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BEGIN:VEVENT
SUMMARY:An overview of some new features of deal.II 9.0
DTSTART;VALUE=DATE-TIME:20180727T070000Z
DTEND;VALUE=DATE-TIME:20180727T074500Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-190@indico.sissa.it
DESCRIPTION:Speakers: Luca Heltai (SISSA)\nVersion 9.0.0 of the `deal.II`
library offers many new features and interfaces with several new external
libraries. \n\nIn this talk I will provide an overview of some of the new
features that I have contributed in adding to the library\, including (in
no particular order)\n\n - Improved support for curved geometries \n - Non
-standard quadrature rules\n - Improved support for user-defined run-time
parameters\n - Support for GMSH\n - Support for Assimp\n - Support for Nan
oFlann\n - Support for SUNDIALS\n\nhttps://indico.sissa.it/event/23/contri
butions/190/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Coupling a temperature field to level set advection in a Stefan ph
ase change problem
DTSTART;VALUE=DATE-TIME:20180723T092000Z
DTEND;VALUE=DATE-TIME:20180723T094000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-187@indico.sissa.it
DESCRIPTION:Speakers: Sean McGovern (Forschungszentrum Juelich)\nGiven the
context of distributed parallelism\, the purpose of this contribution is
to consider a solution procedure to the classical Stefan phase change prob
lem\, an example of a free boundary problem. In the Stefan problem\, the i
nterface between water and ice moves through a domain as the ice melts due
to a heat source. As an example of an interface problem\, we choose to ap
ply the level set method to implicitly track the evolution of the ice/wate
r interface. The diffusive temperature equation must be solved over the w
hole domain while an evolving interface separates regions endowed with dif
ferent material properties\, i.e. specific heat of water and ice. The Gibb
s-Thomson relation gives the discontinuity in the temperature field at the
interface and the interface velocity is given by the jump in the heat flu
x. \n\nTo solve this kind of coupled nonlinear problem\, we can 1) evolve
the interface and 2) solve the temperature equation iteratively. The firs
t is a hyperbolic advection equation and the second is parabolic. As is we
ll-known\, these require different solution tactics. We consider a setup f
or which an analytical solution exists.\nThe approach remains pedagogical
as I would like to package this as a possible tutorial step.\n\nhttps://in
dico.sissa.it/event/23/contributions/187/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:CFL: A domain-specific language for simplifying integration kernel
s
DTSTART;VALUE=DATE-TIME:20180724T074500Z
DTEND;VALUE=DATE-TIME:20180724T083000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-188@indico.sissa.it
DESCRIPTION:Speakers: Daniel Arndt (University Heidelberg)\nThere are seve
ral different ways of describing bilinear forms in `deal.II`. All of these
require to describe the assembly loop inside the program. This talk discu
sses an approach for providing the assembly operator from the outside usin
g a domain-specific language.\nIn particular\, this easily allows changing
the backend used in the end. `CFL` also provides the possibility to gener
ate the Newton linearization from a residual operator described in this la
nguage.\n\nhttps://indico.sissa.it/event/23/contributions/188/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Accelerating augmented and deflated Krylov space methods for conve
ction-diffusion problems
DTSTART;VALUE=DATE-TIME:20180723T090000Z
DTEND;VALUE=DATE-TIME:20180723T092000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-189@indico.sissa.it
DESCRIPTION:Speakers: Giuseppe Pitton (SISSA)\nIn this talk I will recall
some basic notions of augmented and deflated Krylov space methods for the
iterative solution of linear systems.\nThen I will discuss a few strategie
s to apply these techniques to the solution of linear systems coming from
nonlinear scalar convection-diffusion equations.\nA simple back-of-the-env
elope analysis allows to argue that in some cases it may be convenient to
exploit alternative recycling strategies based on the SVD selection of pre
vious solutions\, and this conclusion is corroborated by numerical tests b
ased on Finite Element and Spectral Element discretisations.\n\nhttps://in
dico.sissa.it/event/23/contributions/189/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fluid-Structure Interaction: simulating the cavitation phenomenon
DTSTART;VALUE=DATE-TIME:20180724T090000Z
DTEND;VALUE=DATE-TIME:20180724T092000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-192@indico.sissa.it
DESCRIPTION:Speakers: Dario Abbondanza (Sapienza University of Rome)\nIt h
as been recently shown that a Diffuse Interface model is able to fully des
cribe the dynamics of multiphase flows. In particular\, the possibility of
deriving a set of equations addressing the dynamic of the entire domain o
f simulation\, makes it ideal to describe phenomena such as vapor bubble d
ynamics in a surrounding liquid. The model is able to capture surface tens
ion effects\, phase changes (condensation and evaporation) and even transi
tions to supercritical conditions\, bubble collapse stages and the related
shock-wave emissions. The diffuse interface model is intrinsically multis
cale\, enabling the study of all the characteristic size of the bubbles (f
rom nm up to mm of radius) and the typical frequencies of evolution (of or
der 1-100 MHz). Moreover\, the numerical simulations gives access to all t
he fields\, anywhere in the domain\, in particular predicting the pressure
and thermal loads on the nearby solid walls.\nA main application we are i
nterested in is the cavitation phenomenon (implosion of vapor bubbles near
solid surfaces)\, in order to take advantage of the high mechanical stres
ses (for biomedical applications\, e.g.) or prevent them (to reduce or pre
vent structural damages). A full understanding of this complex phenomena r
equires\, on one hand\, a full description of the fluid part\, and on the
other hand\, a suitable modeling of the solid dynamics with particular att
ention to plasticity and damage analysis. In this context\, the use of the
deal.II library could help thanks to its ability in automatically refinin
g the mesh (i.e. in solving the smallest scales involved in the dynamics)\
, and thanks to the large implementation possibility\, already offered fro
m the structural point of view\, in terms of plasticity models.\n\nhttps:/
/indico.sissa.it/event/23/contributions/192/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non matching grids in a distributed setting
DTSTART;VALUE=DATE-TIME:20180725T090000Z
DTEND;VALUE=DATE-TIME:20180725T092000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-193@indico.sissa.it
DESCRIPTION:Speakers: Giovanni Alzetta (SISSA)\nI am beginning this talk w
ith a quick recall of the general difficulties faced when using multiple g
rids on a distributed memory setting and some possible solutions.\nAs a mo
del problem I am presenting briefly the Lagrange-multiplier method of step
-60\, where a harmonic equation with values prescribed at the boundary and
on a sub-domain is solved\, with a particular focus on the coupling matri
x used. After discussing how a partial solution making use of bounding box
es was implemented in deal.II 9.0\, I am discussing its current limitation
s and intended developements.\n\nhttps://indico.sissa.it/event/23/contribu
tions/193/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model Order Reduction and Computational Homogenisation of Magnetor
heological Elastomers
DTSTART;VALUE=DATE-TIME:20180724T092000Z
DTEND;VALUE=DATE-TIME:20180724T094000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-194@indico.sissa.it
DESCRIPTION:Speakers: Benjamin Brands (Friedrich-Alexander-Universität Er
langen-Nürnberg)\nThe mechanical response of magnetorheological composite
s is highly affected by an applied magnetic field. Since a generally valid
constitutive law does not exist for such heterogeneous materials\, multis
cale techniques like computational homogenisation are commonly used to app
roximate effective macroscopic properties. In our approach the macroscopic
quantities at a material point of a magnetorheological elastomer are deri
ved from the response of the underlying micro-structure\, where the consti
tutive law is known\, using first-order homogenisation.\n\nThe computation
al cost of this nested solution scheme known as the FE² method prohibits
the simulation of complex macroscopic problems. To mitigate the computatio
nal bottleneck the FE models on the microscale are replaced by reduced-ord
er models (ROMs). In projection-based ROM the governing equations are proj
ected onto the reduced basis\, which is an approximation of the solution m
anifold of the parametrised partial differential equations (pPDE). The red
uced basis is commonly constructed using previously computed solutions of
the pPDE\, e.g. by applying proper orthogonal decomposition or the reduced
basis method.\n\nWe will present our approach for the construction and co
mputation of the reduced-order models on the microscale. Through various n
umerical examples the accuracy and time savings of the reduced models will
be discussed.\n\nhttps://indico.sissa.it/event/23/contributions/194/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multilevel solver for discontinuous viscosity Stokes problem
DTSTART;VALUE=DATE-TIME:20180725T092000Z
DTEND;VALUE=DATE-TIME:20180725T094000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-195@indico.sissa.it
DESCRIPTION:Speakers: Michal Wichrowski (Instytut Podstawowych Problemów
Techniki)\nThe goal of my work is to develop robust scalable solver for l
inear system arising from finite element discretization of Stokes problem
with strongly variable viscosity. Such linear systems appear in fluid-stru
cture problems. \nSymmetric positive define problems with discontinuous c
oefficient can be solved effectively by multigrid preconditioned Krylov su
bspace methods. Here we extend this idea on saddle point problems by usin
g multilevel preconditioned GMRes. The multilevel method developed by Brea
ss and Sarazin and further refined by Zulehner is applied. A multigrid alg
orithm works on the saddle point problem by applying constrained smoother.
The relaxation allows the iterative procedure to remain in divergence fre
e subspace while smoothing out the error in both pressure and velocity. Si
milarly to other multilevel methods\, the algorithm presented here does no
t require explicitly storing the matrix and thus\, deal.II matrix-free fr
amework can be used.\n\nhttps://indico.sissa.it/event/23/contributions/195
/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deal.II in cosmic ray propagation
DTSTART;VALUE=DATE-TIME:20180723T094000Z
DTEND;VALUE=DATE-TIME:20180723T100000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-196@indico.sissa.it
DESCRIPTION:Speakers: Jiaxin Wang (SISSA)\nCosmic ray propagation in fluid
approach can be described as a PDE system\,\n\nwhich lives in 6D spatial-
spectral space.\n\nIn our project\, we attempt to build up a solver for su
ch a system\, \n\nby combining independent triangulation in two domains (s
patial and spectral).\n\nIn this talk\, I will present why and how we buil
d this framework with Kronecker\n\nproduct.\n\nhttps://indico.sissa.it/eve
nt/23/contributions/196/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integration and application of symbolic and automatic differentiat
ion frameworks in deal.II
DTSTART;VALUE=DATE-TIME:20180724T070000Z
DTEND;VALUE=DATE-TIME:20180724T074500Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-197@indico.sissa.it
DESCRIPTION:Speakers: Jean-Paul Pelteret (Chair of Applied Mechanics\, Fri
edrich-Alexander University Erlangen-Nuremberg)\nIn recent years there has
been a notable growth in research among fields involving coupled media\,
and in multi-physics problems in general. As the complexity of the physics
describing the material loading and response increases\, so does the time
cost and sophistication of the computational tools used to analyse these
problems both in the academic and industrial settings. Associated with thi
s are further challenges\, one example being that potential errors in impl
ementation and subsequent numerical instabilities could be misinterpreted
as physically plausible material instabilities.\n\nTools that automate dif
ferentiation are one mechanism to tackle the challenges of constitutive la
w and finite element formulation prototyping\, development and validation.
In this work we discuss the implementation of frameworks to perform assis
ted differentiation within the deal.II finite element library. We outline
and discuss some of the challenges surrounding the integration of two algo
rithmic (automatic) and symbolic differentiation libraries within the pre-
established tensor and finite element frameworks. Lastly\, we discuss appl
ications in the simulation of magnetorheological elastomers\; these are sm
art\, field-responsive composite materials that are of increasing interest
in numerous industries. We demonstrate and benchmark the current implemen
tation in the context of two problems\, namely (i) a rate-dependent magnet
ic field-response constitutive law and (ii) homogenisation of representati
ve volume element for a rate-independent magneto-rheological elastomer.\n\
nhttps://indico.sissa.it/event/23/contributions/197/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Welcome remarks. Past and future of deal.II
DTSTART;VALUE=DATE-TIME:20180723T070000Z
DTEND;VALUE=DATE-TIME:20180723T074500Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-198@indico.sissa.it
DESCRIPTION:Speakers: Wolfgang Bangerth (Colorado State University)\ndeal.
II is now 20 years old. I'll give a brief overview of how it started\, how
it has developed\, and where I see it going in the future. This includes
both the technical side and\, in particular\, the social side: deal.II is
not just a software project\, but also a community of developers and users
.\n\nhttps://indico.sissa.it/event/23/contributions/198/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Closing remarks
DTSTART;VALUE=DATE-TIME:20180727T103000Z
DTEND;VALUE=DATE-TIME:20180727T110000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-199@indico.sissa.it
DESCRIPTION:Speakers: Luca Heltai (SISSA)\, Timo Heister (Clemson Universi
ty)\, Wolfgang Bangerth (Colorado State University)\nSome conclusions and
some plans for future developments and opportunities. In particular:\n\n -
How to attract funds to `deal.II`\n - How to attract new users\n - Open d
iscussions on the best platforms for Forums/Discussions/Mailinglists\n - A
nything else\n\nhttps://indico.sissa.it/event/23/contributions/199/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Supports for GPU in deal.II
DTSTART;VALUE=DATE-TIME:20180725T070000Z
DTEND;VALUE=DATE-TIME:20180725T074500Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-200@indico.sissa.it
DESCRIPTION:Speakers: Bruno Turcksin (ORNL)\nGPUs are extensively used in
supercomputers both in Europe with Piz Daint and in the United States with
Titan\, Sierra\, and Summit. The main reason is that they offer great flo
ating points performance for a given power envelope. GPUs are also the de
facto standard architectue for neural networks whose usage has been increa
sing quite rapidly in the last few years. It is therefore very advantageou
s if other applications can use the same infrastructure as the one used fo
r AI. However\, progamming on GPU is not the same as programming on CPU. G
PUs offer a lot more parallelism but GPU cores are a lot less powerful tha
n CPU cores.\n\nIn this talk\, we will discuss how to use deal.II on GPUs
for matrix-based and matrix-free applications. For matrix-based applicatio
ns\, we rely on cuSPARSE and cuSOLVER for operations on sparse matrices an
d for some solvers. Matrix-free methods rely on the fact that many modern
codes are using Krylov methods as their solver of choice. These solvers do
not require the matrix of the system but only the result of a sparse matr
ix-vector multiplication. This operation is memory bound both on CPU and G
PU. Matrix-free methods reduce drastically the memory requirement and thus
\, allow for a better utilization of the hardware. Moreover\, the extensiv
e use of tensor products make these methods extremely interesting for high
-order finite elements. High-order finite elements are attractive not only
because of the convergence properties but also because they introduce str
ucture even on unstructured meshes. Finally\, the lesser memory requiremen
t of matrix-free algorithms is very advantageous for GPUs since they do no
t have a lot of memory per core. We will show some results and discuss our
path forward.\n\nhttps://indico.sissa.it/event/23/contributions/200/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Creative freedom for computational mesh generation in deal.II
DTSTART;VALUE=DATE-TIME:20180725T074500Z
DTEND;VALUE=DATE-TIME:20180725T083000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-201@indico.sissa.it
DESCRIPTION:Speakers: Nicola Giuliani (SISSA)\nMany modern 3D modelling to
ols offer the possibility of creating complex geometries in a very straigh
tforward way (what is usually called creative freedom). Such softwares are
extensively used in computer graphics (video-gaming\, animation studios)
and they are able to produce smooth surfaces exploiting the subdivision su
rface modelling which was derived by Edwin Catmull and Jim Clark in 1978 a
s a generalisation of bi-cubic uniform B-spline surfaces to arbitrary topo
logy. We believe that a bridge between such computer graphics techniques a
nd scientific Finite Element computations can open new perspectives for th
e deal.II users community.\nWe present the possibility to use such tools t
o generate a complex geometry to be integrated as a computational mesh ins
ide the deal.II library. \n\nTo demonstrate the possibilities of our appro
ach we use Blender\, an Open Source python based software which has emerge
d as one of the most successful 3D modelling tool. We believe that its suc
cess is due both to its outstanding possibilities and spreading\, in parti
cular we stress that Blender \n\n- is Open Source software\,\n- allows for
straightforward geometry creation using Graphic User Interface\,\n- is hi
ghly scriptable using a Python 3 based Text User Interface\,\n- has a larg
e user community (tutorials\, manuals\, youtube channel\, wikipedia).\n\n\
nWe use the Open Asset Import Library (ASSIMP) to convert the standard Ble
nder format into a deal.II geometry through the interface that is already
inside the library. These passages allow deal.II users to generate complex
three dimensional surfaces in a very controllable way. \n\nWe prove the c
apabilities of our approach in different framework varying from Boundary E
lement Method for Stokes flows\, to the discretisation of surface operator
s on non trivial geometries.\n\nhttps://indico.sissa.it/event/23/contribut
ions/201/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Numerical (micro)aquarium using the deal.II library
DTSTART;VALUE=DATE-TIME:20180724T094000Z
DTEND;VALUE=DATE-TIME:20180724T095000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-202@indico.sissa.it
DESCRIPTION:Speakers: Nicola Giuliani (SISSA)\nDuring the last 8 years the
mathLab laboratory at SISSA has analysed the swimming mechanisms of micro
-organisms (unicellular beings as protists\, algae or bacteria) both from
a theoretical and an experimental point view. In this work we present a wa
y to derive an accurate and reliable numerical setting for the resolution
of general swimming mechanism. Such a framework can be seen as a numerical
microscope.\n\nA general swimming motion (both for micro than macro organ
ism) can be seen as a Fluid Structure Interaction problem. \nGiven the cha
racteristic length-scale of the problem (100 microns at most) the fluid pa
rt of the problem is well described by the Stokes equations (in particular
we use the Boundary Integral Equations for the Stokes system). For what c
oncerns the structural part of the system the typical swimming mechanisms
(flagellar movements\, body deformations) involve large domain deformation
s which pose severe mesh quality problems to finite element or finite volu
me solvers\, and make Boundary Element Method an ideal discretisation stra
tegy for these FSI problems\, requiring only the discretisation of the dom
ain boundaries.\n\nWe present a series of tools that allows the resolution
of swimming problem starting from the analysis of an experimental video.
In particular we isolate the shape changes of the swimmer and we use this
informations as input data to recover the rigid movements of the overall o
rganism. We use an OpenSource 3D modelling tool (Blender) to generate the
computational mesh and we use an efficient MPI parallel solver (based on d
eal.II) for Stokes problems exploiting a collocation Boundary Element Meth
od. The BEMStokes library\, released under LGPL license\, solve both 2D an
d 3D problem and it is rigorously tested using continuous integration over
more than 120 different test cases. \n\nThe resulting softwares constitut
es what we call a "numerical aquarium" since it allows for an efficient an
d reliable study of complex swimming organisms complementing the analysis
that can be obtained through a real microscope.\n\nhttps://indico.sissa.it
/event/23/contributions/202/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algorithms and data structures for matrix-free finite element oper
ators with MPI-parallel sparse multi-vectors
DTSTART;VALUE=DATE-TIME:20180726T070000Z
DTEND;VALUE=DATE-TIME:20180726T074500Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-203@indico.sissa.it
DESCRIPTION:Speakers: Denis Davydov (Friedrich-Alexander University Erlang
en-Nuremberg)\nTraditional solution approaches for problems in quantum mec
hanics scale as $\\mathcal O(N^3)$\, where $N$ is the number of electrons.
Various methods have been proposed to address this issue and obtain linea
r scaling $\\mathcal O(N)$. One promising formulation is the direct minimi
zation of energy. Such methods take advantage of physical localization of
the solution\, namely that the solution can be sought in terms of non-orth
ogonal orbitals with local support. This is often called the near-sightedn
ess principle of matter.\n\nIn this talk we present numerically efficient
implementation of sparse parallel vectors within the deal.II open-source f
inite element library suitable for matrix-free operator evaluation. Based
on the a-priori chosen support for each vector\, we develop algorithms and
data structures to perform (i) matrix-free sparse matrix multi-vector pr
oducts (SpMM) (ii) projection of an operator onto a sparse sub-space (inne
r products) (iii) post-multiplication with a matrix. Strong and weak scali
ng results are reported for a typical benchmark problem using quadratic an
d quartic finite element bases.\n\nhttps://indico.sissa.it/event/23/contri
butions/203/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Numerical Approximation of the Integral Fractional Laplacian
DTSTART;VALUE=DATE-TIME:20180726T074500Z
DTEND;VALUE=DATE-TIME:20180726T083000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-204@indico.sissa.it
DESCRIPTION:Speakers: Wenyu Lei (Texas A&M University)\nIn this talk\, we
propose a new nonconforming finite element algorithm to approximate a line
ar problem involving the integral fractional Laplacian. The method is base
d on the Dunford-Taylor integral representation of the bilinear form corre
sponding to the variational formulation. We obtain the approximated soluti
on using the deal.II finite element library with a non-uniform mesh settin
g. Finally\, as an application\, we consider an obstacle problem involving
the integral fractional Laplacian and several numerical simulations are a
lso provided.\n\nhttps://indico.sissa.it/event/23/contributions/204/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fast Tensor Product Schwarz Smoothers
DTSTART;VALUE=DATE-TIME:20180725T094000Z
DTEND;VALUE=DATE-TIME:20180725T100000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-205@indico.sissa.it
DESCRIPTION:Speakers: Julius Witte (Heidelberg University)\nThe goal of th
e ExaDG project is to provide efficient finite element solvers relying on
`deal.II`'s `MatrixFree` framework based on higher order DG methods. Howev
er\, the matrix-free operators restrict the choice of preconditioners. A p
owerful tool is offered by a geometric multigrid algorithm having a favora
ble linear complexity. The quality of multigrid preconditioners is crucial
ly dependent on the choice of the smoother. Overlapping Schwarz smoothers
using local spaces supported on vertex patches were introduced by Arnold\,
Falk\, and Winther and provide robust convergence in particular for diver
gence-constrained problems and almost incompressible elasticity. In classi
c finite element codes\, the local stiffness matrices are extracted from t
he global system matrix. Therefore\, such smoothers are expensive to compu
te and store\, especially for higher order DG discretizations. Exploiting
again the tensor product finite elements on the subproblem level offers a
remedy to both and fits well into a matrix-free framework. Thus\, we appro
ximate the global bilinear form by separable problems in the smoother.\n\n
First\, we show how to reduce the complexity of inverting and storing subs
pace problems by means of the fast diagonalization method. Second\, a gene
ral tensor product setting is presented to illustrate the sum-factorizatio
n approaches used in finite element related matrix-vector products resulti
ng from the global forward as well as local inverse problems. Finally\, th
e efficiency of our proposed fast diagonalized Schwarz smoothers is underl
ined by numerical experiments and we close with a brief overview of future
plans.\n\nhttps://indico.sissa.it/event/23/contributions/205/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Present and Future of adaptive\, parallel\, geometric multigrid in
deal.II
DTSTART;VALUE=DATE-TIME:20180723T074500Z
DTEND;VALUE=DATE-TIME:20180723T083000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-206@indico.sissa.it
DESCRIPTION:Speakers: Timo Heister (Clemson University)\nMultigrid methods
are the only known approach to efficiently solve large\nlinear systems fo
r solving PDEs by having runtime cost proportional to the\nnumber of unkno
wns. Algebraic multigrid methods construct a hierarchy of\nproblems from t
he system matrix\, while geometric multigrid methods use the\nmesh hierarc
hy and system matrices from each level of this hierarchy.\n\nWhile algebra
ic multigrid methods have been successful in the past and are\nstill the m
ethod of choice for large problems in deal.II\, they have several\ndisadva
ntages over geometric multigrid methods when implemented in a\nmatrix-free
version: First\, scaling to more than a few thousand cores is\nlimited du
e to the large setup cost. Second\, the low arithmetic intensity does\nnot
lend itself to modern architectures. Third\, implementation of\nmultithre
ading is difficult. Fourth\, the matrices consume large amounts of\nsystem
memory.\n\nHere we present the current status of adaptive\, parallel\, ge
ometric multigrid\nhow it is implemented in deal.II. Several numerical tes
ts demonstrate the\napproach. Finally\, we will close with future plans.\n
\nhttps://indico.sissa.it/event/23/contributions/206/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:deal.II interface with CAD date structures: description\, results
and open issues
DTSTART;VALUE=DATE-TIME:20180726T090000Z
DTEND;VALUE=DATE-TIME:20180726T092000Z
DTSTAMP;VALUE=DATE-TIME:20190616T214854Z
UID:indico-contribution-23-207@indico.sissa.it
DESCRIPTION:Speakers: Andrea Mola (SISSA)\nTo exploit the automated mesh g
eneration and adaptive refinement capabilities offered by deal.II\, the us
er must provide its program with a suitable description of the domain geom
etry. In particular\, it is fundamental that the geometries of boundary an
d internal surfaces are available to the triangulation so that the nodes g
enerated across each mesh refinement are placed onto such surfaces\, in a
way that preserves mesh quality. This task is currently carried out by the
manifold classes. A wide variety of manifold descriptors for the most com
mon analytical geometries is available in the library. Along with such use
ful instruments\, a set of manifold descriptors which import and interroga
te CAD files has been implemented to treat also arbitrary geometries. All
such manifolds are based on wrappers of functions contained in the OpenCAS
CADE library\, that are included in the corresponding deal.II namespace. T
his contribution will discuss such manifold descriptors and their working
principles\, mentioning relevant details of their implementation and provi
ding examples and results of their applications. The discussion will then
move to a series of open issues which currently limit the OpenCASCADE mani
folds computational efficiency.\n\nhttps://indico.sissa.it/event/23/contri
butions/207/
LOCATION:SISSA Main Building Meeting Room -- VII Floor
URL:https://indico.sissa.it/event/23/contributions/207/
END:VEVENT
END:VCALENDAR