epshteyn (at) math.utah.edu
)January 23. Note: 3:55pm - 5:00pm, Room LCB 225
Speaker: Alexander Mamonov, Schlumberger
Title: Reduced order models for seismic full waveform inversion.
Abstract:We present a framework for the numerical solution of the seismic full
waveform inversion (FWI) problem using the reduced order models
(ROMs). In FWI one determines the spatial distribution of the acoustic
or elastic properties of the subsurface from the surface or well-bore
measurements of the seismic data induced by sources. In our approach
the ROM is a projection of the acoustic or elastic PDE operator on the
subspace spanned by the snapshots of the solutions to the forward
problem. The ROM can be found directly from the measured time domain
seismic data. The use of the ROM in inversion is twofold. First, after
the transformation to the block tridiagonal (finite difference) form
the ROM misfit can be used as an objective functional for
optimization. Such functional is more convex than the conventional
data misfit and thus is less prone to common issues like abundant
local minima (cycle skipping), multiple reflection artifacts, etc.
Second, if a background kinematic model is available the projected PDE
operator can be backprojected to obtain a seismic image directly. This
leads to a non-linear migration algorithm that recovers not only the
locations of discontinuities (reflectors) but also their relative
strength, the process known as the true amplitude migration.
January 26 (Student Talk)
Speaker: Predrag Krtolica, Department of Mathematics, University of Utah
Title: Compatibility Conditions in Discrete Structures
Abstract:The talk will be about the analysis of compatibility
conditions of 2-dimensional hexagonal frameworks, which, in the limit,
lead to the continuum compatibility condition, suggesting the
equivalence. This fact has many applications, as it is much easier to
study brittleness of materials on a discrete model than on a
continuum.
February 2
Speaker: Ching-Shan
Chou, Department of Mathematics, Ohio State University
Title: Computer Simulations of Yeast Mating Reveal Robustness Strategies for Cell-Cell
Interactions
Abstract: Cell-to-cell communication is fundamental to biological processes which require
cells to coordinate their functions. A simple strategy adopted by many biological
systems to achieve this communication is through cell signaling, in which
extracellular signaling molecules released by one cell are detected by other cells
via specific mechanisms. These signal molecules activate intracellular pathways to
induce cellular responses such as cell motility or cell morphological changes.
Proper communication thus relies on precise control and coordination of all these
actions.
February 9
Speaker: Hyeonbae Kang, Department of Mathematics, Inha University
Title: Spectral theory of Neumann-Poincare
operator and applications
Abstract:The Neumann-Poincare (NP) operator is a boundary integral
operator which arises naturally when solving boundary value problems using
layer potentials. It is not self-adjoint with the usual inner product. But
it can symmetrized by introducing a new inner product on $H^{-1/2}$ spaces
using Plemelj's symmetrization principle. Recently many interesting
properties of the NP operator have been discovered. I will discuss about
this development and various applications including solvability of PDEs
with complex coefficients and plasmonic resonance.
February 23
Speaker: Lajos Horvath, Department of Mathematics, University of Utah
Title: Functional Data Analysis with Some
Applications
Abstract:TBA
February 27, Special Joint Time
Series/Stochastics/Applied Math Seminar
Note: Time 3pm, Room LCB 219
Speaker: Alexander
Aue, Department of Statistics, University of California, Davis
Title: TBA
Abstract:TBA
March 9
Speaker: Jay Gopalakrishnan, Department of Mathematics, Portland State University
Title: TBA
Abstract:TBA
March 13
Speaker:
Vladimir Druskin, Schlumberger
Title: Reduced order models for large scale wave problems
Abstract:Reduced order models approximate transfer functions of large-scale linear dynamical
systems by small equivalent ones. Their matrices can be geometrically interpreted
as finite-difference operators discretized on so-called optimal grids, a. k. a.
spectrally matched grids or finite-difference Gaussian quadrature rules. In this
talk we discuss some recent applications of this powerful approach to numerical
solution of hyperbolic problems in the time and frequency domains. They include
optimal discretization of perfectly matched layers and multi-scale elastic wave
propagation. Time permitting, I will discuss another recent model reduction approach
for wave propagation in unbounded domains, based on scattering resonance
representation.
March 23
Speaker: Becca Thomases, Department of Mathematics, University of California, Davis
Title: TBA
Abstract:TBA
March 30
Speaker: Maxence Cassier, Department of Mathematics, University of Utah
Title: The limiting amplitude principle in a medium composed of a dielectric and
a metamaterial
Abstract:TBA
April 13 (Student Talk)
Speaker: Ornella Mattei, Visiting Department of Mathematics, University of Utah
Title: Variational
formulations for the linear viscoelastic
problem in the time domain
Abstract:TBA
April 20 (reserved)
Speaker: TBA
Title: TBA
Abstract:TBA
epshteyn (at) math.utah.edu
).
Past lectures: Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.