BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Hybrid numerical-asymptotic methods for wave scattering problems
DTSTART;VALUE=DATE-TIME:20160204T142500Z
DTEND;VALUE=DATE-TIME:20160204T150000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2892@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stephen Langdon (University of Reading)\n\nLinear wa
ve scattering problems (e.g. for acoustic\, electromagnetic and elastic wa
ves) are ubiquitous in science and engineering applications. However\, co
nventional numerical methods for such problems (e.g. FEM or BEM with piece
wise polynomial basis functions) are prohibitively expensive when the wave
length of the scattered wave is small compared to typical lengthscales of
the scatterer (the so-called "high frequency" regime). This is because the
solution possesses rapid oscillations which are expensive to capture usin
g conventional approximation spaces. In this talk we outline recent progre
ss in the development of "hybrid numerical-asymptotic" methods\, which inc
ur significantly reduced computational cost. These methods use approximati
on spaces containing oscillatory basis functions\, carefully chosen to cap
ture the high frequency asymptotic behaviour. In particular we discuss som
e of the interesting challenges arising from nonconvex\, penetrable and th
ree-dimensional scatterers.\n\nhttps://indico.math.cnrs.fr/event/902/contr
ibutions/2892/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2892/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quasi-optimal domain decomposition methods for time-harmonic acous
tic and electromagnetic wave problems
DTSTART;VALUE=DATE-TIME:20160204T105500Z
DTEND;VALUE=DATE-TIME:20160204T113000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2887@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christophe Geuzaine (Université de Liège)\n\nIn te
rms of computational methods\, solving three-dimensional time-harmonic\nac
oustic or electromagnetic wave problems is known to be challenging\, espec
ially\nin the high frequency regime and in the presence of inhomogenous me
dia. The\nbrute-force application of the finite element method in this cas
e leads to the\nsolution of very large\, complex and possibly indefinite l
inear systems. Direct\nsparse solvers do not scale well for such problems\
, and Krylov subspace\niterative solvers can exhibit slow convergence\, or
even diverge. Domain\ndecomposition methods provide an alternative\, iter
ating between subproblems of\nsmaller sizes\, amenable to sparse direct so
lvers. In this talk I will present a\nclass of non-overlapping Schwarz do
main decomposition methods that exhibit\nquasi-optimal convergence propert
ies\, i.e.\, with a convergence that is optimal\nfor the evanescent modes
and significantly improved compared to competing\napproaches for the remai
ning modes [1\, 2]. These improved properties result from\na combination o
f an appropriate choice of transmission conditions and a suitable\nlocaliz
ation of the optimal\, integral operators associated with the\ncomplementa
ry of each subdomain [3]. The resulting algorithms are well suited\nfor hi
gh-performance\, large scale parallel computations in complex geometrical\
nconfigurations when combined with appropriate preconditionners [4].\n\n[1
] Y. Boubendir\, X. Antoine and C. Geuzaine\, A quasi-optimal non-overlapp
ing\ndomain decomposition algorithm for the Helmholtz equation. Journal of
\nComputational Physics 231 (2)\, pp. 262-280\, 2012.\n\n[2] M. El Bouajaj
i\, B. Thierry\, X. Antoine and C. Geuzaine. A quasi-optimal\ndomain decom
position algorithm for the time-harmonic Maxwell's\nequations. Journal of
Computational Physics 294\, pp. 38-57\, 2015.\n\n[3] M. El Bouajaji\, X. A
ntoine\, C. Geuzaine. Approximate local\nmagnetic-to-electric surface oper
ators for time-harmonic Maxwell's\nequations. Journal of Computational Phy
sics 279 (15)\, 241-260\, 2014.\n\n[4] A. Vion and C. Geuzaine. Double swe
ep preconditioner for optimized Schwarz\nmethods applied to the Helmholtz
problem. Journal of Computational Physics 266\,\n171-190\, 2014.\n\nhttps:
//indico.math.cnrs.fr/event/902/contributions/2887/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2887/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solution schemes and approximation tools devoted to the simulation
of electromagnetic testing by the boundary element method
DTSTART;VALUE=DATE-TIME:20160205T100500Z
DTEND;VALUE=DATE-TIME:20160205T104000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2888@indico.math.cnrs.fr
DESCRIPTION:Speakers: Edouard Demaldent (CEA)\n\nElectromagnetic testing i
s widely used for the characterization of a medium as to the detection of
defects. In particular\, the eddy current non-destructive testing of tubes
in steam generators is determinant to diagnose the integrity of heat exch
angers in nuclear industry. A valuable support to the mastering of these p
rocesses is brought by modeling and the finite boundary element method (BE
M) is an appropriate simulation tool to many inspection configurations. Th
e department of imaging and simulation for the control at CEA LIST is deve
loping a BEM code devoted to these applications\, mostly for eddy current
testing. Some of these tools are\, or will be\, integrated into the CIVA s
oftware platform\, whose target users are experts in non-destructive testi
ng (non numericians).\n\nIn this talk\, we will present our research work
and review the technical options related to this activity. We will start w
ith an overview of a recent study carried out in collaboration with IRSN (
the French public expert in nuclear and radiological risks) to illustrate
our practical use of BEM. We will then introduce low frequency formulation
s that are studied in collaboration with the research group POEMS. We will
in particular discuss a multi-step algorithm for solving the transmission
problem (known as PMCHWT)\, which is stable over a wide range of paramete
rs that are relevant to electromagnetic testing\, and in particular go bey
ond eddy currents. The third part of the talk will focus on the discretiza
tion tools developed for the BEM code at LIST. They are based on the use o
f basic interpolation techniques to simplify the construction of complex a
pproximation spaces that meet our needs for light but accurate computation
s (such as the Helmholtz decomposition of high-order edge functions).\n\nh
ttps://indico.math.cnrs.fr/event/902/contributions/2888/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2888/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modelling tools for scattering and antennas problems
DTSTART;VALUE=DATE-TIME:20160204T102000Z
DTEND;VALUE=DATE-TIME:20160204T105500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2889@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jérôme Simon (Onera Palaiseau)\n\nThe Surface Inte
gral Equation is one of the most used methods in the simulation of electro
magnetic problems. Its implementation combined with a fast multipole algor
ithm (MLFMM) and iterative solvers leads efficient and accurate methods fo
r the analysis of radar cross section (RCS) for a target.\n\n \nDifferent
methods (MLFMM\, ACA\, Domain Decomposition Method …) and formulations E
FIE (Electric Field Integral Equation)\, MFIE (Magnetic Field Integral Equ
ation)\, CFIE (Combined Field Integral Equation) and GCSIE (integral formu
lations inherently well-conditioned using a regularizing operator ) were i
mplemented at ONERA. \n\n\nIn this talk\, we will present various applica
tions obtained with our tools like radar cross section (RCS)\, antenna rad
iation\, ….\n\nhttps://indico.math.cnrs.fr/event/902/contributions/2889/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2889/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Second-Kind Single Trace Boundary Integral Equations
DTSTART;VALUE=DATE-TIME:20160205T130000Z
DTEND;VALUE=DATE-TIME:20160205T133500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2890@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ralf Hiptmair (ETH Zürich)\n\nFor second-order line
ar transmission problems involving a single closed interface separating tw
o homogeneous materials\, a well-posed second-kind boundary integral formu
lation has been known for a long time. It arises from a straightforward co
mbination of interior and exterior Calderon identities. Apparently\, this
simple approach cannot be extended to "composite" settings involving more
than two materials.\n\n\nThe key observation is that the same second-kind
boundary integral equations (BIE) can also be obtained through a multi-pot
ential representation formula. We can attach a potential to each boundary
of a material sub-domain\, add them all up to a multi potential\, and then
we notice that\, thanks to a null-eld property\, the sum provides a repre
sentation of the field solution\, when its traces a plugged into the poten
tials. Taking traces yields a BIE on the skeleton of the sub-domain partit
ion. The skeleton traces of the unknown field will solve it.\n\n\nUsing th
e fact that multi-potentials for a single homogeneous material must vanish
\, the BIE can be converted into second-order form: for the scalar case (a
coustics) its operator becomes a compact perturbation of the identity in $
L^2$. Galerkin matrices arising from piecewise polynomial Galerkin boundar
y element (BEM) discretization will be intrinsically well-conditioned.\n\n
\nThe new second-kind boundary element method has been implemented both fo
r acoustic and electromagnetic scattering at composite objects. Numerical
tests confirm the excellent mesh-size independent conditioning of the Gale
rkin BEM matrices and the resulting fast convergence of iterative solvers
like GMRES. Furthermore\, by simple post-processing\, we obtain discrete s
olutions of competitive accuracy compared to using BEM with the standard f
irst-kind BIE.\nWell-posedness of the new second-kind formulations is an o
pen problem\, as is the compactness\nof the modulation of the identity in
the case of Maxwell's equations. Reassuringly\,\ncomputations have never h
inted at a lack of stability.\n\n\n\nReferences\n\n\n[1] X. Claeys\, R. Hi
ptmair\, and E. Spindler\, Second-kind boundary integral equa-\ntions for
scattering at composite partly impenetrable objects\, Tech. Rep. 2015-19\,
Seminar for Applied Mathematics\, ETH Zurich\, Switzerland\, 2015. Submi
tted to BIT.\n\n\n[2] X. Claeys\, R. Hiptmair\, and E. Spindler\, A second
-kind galerkin boundary\nelement method for scattering at composite object
s\, BIT Numerical Mathematics\, 55\n(2015)\, pp. 33-57.\n\n\n\nhttps://ind
ico.math.cnrs.fr/event/902/contributions/2890/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2890/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A new a posteriori error estimate for the BEM
DTSTART;VALUE=DATE-TIME:20160205T091000Z
DTEND;VALUE=DATE-TIME:20160205T094500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2893@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sébastien Pernet (Onera Toulouse)\, Marc Bakry\n\nA
posteriori error estimates are tools which enable a measure of the numeri
cal error. They are required to be equivalent to the norm of the error and
to be locally computable. They are norms of values which can be computed
from the numerical solution and the problem parameters. In the context of
BEM\, there is a loss of locality of the norms and therefore of the estima
tes. Standard localization techniques partially solve the issue but lead t
o a loss of control between the norm of the error and the estimate.\n\nWe
introduce a new localization technique based on the computation of the res
idual\n(the norm of the residual is an equivalent norm of the error). By a
pplying a well-chosen\nisomorphism to the residual\, we can "carry" it in
some functional space where the norm\nis local (typically L2). We rst int
roduce the concept for the BEM in 3D-acoustics\, then\nwe give an introduc
tion on what this -estimation would look like for the EFIE.\n\nhttps://ind
ico.math.cnrs.fr/event/902/contributions/2893/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2893/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preconditionning integral equations on the unit disc in 3d
DTSTART;VALUE=DATE-TIME:20160204T131500Z
DTEND;VALUE=DATE-TIME:20160204T135000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2894@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-Claude Nédélec (Ecole Polytechnique)\n\nhttps
://indico.math.cnrs.fr/event/902/contributions/2894/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2894/
END:VEVENT
BEGIN:VEVENT
SUMMARY:High Order Impedance Boundary Condition for 3D Integral Equations
DTSTART;VALUE=DATE-TIME:20160205T083500Z
DTEND;VALUE=DATE-TIME:20160205T091000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2895@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paul Soudais (Dassault Aviation)\n\nImpedance Bounda
ry Conditions (IBC) are widely used in computational\nelectromagnetics to
model thin coatings on perfectly conducting (PEC) objects.\nThe IBC is use
d to reduce drastically the number of unknowns of the integral\nequations
models and to obtain a better conditioned linear system that can be\nmore
efficiently iteratively solved.\n\nIntegral equations models can be built
that mix homogeneous regions\, whose\nmaterial characteristics are defined
by their electrical permittivities and magnetic\npermeabilities\, PEC reg
ions and IBC. These models are very efficient for the\nmodeling of complex
structures.\n\nUsually\, the impedance of a coating is assumed to be the
same for all incidence\nangles and polarizations (standard IBC). This assu
mption is valid for coatings\nwith high refractive index or significant lo
sses. For coatings with smaller\nrefractive index or lower losses\, the ac
curacy of the IBC can be greatly improved\nby approximating it as a partia
l derivative equation ([1] D.J. Hoppe\, Y. Rahmat-\nSamii\, Impedance Boun
dary Conditions in Electromagnetics\, Taylor and Francis\,\n1995). The sec
ond order IBC can be written as:\n\n$E_t+b_1\\nabla_\\Gamma div E_t-b_2 ro
t_\\Gamma rot _\\Gamma E_t = a_0 J + a_1 \\nabla_\\Gamma div J - a_2 rot_\
\Gamma rot_\\Gamma J$\n$E_t$ and $J$ are respectively the tangent electric
field and the electric current.\nIntegral equations formulations for stru
ctures with homogeneous regions\, PEC\nregions and SIBC can be generalized
to take into account second order IBC.\nIn [1]\, the second order IBC is
discretized with spline basis functions for 2D and\nbody of revolution pro
blems. Here\, the second order IBC is applied to 3D\nproblems. The current
s $J$ and $M= Exn$ are discretized with the lower order\nHDiv functions th
at can be used to model objects both smooth or with sharp\nedges.\n\nA fir
st set of validations will be presented that show the increased accuracy o
f\nhigh order IBC over standard IBC while the computational effort for sol
ving the\noverall integral equations model remains similar.\n\nhttps://ind
ico.math.cnrs.fr/event/902/contributions/2895/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2895/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An H-matrix based direct solver for the Boundary Element Method in
3D elastodynamics
DTSTART;VALUE=DATE-TIME:20160205T154000Z
DTEND;VALUE=DATE-TIME:20160205T161500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2896@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stéphanie Chaillat\n\nThe main advantage of the Bou
ndary Element Method (BEM) is that only the domain boundaries are discreti
zed leading to a drastic reduction of the total number of degrees of freed
om. \n\nIn traditional BE implementation the dimensional advantage with r
espect to domain discretization methods is offset by the fully-populated n
ature of the BEM\n coefficient matrix. In the present work\, we propose a
fast method to solve the BEM system in 3-D frequency-domain elastodynamic
s.\n\nUsing the H-matrix arithmetic and low-rank approximations (performed
with Adaptive Cross Approximation)\, we derive a fast direct solver. \nWe
assess the numerical efficiency and accuracy on the basis of numerical r
esults obtained for problems having known solutions. \n In particular\, we
study the efficiency of low-rank approximations when the frequency is i
ncreased. \nThe efficiency of the method is also illustrated to study sei
smic wave propagation in 3-D domains.\n\nThis is a joint work with Patrick
Ciarlet and Luca Desiderio\n\nhttps://indico.math.cnrs.fr/event/902/contr
ibutions/2896/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2896/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fast boundary element methods in industrial applications
DTSTART;VALUE=DATE-TIME:20160205T150500Z
DTEND;VALUE=DATE-TIME:20160205T154000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2897@indico.math.cnrs.fr
DESCRIPTION:Speakers: Olaf Steinbach\n\nIn this talk we consider direct an
d indirect boundary integral formulations for the\nsolution of electro–
and magnetostatic field computations in industrial applications.\nParticul
ar interest is on the use of floating potentials in a multi–dielectric\n
setting with high permittivity.\n\nThis talk summarizes joint work with A.
Blaszczyk and Z. Andjelic (ABB)\, and\nwith D. Amann\, G. Of\, and P. Urt
haler (TU Graz).\n\n\n\nReferences\n\n\n[1] Z. Andjelic\, G. Of\, O. Stein
bach\, P. Urthaler: Fast boundary element\nmethods for industrial applicat
ions in magnetostatics. In: Fast Boundary\nElement Methods in Engineering
and Industrial Applications (U. Langer\,\nM. Schanz\, O. Steinbach\, W. L.
Wendland eds.)\, Lecture Notes in Applied\nand Computational Mechanics\,
vol. 63\, Springer\, Heidelberg\, pp. 111–143\,\n2012.\n\n\n[2] Z. Andje
lic\, G. Of\, O. Steinbach\, P. Urthaler: Boundary element methods\nfor ma
gnetostatic field problems: A critical view. Comput. Visual. Sci. 14\n(201
1) 117–130.\n\n\n[3] D. Amann\, A. Blaszczyk\, G. Of\, O. Steinbach: Sim
ulation of floating potentials\nin industrial applications by boundary ele
ment methods. J. Math.\nInd. 4:13 (2014) 15p.\n\nhttps://indico.math.cnrs.
fr/event/902/contributions/2897/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2897/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Windowed Green function method for layered-media scattering
DTSTART;VALUE=DATE-TIME:20160204T152000Z
DTEND;VALUE=DATE-TIME:20160204T155500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2898@indico.math.cnrs.fr
DESCRIPTION:Speakers: Catalin Turc (New Jersey Institute of Technology)\n\
nWe present a new Windowed Green Function (WGF) method for the numerical i
ntegral-equation solution of problems of electromagnetic scattering by obs
tacles in presence of dielectric or conducting half-planes. The WGF method
\, which is based on use of integral kernels that can be expressed directl
y in terms of the free-space Green function\, does not require evaluation
of expensive Sommerfeld integrals. The proposed approach is fast\, accurat
e\, flexible and easy to implement. In particular straightforward modifica
tions of existing solvers suffice to incorporate the WGF capability. The p
roposed method can be up to thousands of times faster\, for a given accur
acy\, than a corresponding method based on the layer-Green-function.\n\nht
tps://indico.math.cnrs.fr/event/902/contributions/2898/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2898/
END:VEVENT
BEGIN:VEVENT
SUMMARY:New results in BEM for Electromagnetic Compatibility
DTSTART;VALUE=DATE-TIME:20160205T133500Z
DTEND;VALUE=DATE-TIME:20160205T141000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2899@indico.math.cnrs.fr
DESCRIPTION:Speakers: Toufic Abboud (IMACS)\n\nElectromagnetic Compatibili
ty (EMC) modelling is a major issue in aeronautic industry\, with applicat
ions like Lightning Indirect Effects\, High-Intensity Radiated Fields\, an
tenna coupling\, wifi… These simulations represent many challenges for t
he numerical solvers: very large frequency band (starting from DC)\, need
for local models (wires\, slots\, equipment…)\, low levels of currents a
nd fields inside cavities\, presence of geometric and data singularities a
nd the need of robust adaptive meshing procedures… and finally the model
size requires efficient fast and parallel solvers. We present new results
on these issues.\n\nhttps://indico.math.cnrs.fr/event/902/contributions/2
899/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2899/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boundary Element Solutions of Electromagnetic Problems Based on He
lmholtz Projectors
DTSTART;VALUE=DATE-TIME:20160205T141000Z
DTEND;VALUE=DATE-TIME:20160205T144500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2900@indico.math.cnrs.fr
DESCRIPTION:Speakers: Francesco Andriulli (Télécom Bretagne)\n\nIntegral
equation solvers are widely used for simulating electromagnetic scatterin
g and radiation from metallic and penetrable objects. Long popular in acad
emic circles\, these solvers have been in recent years incorporated int
o several commercial electromagnetic analysis and design tools\, after the
advent of fast multipole and related algorithms. The effectiveness of the
se solvers notwithstanding\, boundary element methods are often plagued by
several issues related to ill-conditioning and numerical instabilities bo
th for low and high frequencies.\n\nThis talk will focus on a new family o
f schemes which can effectively solve several of these issues. These solve
rs are based on implicit discrete Helmholtz decompositions obtained via su
itably defined projectors. The use of these projectors\, we will briefly d
elineate\, allows to obtain electric/magnetic/combined Calderon equations
with peculiarly favorable properties (both in frequency and time domain)\,
efficient wavelet preconditioners\, as well as Calderon-like approaches t
hat do not require the use of dual boundary elements.\n\nhttps://indico.ma
th.cnrs.fr/event/902/contributions/2900/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2900/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A low dispersive Trefftz DG method based on a local BEM for the so
lution of the Helmholtz equation
DTSTART;VALUE=DATE-TIME:20160205T104000Z
DTEND;VALUE=DATE-TIME:20160205T111500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2901@indico.math.cnrs.fr
DESCRIPTION:Speakers: Abderrahmane Bendali (INSA Toulouse)\n\nWe first bri
efly present the dispersion phenomenon and show how it damages the numeric
al solution of wave problems over large distances of propagation. We then
introduce a Trefftz Discontinuous Galerkin (TDG) symmetric formulation for
the Helmholtz equation with piecewise constant coefficients. Recall that
Trefftz methods are discretization processes based on the use of exact int
erior either local or global solutions. The Trefftz method considered in t
his work is based on using locally a Boundary Element Method (BEM)\, thus
avoiding the restriction on the type of the local waves used in the usual
TDG methods. We show then that accurate local approximations of the Dirich
let-to-Neumann map have a direct impact on the reduction of the dispersion
error. We then present some numerical tests bringing out that the obtaine
d procedure can completely rub out the dispersion error contrary to the be
st Interior Penalty DG (IPDG) methods.\n\nhttps://indico.math.cnrs.fr/even
t/902/contributions/2901/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2901/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fast Boundary Elements Methods and applications
DTSTART;VALUE=DATE-TIME:20160204T155500Z
DTEND;VALUE=DATE-TIME:20160204T163000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2902@indico.math.cnrs.fr
DESCRIPTION:Speakers: Matthieu Aussal (Ecole Polytechnique)\n\nFast convol
ution on unstructured grids have been developed for many\napplications (e.
g. electrostatics\, magnetostatics\, acoustics\, electro-\nmagnetics\, etc
.). The goal is to reduce the complexity of matrix-vector\nproducts\, from
O(N^2) to O(N log N ). In this presentation\, we describe\na new efficien
t numerical method called Sparse Cardinal Sine Decomposition \n(SCSD)\, ba
sed on a suitable Fourier decomposition of the Green\nkernel\, sparse quad
rature formulae and Type-III Non Uniform Fast Fourier\nTransforms (type-II
I NUFFT). This talk summarizes this new way\, provide\ncomparisons between
SCSD\, FMM and H-Matrix\, and gives numerical\nresults from our new Bound
ary Element solver\, MyBEM.\n\nhttps://indico.math.cnrs.fr/event/902/contr
ibutions/2902/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2902/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connecting Integral Equation and Unified Transform Methods for Wav
e Scattering
DTSTART;VALUE=DATE-TIME:20160205T080000Z
DTEND;VALUE=DATE-TIME:20160205T083500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2903@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simon N. Chandler-Wilde (University of Reading)\n\nI
n this talk we discuss the application of the unified transform method\, d
ue to A.S. Fokas and co-authors\, to interior and exterior problems for ti
me harmonic waves. Like integral equation methods\, the method reduces to
the solution of a problem on the boundary of the domain in question. We di
scuss numerical implementations\, restricting the solution space to a fini
te-dimensional subspace\, and explain how some implementations can be inte
rpreted as Galerkin methods\, the convergence of which can be established
by standard arguments. We focus particularly on implementations that are b
ased on approximation by plane waves (and generalised\, evanescent plane w
aves)\, and explain that these can be implemented in such a way that the n
umerical solution is precisely the best approximation from the plane wave
subspace. In the case of scattering by diffraction gratings we note that t
his particular unified transform method is in fact precisely the SS* metho
d proposed previously (though with a less precise analysis) in Arens\, Cha
ndler-Wilde and De Santo (2006)\, where it is derived as a first kind inte
gral equation formulation. Further details can be found in [1\,2].\n\n\n[1
] Acoustic scattering: high frequency boundary element methods and unified
transform methods. S N Chandler-Wilde & S Langdon\, in “Unified Transfo
rm for Boundary Value Problems: Applications and Advances”\, A S Fokas &
B Pelloni (editors)\, SIAM\, 2015.\n\n\n[2] When all else fails\, integra
te by parts" - an overview of new and old variational formulations for lin
ear elliptic PDEs. E A Spence in "Unified Transform Method for Boundary Va
lue Problems: Applications and Advances"\, A S Fokas & B Pelloni (editors)
\, SIAM\, 2015.\n\nhttps://indico.math.cnrs.fr/event/902/contributions/290
3/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2903/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volume integral equation formulation for anisotropic elastodynamic
scattering: solvability\, application to small-inclusion asymptotics
DTSTART;VALUE=DATE-TIME:20160204T081500Z
DTEND;VALUE=DATE-TIME:20160204T085000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2904@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marc Bonnet (ENSTA)\n\nIn contrast with the vast exi
sting literature on the mathematical aspects of boundary integral equation
s and their application to scattering by impenetrable obstacles characteri
zed by Dirichlet\, Neumann or impedant boundary conditions\, comparatively
few studies are available regarding the mathematical properties of volume
integral equation (VIE) formulations. This communication addresses the so
lvability of VIEs arising in elastodynamic scattering by penetrable obstac
les. The elasticity tensor and mass density are allowed to be smoothly het
erogeneous inside the obstacle and may be discontinuous across the backgro
und-obstacle interface\, the background elastic material being homogeneous
. Both materials may be anisotropic\, within certain limitations for the b
ackground medium. The VIE associated with this problem is first derived\,
relying on known properties of the background fundamental tensor. To avoid
difficulties associated with existing radiation conditions for anisotropi
c elastic media\, we also propose a definition of the radiating character
of transmission solutions. The unique solvability of the volume integral e
quation (and of the scattering problem) is established. For the important
special case of isotropic background properties\, our definition of a radi
ating solution is found to be equivalent to the Sommerfeld-Kupradze radiat
ion conditions. Moreover\, usefulness of this result for the derivation an
d justification of small-inclusion asymptotic approximations is discussed.
\n\nhttps://indico.math.cnrs.fr/event/902/contributions/2904/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2904/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytical preconditioners for the solution of three-dimensional s
urface scattering problems
DTSTART;VALUE=DATE-TIME:20160204T135000Z
DTEND;VALUE=DATE-TIME:20160204T142500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2905@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marion Darbas (Université de Picardie)\n\nThe numer
ical solution of time-harmonic scattering problems remains challenging in
the high frequency regime due to its specific computational bottlenecks. T
he techniques based on integral equations lead to the resolution of linear
systems where the involved matrices are dense and usually badly condition
ed. The improvement of these methods is a timely research area. One possib
ility to reduce the computational cost is to precondition iterative solver
s (to speed up the convergence) and on the other hand to use fast methods
to compute the matrix-vector products needed at each iteration.\n\n\nWe pr
opose an analytical preconditioner taking inspiration of On-Surface Radiat
ion Condition techniques. This preconditioner is an accurate approximation
to the Dirichlet-to-Neumann map. The associated integral equations are of
the second kind. Moreover\, the proposed preconditioner shows highly desi
rable advantages: sparse structure\, ease of implementation and low additi
onal computational cost.\n\n\nIn this talk\, we present first the principl
e of the method in the acoustic case. We show numerical simulations for va
rious configurations. Next\, we explain how to extend the approach to othe
r types of waves\, namely elastic waves (joint work with Stéphanie Chaill
at et Frédérique Le Louër).\n\nhttps://indico.math.cnrs.fr/event/902/co
ntributions/2905/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2905/
END:VEVENT
BEGIN:VEVENT
SUMMARY:H-matrix Solver for BEM: a task-based approach
DTSTART;VALUE=DATE-TIME:20160204T085000Z
DTEND;VALUE=DATE-TIME:20160204T092500Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2906@indico.math.cnrs.fr
DESCRIPTION:Speakers: Guillaume Sylvand (Airbus Group)\n\nFor the numerica
l simulation of wave propagation in acoustics\, Airbus Group Innovations r
elies on integral\nequations solved with the Boundary Elements Method. The
advantages of this approach are well known: mainly\naccuracy\, and simple
r (surfacic) mesh. The main algorithm drawback is the need to cope with a
dense matrix\nwhose size can be quite large for wave propagation problems\
, where the mesh step is governed by the wavelength\nof the physical probl
em treated (in frequency domain).\n\nSince the late 90's\, fast methods ha
ve been introduced to deal with these limitations. First\, the Fast Multip
ole\nMethod (FMM) allowed to compute fast matrix-vector products (in O(n l
og2(n)) instead of O(n2) for the\nstandard algorithm)\, and hence to desig
n fast solvers using iterative methods. Lately\, H-Matrix methods\nhave ga
ined wide acceptance by introducing fast direct solvers\, allowing to solv
e systems in O(n log2(n)) - or\nless - without the hassle of using iterati
ve solvers (unknown convergence rate and difficulty to find a goodprecondi
tionner).\n\nH-Matrix [1] is a lossy\, hierarchical storage scheme for mat
rices that\, along with an associated arithmetic\,\nprovides a rich enough
set of approximate operations to perform the matrix addition\, multiplica
tion\, factorization (e.g. LU or LDLT ) and inversion. It relies on two co
re ideas : (a) nested clustering of the degrees of\nfreedom\, and of their
products\; and (b) adaptative compression of these clusters. Several choi
ces exist in the\nliterature for these two ingredients\, the most common b
eing Binary Space Partitioning for the clustering and\nAdaptative Cross Ap
proximation for the compression.\n\nTogether\, they allow for the construc
tion of a fast direct solver [2]\, which is especially important for BEM\n
applications as it gracefully handles a large number of Right-Hand Sides (
RHS). They also provide a kernel-independent fast solver\, allowing one to
use the method for dierent physics.\n\nAirbus Group Innovations has recen
tly implemented the H-Matrix arithmetic and successfully applied it to\na
wide range of industrial applications in electromagnetism and acoustics. F
urthermore\, these algorithms are\nhard to eciently parallelize\, as the v
ery scarce literature on the subject shows [3]. We developed a parallel\ns
olver that goes beyond the aforementioned reference\, using innovative tec
hniques on top of a state-of-the-art\nruntime system StarPU [4][5]. This e
nables the solving of very large problems\, with a very good eciency. In\n
this presentation\, we show some results on the accuracy of this method on
several challenging applications\, and\nits fast solving time and ecient
use of resources.\n\n\n\nReferences\n\n\n[1] W. Hackbusch\, A Sparse Matri
x Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices\,\nCo
mputing\, Volume 62\, Issue 2 (1999)..\n\n\n[2] L. Grasedyck\, W. Hackbusc
h\, Construction and Arithmetics of H-Matrices\, Computing\, Volume 70\, I
ssue\n4 (2003).\n\n\n[3] R. Kriemann\, Parallel H-Matrix Arithmetics on Sh
ared Memory Systems\, Computing\, Volume 74\, Issue 3\n(2005).\n\n\n[4] B.
Lize\, Resolution directe rapide pour les elements nis de frontiere en el
ectromagnetisme et acoustique :\nH-Matrices. Parallelisme et applications
industrielles\, PhD thesis\, Paris 13\, 2014.\n\n\n[5] C. Augonnet\, S. Th
ibault\, R. Namyst\, and P.-A. Wacrenier\, StarPU: A Unified Platform for
Task Scheduling on Heterogeneous Multicore Architectures\, Concurrency and
Computation: Practice and Experience\,\nSpecial Issue: Euro-Par 2009\, vo
l. 23\, pp. 187198\, Feb. 2011.\n\nhttps://indico.math.cnrs.fr/event/902/c
ontributions/2906/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2906/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quasi-local multi-trace formulations
DTSTART;VALUE=DATE-TIME:20160204T094500Z
DTEND;VALUE=DATE-TIME:20160204T102000Z
DTSTAMP;VALUE=DATE-TIME:20220924T154800Z
UID:indico-contribution-2907@indico.math.cnrs.fr
DESCRIPTION:Speakers: Xavier Claeys (UPMC)\n\nIn the context of time harmo
nic wave scattering by piecewise homogeneous penetrable objects\, we prese
nt a new variant of the multi-trace boundary integral formulations (MTF).
This new approach differs from the so-called "local" MTF by the presence o
f regularisation terms involving boundary integral operators and localised
at junctions i.e. points where at least three subdomains abut. It lends i
tself to much more standard analysis: all operators are continuous in stan
dard Sobolev trace spaces\, a Garding inequality can be proved\, which imp
lies quasi-optimal approximation property for conformal Galerkin discretis
ations. As regards numerical performances\, this new formulation also appe
ars slightly more accurate compared to pre-existing MTF\, while the speed
of convergence of iterative solvers remains comparable.\n\n\nReferences:\n
\n[1] X.Claeys\, Quasi-local multi-trace boundary integral formulations\,
Numer. Methods Partial Differential Equations\, 31(6):2043–2062\, 2015.\
n\n[2] X.Claeys and R. Hiptmair and C. Jerez-Hanckes\, Multi-trace boundar
y integral equations\, chapter in Direct and Inverse Problems in Wave Prop
agation and Applications\, 51–100\, Radon Ser. Comput. Appl. Math.\, 14\
, De Gruyter\, Berlin\, 2013.\n\n\n\nhttps://indico.math.cnrs.fr/event/902
/contributions/2907/
LOCATION:Amphi Becquerel (Ecole Polytechnique)
URL:https://indico.math.cnrs.fr/event/902/contributions/2907/
END:VEVENT
END:VCALENDAR