional problems. An extensive set of linear and
nonlinear Vlasov test examples are performed to show the high order
spatial and temporal convergence of the algorithm with mesh refinement
up to SVD-type truncation, the significant computational savings of the
proposed low-rank approach especially for high dimensional problems, the
improved performance of the flow map approach for solutions with
filamentations.<br></p> | 12/3/2021 4:00:00 PM | 12/3/2021 5:00:00 PM | | |
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