Simon Chandler-Wilde
Anne-Sophie Bonnet -Ben Dhia, Sonia Fliss, Christophe Hazard POEMS (CNRS-INRIA -ENS TA Paris)
Karl -Mikael Perfekt
Reading Yohanes TjandraWidjaja
Technische Universiteit Dortmund
This talk is about combining :
Half-Space Matching ( HSM) Method Fliss rJoly (2009), Ott (2017) , Bonnet-Ben Dh iaet al (2018,119
Complex scaling used in PML
Ott , PhD , KIT (2017)
This talk is about combining :
Half-Space Matching ( HSM) Method Fliss rJoly (2009), Ott (2017) , Bonnet-Ben Dh iaet al (2018,19)
Complex scaling used in PML
Ott , PhD , KIT (2017)
, Langlois et al, Acta Acustica, 2020
Part I : Half .
Plane Solutions : the
Dutko -_ O
,
Er - iku=o(r -"2) ,
,
,
MESSAGE : we can •
Example I : Propagation from Cutting
Fr - ik u = o (r-"2) ,
as r→a
T = O
ai f
Dutko -_ f S2 zu
Dutkuf In - iku=O
problem in R .
Dutko -_ f 52 Dutkef
problem in R .
Dutko -_ f S2 Dutkef
problem in R with
s •
Dutko -_ 8 , I
. and
Let too vk.hr EEO
Dutko -_ 8% R o
Users Etters) - ethers)
. and
. and
Users others) - Etters)
IDutko -_8%52 o SL Sommerfeld u=4o=UstU't,) rad
. and
us 40=144310 ,
j Thm .
Usk) otters) - Etters) then # equivalent to original BVP and HDHec.sc/ .
Part II : Half-Plane Solutions Enable
solution of More Complex Problems
MESSAGE : we can MESSAGE . Half -plane couple explicit solutions can be coupled .
half-plane solutions to local FEM solves
Part III : PML-type complex- scaling works for integral equations
Deforming paths of integration for E. g . Deano
,
Iserles ,
( Itt ) 't
,
Iserles ,
O Rez
Q
Im z
Q
as r→a
Dutko -_ O y
y •
R = Fixed .
E- Cosy)
But is g analytic? y •
E- Cosy)
and bounded in
o if u is field due to
R = fyFEc.ge .
y •
* O Rez
Imz> O .
to
Im⇒ O .
R~z ,
R
* O Rez
Assume gtz) analytic, bounded in Rez >O ,
Im⇒ O .
R~z ,
R
y
r "
Toi .
O
Dutko -_ 8 , I
. and
Dutko -8%52 o d '
Sommerfeld u=fo=UstU't,) rad
. and
Letolocttoceiot
Dutko -8%52 o & Sommerfeld u=4o=UstU¥foI rad
. and
Letolocttoceiot
Dutko -8%52 o & Sommerfeld u=fo=UstU¥o) rad
. and
Dutko -_8%52 o & Sommerfeld u=fo=UstU¥foI rad
. and
.
-hen # equivalent to original BVP and HDotlec.sc !
← En - iku=h
h --I - ikv
Take- Home Messages
att-plane solutions coupled with local FEM can solve scattering in complex backgrounds
• We can deform paths of integration in Ott (2017) integral equations into the complex plane giving less oscillation and exponential decay
BB etat@020)