MSFrD25
Emerging PDEs: Analysis and Computation  Part III of IV
For Part I, see MSThD25
For Part II, see MSThE25
For Part IV, see MSFrE25
Date: August 14
Time: 13:3015:30
Room: 210A
(Note: Click title to show the abstract.)
Organizer:
Chen, Zhiming (AMSS, Chinese Acad. of Sci.)
Nochetto, Ricardo (Univ. of Maryland)
Zhang, Chensong (Acad. of mathematics & Sys. Sci.)
Abstract: Novel models in science and engineering are governed by nonlinear integrodifferential equations with increasing complexity which demand innovative techniques in both analysis and computation, such as adaptivity, fast methods and preconditioning, and structure preserving algorithms. Areas of special interest include complex fluids and new materials, electromagnetism and wave propagation, uncertainty quantification, and fractional PDEs, among others.
This minisymposium intends to gather about 16 world experts and young researchers in analysis and computation of PDE to discuss the most recent progress in this exciting field as well as future directions for research.
MSFrD251
13:3014:00
Preasymptotic error analysis of higher order FEM and CIPFEM for Helmholtz equation with high wave number
Wu, Haijun (Nanjing Univ.)
Abstract: $H^1$ and $L^2$ error estimates with explicit dependence on the wave number $k$ are derived for the FEM and CIPFEM. In particular, it is shown that if $k^{2p+1}h^{2p}$ is sufficiently small, then the pollution errors of both methods in $H^1$norm are bounded by $O(k^{2p+1}h^{2p})$, which coincides with the phase error of the FEM obtained by existent dispersion analyses on Cartesian grids.
MSFrD252
14:0014:30
Semiclassical Computational Methods for Quantum Dynamics with
Bandcrossings
Jin, Shi (Univ. of WisconsinMadison & Shanghai Jiao Tong Univ.)
Abstract: We develop semiclassical models and multiscale computational methods for
quantum dynamics with nonadiabatic effects. Applications of such methods
include surface hopping, Schrodinger equation with periodic potentials,
elastic and electromagnetic waves with polarizations, and graphene. We use
the Wigner transform to derive these models. The key idea is to evolve the
dynamics of the entire Wigner
matrices, which contain important nonadiabatic terms,
not just the diagonal projections corresponding to the
eigenstates of the Hamiltonians. We also develop multiscale computational
methods based on these models and numerical examples will be used to show
the validity of these models in captuing the qunatum transitions at the
crossingpoints.
MSFrD253
14:3015:00
A rate of convergence for MongeAmp¨Śre equation
Zhang, Wujun (Univ. of Maryland, College Park)
Nochetto, Ricardo (Univ. of Maryland)
Abstract: MongeAmp¨Śre equation arises naturally from differential geometry, optimal transportation and other fields of science and engineering.
In this talk, we shall review the viscosity solution of MongeAmp¨Śre equation. We design a numerical approximation of MongeAmp¨Śre equation by using its geometric interpretation. Applying this geometric interpretation and discrete Alexandroff estimate, we derive a rate of convergence to the viscosity solution for MongeAmp¨Śre equations.
MSFrD254
15:0015:30
Analysis and Computation of Discretized Coupled PDEs
Xu, Jinchao (PKU,and The Pennsylvania State Univ.)
Abstract: I will report some recent works on structurepreserving and stable discretization of some multiphysics models and robust preconditioning methods for the resulting algebraic systems. In particular, judging from theoretical and/or numerical analysis of several mathematical models for magnetohydrodynamics (MHD) which involve the coupling of NavierStokes or Euler equations with Maxwell equations, I will argue that some more complicated models may be easier to simulate than some simplified models that have been often used in practice.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
