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SUMMARY:David Williams (Penn State University)
DTSTART;VALUE=DATE-TIME:20221104T223000Z
DTEND;VALUE=DATE-TIME:20221104T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/2
DESCRIPTION:Title: Space-Time Finite Element Methods: Challenges and Perspectives\nby
David Williams (Penn State University) as part of SFU Applied and Computa
tional Math Seminar\n\nLecture held in K9509.\n\nAbstract\nSpace-time fini
te element methods (FEMs) are likely to grow in popularity due to the ongo
ing growth in the size\, speed\, and parallelism of modern computing platf
orms. The allure of space-time FEMs is both intuitive and practical. From
the intuitive standpoint\, there is considerable elegance and simplicity i
n accommodating both space and time using the same numerical discretizatio
n strategy. From the practical standpoint\, there are considerable advanta
ges in efficiency and accuracy that can be gained from space-time mesh ada
ptation: i.e. adapting the mesh in both space and time to resolve importan
t solution features. However\, despite these considerable advantages\, the
re are numerous challenges that must be overcome before space-time FEMs ca
n realize their full potential. These challenges are primarily associated
with four-dimensional geometric obstacles (hypersurface and hypervolume me
sh generation)\, four-dimensional approximation theory (basis functions an
d quadrature rules)\, four-dimensional boundary condition enforcement (wel
l-posed\, moving boundary conditions)\, and iterative-solution techniques
for large-scale linear systems. In this presentation\, we will provide a b
rief overview of space-time FEMs\, and discuss some of the latest research
developments and ongoing issues.\n\nDavid M. Williams is an assistant pro
fessor at The Pennsylvania State University in the Mechanical Engineering
Department. He came to Penn State from the Flight Sciences division of Boe
ing Commercial Airplanes and Boeing Research and Technology\, where he wor
ked for several years as a computational fluid dynamics engineer. Williams
received his M.S. and Ph. D. in Aeronautics and Astronautics at Stanford
University. He holds a B.S.E. in Aerospace Engineering from the University
of Michigan. He has made significant advances in the design of numerical
algorithms for computational fluid dynamic simulations. Currently\, his re
search focuses on employing high-order Finite Element schemes to more accu
rately predict unsteady flows.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Messenger (University of Colorado Boulder)
DTSTART;VALUE=DATE-TIME:20221007T223000Z
DTEND;VALUE=DATE-TIME:20221007T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/4
DESCRIPTION:Title: Weak-form sparse identification of differential equations from noisy m
easurements\nby Daniel Messenger (University of Colorado Boulder) as p
art of SFU Applied and Computational Math Seminar\n\nLecture held in K9509
.\n\nAbstract\nData-driven modeling refers to the use of measurement data
to infer the parameters and structure of a mathematical model\, or to aid
in forward simulations of a partially known mathematical model. Motivated
by problems in collective cell biology\, this talk will explore algorithms
which automate the map from experimental data to governing differential e
quations\, specifically using weak formulations of the dynamics. We will s
how that the weak form is an ideal framework for identifying models from d
ata if the performance criteria are robustness to data corruptions\, highl
y accurate model recovery when corruption levels are low\, and computation
al efficiency. We will first demonstrate the advantages of the resulting w
eak-form sparse identification for nonlinear dynamics algorithm (WSINDy) i
n the discovery of correct underlying model equations across several key m
odeling paradigms\, including ordinary differential equations (ODEs)\, par
tial differential equations (PDEs)\, and interacting particle systems (IPS
). We will then discuss more recent extensions of this framework\, includi
ng weak-form identification of PDEs from streaming data\, enabling identif
ication of time-varying coefficients\, and the use of weak-form model sele
ction as a classifier to determine species membership in a heterogeneous p
opulation of initially unlabeled cells. We will conclude with an overview
of possible next directions\, including open questions related to numerica
l analysis and theoretical recovery guarantees.\n\nPasscode 696604\n
LOCATION:https://researchseminars.org/talk/AppliedMath/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hansol Park (SFU)
DTSTART;VALUE=DATE-TIME:20221014T223000Z
DTEND;VALUE=DATE-TIME:20221014T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/5
DESCRIPTION:Title: The Watanabe-Strogatz transform and constant of motion functionals for
kinetic vector models\nby Hansol Park (SFU) as part of SFU Applied an
d Computational Math Seminar\n\n\nAbstract\nWe present a kinetic version o
f the Watanabe-Strogatz (WS) transform for vector models in this paper. Fr
om the generalized WS-transform\, we can reduce the kinetic vector model i
nto an ODE system. We also obtain the cross-ratio type constant of motion
functionals for kinetic vector models under suitable conditions. We presen
t the sufficient and necessary conditions for the existence of the suggest
ed constant of motion functionals. As an application of the constant of mo
tion functional\, we provide the instability of bipolar states of the kine
tic swarm sphere model. We also provide the WS-transform and constant of m
otion functionals for non-identical kinetic vector models.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Solomon (MIT)
DTSTART;VALUE=DATE-TIME:20221021T220000Z
DTEND;VALUE=DATE-TIME:20221021T230000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/6
DESCRIPTION:Title: Volumetric Methods for Modeling\, Deformation\, and Correspondence
\nby Justin Solomon (MIT) as part of SFU Applied and Computational Math Se
minar\n\n\nAbstract\nIn 3D modeling\, medical imaging\, and other discipli
nes\, popular techniques for geometry processing often rely on mathematica
l models for surface geometry\, viewing shapes as thin sheets embedded in
$\\mathbb{R}^3$\; this construction neglects the fact that many of these s
urfaces are "boundary representations\," intended to represent boundaries
of volumes. As an alternative\, in this talk we will explore how calculat
ions on the extrinsic space around a surface can benefit geometry processi
ng applications---as well as the mathematical\, numerical\, and computatio
nal challenges of this extension to three dimensions. Our algorithms for
these problems will build on machinery from differential geometry\, geomet
ric measure theory\, vector field design\, and machine learning.\n\n(Joint
work with several members of the MIT Geometric Data Processing Group.)\n
LOCATION:https://researchseminars.org/talk/AppliedMath/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Wiedemann (Universitaet Augsburg)
DTSTART;VALUE=DATE-TIME:20220916T223000Z
DTEND;VALUE=DATE-TIME:20220917T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/11
DESCRIPTION:Title: Homogenization in evolving porous media\nby David Wiedemann (Univ
ersitaet Augsburg) as part of SFU Applied and Computational Math Seminar\n
\n\nAbstract\nNumerical simulations of physical or chemical processes in h
eterogeneous \nmedia require a resolution of the heterogeneous structure.
If\, however\, \nthis heterogeneity is microscopically small while the obj
ect under \nconsideration is large\, a dimensional mismatch occurs and cla
ssical \nnumerical methods become infeasible.\n\nAt this point\, analytica
l homogenization provides effective homogeneous \nsubstitute models\, whic
h can be simulated numerically much more easily. \nOne class of problems t
hat can be treated are processes in porous media. \nIn many biological or
chemical applications\, the pore structure evolves \nin time\, which imped
es classical homogenization. By means of the \ntwo-scale transformation me
thod\, we can overcome this difficulty and \nderive new effective models f
or problems in evolving heterogeneous media.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingwei Hu (University of Washington)
DTSTART;VALUE=DATE-TIME:20220923T223000Z
DTEND;VALUE=DATE-TIME:20220924T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/12
DESCRIPTION:Title: Dynamical low-rank methods for high-dimensional collisional kinetic e
quations\nby Jingwei Hu (University of Washington) as part of SFU Appl
ied and Computational Math Seminar\n\n\nAbstract\nKinetic equations descri
be the nonequilibrium dynamics of a complex system using a probability den
sity function. Despite of their important role in multiscale modeling to b
ridge microscopic and macroscopic scales\, numerically solving kinetic equ
ations is computationally demanding as they lie in the six-dimensional pha
se space. Dynamical low-rank method is a dimension-reduction technique tha
t has been recently applied to kinetic theory\, yet most of the endeavor i
s devoted to linear or collisionless problems. In this talk\, we introduce
efficient dynamical low-rank methods for Boltzmann type collisional kinet
ic equations\, building on certain prior knowledge about the low-rank stru
cture of the solution.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Iwen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20221207T233000Z
DTEND;VALUE=DATE-TIME:20221208T003000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/15
DESCRIPTION:Title: Low-Distortion Embeddings of Submanifolds of $R^n$: Lower Bounds\, Fa
ster Realizations\, and Applications\nby Mark Iwen (Michigan State Uni
versity) as part of SFU Applied and Computational Math Seminar\n\nLecture
held in ASB10908.\n\nAbstract\nLet M be a smooth submanifold of R^n equipp
ed with the Euclidean(chordal) metric. This talk will consider the smalles
t dimension\, m\, for which there exists a bi-Lipschitz function f:M →R^
m with bi-Lipschitz constants close to one. We will begin by presenting a
bound for the embedding dimension m from below in terms of the bi-Lipschit
z constants of f and the reach\, volume\, diameter\, and dimension of M. W
e will then discuss how this lower bound can be applied to show that prior
upper bounds by Eftekhari and Wakin on the minimal low-distortion embeddi
ng dimension of such manifolds using random matrices achieve near-optimal
dependence on dimension\, reach\, and volume (even when compared against n
onlinear competitors). Next\, we will discuss a new class of linear maps f
or embedding arbitrary (infinite) subsets of R^n with sufficiently small G
aussian width which can both (i) achieve near-optimal embedding dimensions
of submanifolds\, and (ii) be multiplied by vectors in faster than FFT-ti
me. When applied to d-dimensional submanifolds of R^n we will see that the
se new constructions improve on prior fast embedding matrices in terms of
both runtime and embedding dimension when d is sufficiently small. Time pe
rmitting\, we will then conclude with a discussion of non-linear so-called
“terminal embeddings” of manifolds which allow for extensions of the
famous Johnson-Lindenstrauss Lemma beyond what any linear map can achieve.
\n\nThis talk will draw on joint work with various subsets of Mark Roach (
MSU)\, Benjamin Schmidt (MSU)\, and Arman Tavakoli (MSU).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Corless (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20221012T223000Z
DTEND;VALUE=DATE-TIME:20221012T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/16
DESCRIPTION:Title: Compact cubic splines and compact finite differences\nby Robert C
orless (University of Western Ontario) as part of SFU Applied and Computat
ional Math Seminar\n\nLecture held in K9509.\n\nAbstract\nIn this paper we
introduce an apparently new spline-like interpolant that we call a compac
t cubic interpolant or compact cubic spline\; this is similar to a cubic s
pline introduced in 1972 by Swartz and Varga\, but has higher order accura
cy at the edges. We argue that for nearly uniform meshes the compact cubic
approach offers some potential advantages\, and offers a simple way to tr
eat the edge conditions\, relieving the user of the burden of deciding to
use one of the three standard options: free (natural)\, complete (clamped)
\, or “not-a-knot” conditions. Finally\, we establish that the matrice
s defining the compact cubic splines (equivalently\, the fourth-order comp
act finite difference formulæ) are totally nonnegative\, if all mesh widt
hs are the same sign\, for instance if the mesh is real and nodes are numb
ered in increasing order.\n\nThe talk will be in-person and use chalk\, in
the wonderful multi-board room that SFU has for the purpose. The YouTube
version linked above was a computer version of the same talk\, with slide
s\, which has some advantages (run it at double speed!). But the chalk ve
rsion offers a chance to slow down and appreciate more of the "big picture
". The topic will be accessible if the listener has heard what a "spline"
is\, but the main point is to prove total nonnegativity of a certain trid
iagonal matrix. I'll also make a connection to the (very useful) subject
of compact finite differences.\n\nThis is joint work with Dr. Leili Rafiee
Sevyeri (CS University of Waterloo)\n
LOCATION:https://researchseminars.org/talk/AppliedMath/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20230106T233000Z
DTEND;VALUE=DATE-TIME:20230107T003000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/18
DESCRIPTION:by TBA as part of SFU Applied and Computational Math Seminar\n
\nLecture held in K9509.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruiwen Shu (University of Georgia)
DTSTART;VALUE=DATE-TIME:20230120T233000Z
DTEND;VALUE=DATE-TIME:20230121T003000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/19
DESCRIPTION:Title: Global Minimizers of a Large Class of Anisotropic Attractive-Repulsiv
e Interaction Energies in 2D\nby Ruiwen Shu (University of Georgia) as
part of SFU Applied and Computational Math Seminar\n\n\nAbstract\nI will
discuss my joint work with José Carrillo on a large family of Riesz-type
singular interaction potentials with anisotropy in two dimensions. Their a
ssociated global energy minimizers are given by explicit formulas whose su
pports are determined by ellipses under certain assumptions. More precisel
y\, by parameterizing the strength of the anisotropic part we characterize
the sharp range in which these explicit ellipse-supported configurations
are the global minimizers based on linear convexity arguments. Moreover\,
for certain anisotropic parts\, we prove that for large values of the para
meter the global minimizer is only given by vertically concentrated measur
es corresponding to one dimensional minimizers. We also show that these el
lipse-supported configurations generically do not collapse to a vertically
concentrated measure at the critical value for convexity\, leading to an
interesting gap of the parameters in between. In this intermediate range\,
we conclude by infinitesimal concavity that any superlevel set of any loc
al minimizer in a suitable sense does not have interior points. Furthermor
e\, for certain anisotropic parts\, their support cannot contain any verti
cal segment for a restricted range of parameters\, and moreover the global
minimizers are expected to exhibit a zigzag behavior. All these results h
old for the limiting case of the logarithmic repulsive potential\, extendi
ng and generalizing previous results in the literature.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Pia Gualdani (UT Austin)
DTSTART;VALUE=DATE-TIME:20230317T223000Z
DTEND;VALUE=DATE-TIME:20230317T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/27
DESCRIPTION:by Maria Pia Gualdani (UT Austin) as part of SFU Applied and C
omputational Math Seminar\n\nLecture held in K9509.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleks Donev (NYU Courant)
DTSTART;VALUE=DATE-TIME:20230519T223000Z
DTEND;VALUE=DATE-TIME:20230519T233000Z
DTSTAMP;VALUE=DATE-TIME:20230205T195639Z
UID:AppliedMath/32
DESCRIPTION:by Aleks Donev (NYU Courant) as part of SFU Applied and Comput
ational Math Seminar\n\nInteractive livestream: https://sfu.zoom.us/j/6892
4786057?pwd=bDdFQjR3SFdsQkJSY0VKM0NuOU8rQT09\nLecture held in K9509.\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/32/
URL:https://sfu.zoom.us/j/68924786057?pwd=bDdFQjR3SFdsQkJSY0VKM0NuOU8rQT09
END:VEVENT
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