Minisymposia |
MS01 - Time integration of partial differential equations
Marlis Hochbruck, Alexander Ostermann
Abstract
In this minisymposium we consider the numerical discretization of
time-dependent evolution equations. Our focus is mainly on aspects of
time-discretization but the talks will also address full
discretizations in time and space.
Recently, a lot of progress has been made on the error and stability
analysis as well as on the construction and the efficient
implementation of implicit methods, splitting methods, local time
stepping methods, or exponential integrators. For the error and
stability analysis, an appropriate functional analytic framework is
required and the evolution problem has to be pursued in a semigroup or
a variational formulation. For the efficient implementation, the
solution of linear or nonlinear systems or the approximation of matrix
functions has to be optimized for the particular application.
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MS02 - Geometric integration of differential equations
Elena Celledoni, Brynjulf Owren
Abstract
The talks will mainly, but not exclusively, focus on the following topics:
Splitting methods, higher order geometric integrators, symplectic and measure preserving integrators,
integrable numerical discretizations, methods which preserve energy or other first integrals,
variational integrators and methods designed for Lie groups and other differentiable manifolds.
The talks will present novel methods, analysis, and applications.
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MS03 - Geometric numerical integration of PDEs
Erwan Faou
Abstract
The main themes of this workshop will be: Numerical approximations of solitary waves,
energy preserving algorithms, and computations of nonlinear transport equations possessing strong geometric structure
(Vlasov-2D Euler).
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MS04 - Advanced time-stepping methods for wave propagation
Marcus Grote, Stéphane Lanteri
Abstract
In recent years, the growing need for high order numerical methods
able to handle unstructured and locally refined meshes
has spurred much research in computational wave propagation.
In this mini-symposium, we shall focus on new time-stepping strategies
for the simulation of waves from different applications such as
computational electromagnetics, geoseismics or aeroacoustics. Topics
of particular interest are local time-stepping strategies, be it
explicit or locally implicit, but also space-time methods or other
numerical schemes that achieve high order time accuracy.
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MS05 - Multiscale and splitting methods: Theory and Applications
Jürgen Geiser
Abstract
The mini-symposium aims to stimulate contacts between specialists active in
academic research and industrial development in all major areas in engineering,
where multiscale and splitting methods are used to solve delicate deterministic
or stochastic differential equations and understand the modeling problems in
real-life problems in physical processes. We invite researchers in mathematics,
physics and engineering, both in the theoretical- and application-fields, to discuss
about their numerical methods based on multiscale and splitting schemes to solve
engineering or physical processes.
The minisymposium calls for papers reflecting the latest tends in the research
including, but not limited to:
- Splitting methods for deterministic and stochastic problems
- Stability and convergence of splitting methods
- Combination of splitting and multiscale methods
- Decomposition methods in parallel computations
- Numerical analysis of multiscale methods
- Parallel and contributed splitting algorithms
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MS06 - Modelling, theory and numerical approximation of nonlinear waves
V.A. Dougalis, A. Duran
Abstract
The purpose of this mini symposium is the theory and the numerical analysis of problems
involving nonlinear wave phenomena. The session will focus on modelling, analysis and
numerical methods for nonlinear dispersive wave equations and related hyperbolic
problems and their applications.
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MS07 - Discontinuous dynamical systems: Theory and numerical methods
Luciano Lopez, Cinzia Elia
Abstract
Discontinuous ODEs are often used to model problems arising from such
fields as mechanics, control theory, economics, electrical engineering.The
discontinuity can be intended in the solution, such as in impact problems,
or in the derivative, such as in switching systems or Filippov systems. One
of the main issues in switching and Filippov discontinuous dynamical
systems is that the derivative is not defined on some given discontinuity
surfaces and on their intersection. This in turn raises questions such as
whether the solution is unique on the discontinuity surfaces, how to
regularize the discontinuous vector fields and how to build numerical
schemes for discontinuous ODEs that retain a given accuracy. In this
minisymposium we will discuss both the theoretical and numerical aspects of
this class of discontinuous ODEs.
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MS08 - Frontiers in numerical continuation methods
Christian Kühn, Daniele Avitabile, Hannes Ücker
Abstract
Numerical continuation methods have been established as a
standard tool in the analysis of differential equations and dynamical
systems. For example, they can be used for efficient parametric studies
of invariant solutions (equilibria, periodic orbits, etc), the detection
of bifurcations and the computation of solution manifolds. This
mini-symposium intends to bring together experts in continuation methods
including theoretical approaches, software developers as well as
practitioners. The goal is to identify and tackle new challenges
in the field, e.g. software design for continuation of partial
differential or demands of modern complex systems applications.
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MS09 - Numerical time integration strategies for highly oscillatory systems of hyperbolic PDEs
Tommaso Benacchio, Luca Bonaventura, Rupert Klein
Abstract
The minisymposium will focus on time integration techniques for hyperbolic models of physical systems on multiple time scales. Matching an efficient numerical treatment of the fast scales with an accurate approximation of the slower scales poses challenges in this context, as existing implementations face the advent of massively parallel computing architectures.
Topics of discussion include semi-implicit and split-explicit schemes as well as parallel-in-time methods and exponential integrators.
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MS10 - Anisotropic mesh adaptation
Weizhang Huang, Lennard Kamenski
Abstract
Anisotropic mesh adaptation has received considerable attention from scientists
and engineers in the past two decades. It has been amply demonstrated that
accuracy and efficiency of the numerical approximation of partial differential
equations can be improved significantly by the use of meshes that contain
elements having large aspect ratio but being aligned to the physical solution.
The aim of this minisymposium is to present recent developments in the design,
analysis, and implementation of anisotropic mesh adaptation algorithms, and
their application to the numerical solution of partial differential equations arising
from various fields of science and engineering.
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MS11 - Simulation and control of constrained dynamical systems
Andreas Steinbrecher, Volker Mehrmann
Abstract
The design of new products or processes requires the simulation, optimization
and control of a mathematical model in form of a constrained dynamical systems.
Differential-algebraic equations (DAEs) are a widely used tool for the modeling of such constrained
dynamical systems and therefore, efficient and robust approaches for simulation and control of dynamical
systems modeled with DAEs are of growing interest.
In this spirit, this mini-symposium focuses on various aspects of simulation and control of constrained
dynamical systems. The presentations will cover important aspects in the numerical
integration and control of DAEs like regularization, time-stepping, error control, uncertainties,
path following, feedback control, or optimal control (and other software issues).
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MS12 - Simulation and control of delay differential-algebraic equations
Benjamin Unger and Volker Mehrmann
Abstract
Differential-algebraic equations (DAEs) are mathematical models in a variety of applications
such as multibody systems, electrical circuit simulations and chemical engineering. Automated
modeling tools like modelica or simulink generate DAEs by first modeling different components
and then combining them via a network. On the other hand, delay differential equations (DDEs)
are a well-known tool in population dynamics, fluid dynamics, chemical process simulation and
feedback control. They are based on memory effects, computation time for feedback control or
lags between result and the corresponding action (as in predator-prey models, harvesting efforts
or investment decisions) and allow for better description of real phenomena. The combination of
both effects yields delay differential-algebraic equations (DDAEs), which are hardly studied due
to their complexity and only few results are known to the present day.
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MS13 - Functional analytic aspects of DAEs
Roswitha März, Caren Tischendorf
Abstract
Recently, the functional-analytic approaches to differential-algebraic equations
(DAEs) have been considerably strengthened, most notably in optimal control
and in the area of partial differential-algebraic equations (PDAEs), but also in
the characterization of DAEs and their treatment by variational methods.
The aim of the minisymposium is to bring the various research activities together
and to promote the interplay of related ideas.
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MS14 - Numerical methods for gradient flows
Bertram Düring, Daniel Matthes
Abstract
Evolution equations with a gradient flow structure have played a
fundamental role in functional analysis, differential geometry and
mathematical physics since long. The qualitative theory for their
solutions is already very rich, yet it is a field with a lot of
current developments. Most notably, the study of gradient flows in
mass transportation metrics lead to numerous profound results in the
areas of long-time asymptotics for nonlinear diffusion, functional
inequalities and the like during the past decade.
Surprisingly, comparatively little seems to be known about a
well-adapted numerical approximation of their solutions. Due to their
smoothing properties, gradient flows are often considered as "easy to
compute". However, to devise truly structure preserving
discretisations - which inherit fundamental properties like energy
monotonicity and metric contraction - poses a challenging problem in
many situations. This minisymposium will be concerned with problem-adapted numerical methods
for computation of specific gradient flows.
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MS15 - Piecewise smooth dynamic simulations via algorithmic piecewise differentation
Andreas Griewank, Todd Munson
Abstract
We consider initial value problems in ODEs where the right hand side has
truly state- dependent kinks or jumps and users may be hard pressed to
provide suitable switching functions for the customary event handling
approaches. Instead kinks and jumps can be detected and handled
automatically, which is possible by an extension of algorithmic
differentiation that provides piecewise linear approximations with second
order error to piecewise smooth and Lipschitz continuous right hand sides.
(Partial) results have been obtained so far concerning
- Analysis of the switching structure of solutions to piecewise smooth systems.
- Recovery of local third order consistency and global second order by generalisations of the midpoint rule and the trapezoidal rue to piecewise smooth continuous systems.
- Gain of one or two orders in the scenario 1 by Richardson/Romberg extrapolation.
- Approximate preservation of energy on piecewise smooth Hamiltonian systems.
- Calculation of some adjoint trajectory despite jumps in the transposed Jacobian.
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MS16 - Multiscale methods for atmosphere-ocean modeling
Daan Crommelin, Onno Bokhoven
Abstract
The multiscale nature of atmospheric and oceanic flows is a major difficulty for numerical modeling and simulation of these systems.
For a proper representation of small-scale phenomena such as moist convection, inertia-gravity waves and mesoscale eddies,
an improved understanding is needed of e.g. their interactions with large scale flows, relevant physical and geometrical constraints,
and statistical properties. Such understanding can inform the development of new numerical and stochastic methods for representing
small-scale phenomena in geophysical flows. In this minisymposium, we will focus on recent advances in these areas.
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MS17 - Set-oriented numerics: coherent structures and invariant sets
Kathrin Padberg-Gehle, Christof Schuette
Abstract
Certain subsets of phase space play a crucial role in dynamical systems theory. For instance, invariant sets, such as attractors and invariant manifolds, are known to form the skeleton of the global dynamics in classical dynamical systems while metastable sets are crucial for understanding the long-term behavior of stochastic dynamics. Nonautonomous systems often possess coherent sets, slowly mixing macroscopic structures that have an import impact on the transport and mixing properties of the underlying flow. Finally, the computation of reachable sets is an important problem of control theory. This minisymposium will discuss recent advances in the efficient and rigorous approximation and numerical analysis of such sets.
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MS18 - Numerical treatment of stochastic differential equations
Kristian Debrabant, Andreas Rößler
Abstract
In this minisymposium we would aim to give an overview over recent developments in the field of numerical solution of stochastic differential equations (SDEs). We expect especially to attract talks about the numerical solution of stiff SDEs or stochastic partial differential equations (SPDEs), about convergence properties under relaxed conditions, variance reduction methods in case of weak approximation, and applications.
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MS19 - Numerical methods for stochastic differential equations
Evelyn Buckwar, David Cohen
Abstract
Complex dynamical systems may be subject to various uncertainties, such as errors in measurement of the input variables,
random environmental fluctuations, errors due to simplifying model assumptions,
and our inability to accurately predict future realisations of natural phenomena.
Such complex systems with model uncertainty are often described by stochastic differential equations. Many applications,
from all disciplines of science and engineering, lead to such kind of problems, for example,
weather and climate prediction; motion of undamped nonlinear stochastic beam equation;
random shallow water waves; motion of shock waves on the surface of the sun;
motion of a suspended cable under wind loading; motion of a strand of DNAfloating in a liquid;
segmentation of images; pricing of energy derivative contracts; porous media flows;
filtering problems; interest rate models; stochastic neuronal models; stochastic ferromagnetism; etc.
With the increased presence of stochastic terms in such mathematical models, there is a
strong demand for advanced numerical algorithms to handle these problems. Furthermore, the
use of numerical simulations often leads to a better understanding of the model equations.
The goal of this minisymposium is to bring together leading researchers working on various aspects
of numerical approximation of stochastic differential equations with a particular
emphasis on the following topics:
- time integration of SDEs;
- numerical methods for SPDEs;
- weak and strong error analysis;
- efficient implementation.
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MS20 - Stochastic partial differential equations: Analytical and numerical aspects
Erika Hausenblas, Sylvie Roelly, Mechthild Thalhammer
Abstract
A variety of mathematical models used nowadays in science and engineering involve stochastic partial differential equations (SPDEs). In particular, time-dependent nonlinear partial differential equations that are driven by Wiener or Lévy noise provide a rich source for fascinating phenomena, but their theoretical study and numerical treatment poses major challenges. The intention of this mini-symposium is to gather mathematicians interconnected through their field of application, the analytical tools, or the numerical methods used, and to discuss recent developments for SPDEs.
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MS21 - Data-driven methods for statistical predictability
John Harlim
Abstract
An emerging important scientific problem is to improve statistical prediction of dynamical systems given availability of various type of data from nature. In this mini-symposium, we will discuss recent methodologies that bring together the integration of data and modeling. In particular, we focus on recent development and ideas from data assimilation, uncertainty quantification, and diffusion maps.
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MS22 - Probabilistic numerical analysis of differential equations
Ben Calderhead
Abstract
Classical approaches to solving Differential Equations approximate the true underlying infinite dimensional solution by providing a single discrete solution, whose accuracy is known up to a particular (user-defined) error tolerance. Recently there has been growing interest in considering such solutions from a statistical perspective, whereby the task is to characterise the epistemic uncertainty in the solution arising from the fact we cannot evaluate the solution of the differential equation at every point on the domain of interest. When considered as a statistical inference problem, we then seek a measure over functions that are consistent with the finite function evaluations that we observe. An early work on probabilistic methods for the solution of differential equations was offered by Skilling (Skilling, 1991), using a Bayesian extrapolation formulation, and more recently, (Chkrebtii, Campbell, Girolami & Calderhead, 2013) have provided further extensions and a more rigorous theoretical analysis. Some connections between Gaussian extrapolators and classic Runge-Kutta methods have also been highlighted (Schober, Duvenaud & Hennig, 2014). A very deep literature exists for any classical approaches such as the Runge-Kutta family of solvers, however probabilistic approaches are still in their infancy. The aim of this mini-symposium is to highlight the latest work in this new field, discuss the many open questions that arise, and present these ideas to the wider mathematical community.
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MS23 - Recent advances in inverse problems
Lidia Aceto, Christine Böckmann
Abstract
Inverse problems consist in using the data provided by some measurements to infer the value of parameters characterizing the equations
which model the real-life phenomenon under investigation.
Many important applications such as medical imaging, signal processing,
oil exploration and oceanography (to quote only few of them) involve
the solution of inverse problems. For this reason and because of
the inherent diffculties encountered in the process of approximating a meaningful solution, the study of inverse problems constitutes a very
active and exciting research area.
The main goal of the symposium is to gather researchers who study
inverse and ill-posed problems to discuss the different numerical strategies
they use to solve them.
The principal subjects covered by the symposium are listed below:
- atmospheric tomography;
- inverse scattering and partial differential equations;
- reconstruction of Sturm-Liouville potentials;
- regularization techniques related to inverse problems.
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MS24 - Enhanced Sampling Methods
Elena Akhmatskaya, Chus Sanz-Serna,Tijana Radivojevic
Abstract
Challenging problems in engineering and drug design, understanding of complex phenomena, spatial search, reliability and risk assessment, decision-making and many other complex problems, signal a high demand for efficient sampling methods.
Advances in hardware technologies contribute to a large extent to the improvement of simulation accuracy and thus predictability and the understanding of complex systems and processes, but by themselves are not enough to solve the most difficult issues.
The development of novel mathematical ideas can help to solve real-life problems not tackled so far. On the other hand, the adaptation of methods to certain applications may result in new techniques that could be further employed in attempts to deal with different kind of problems.
Various interesting and complementary techniques for enhanced simulation of complex systems have been introduced recently. Some of them use Monte Carlo methods (including importance sampling, simulated annealing, hybrid Monte Carlo, etc.), harmonic approximations, coarse-graining, sophisticated integrators, Markov chain methods, ensemble algorithms.
It is evident that the key to the progress in understanding the behavior and features of complex systems lies in the adaptation of mathematical methods to applications and the development of multidisciplinary approaches.
This minisymposium aims at gathering scientists from different areas, such as mathematics, statistics, computer science, engineering and natural sciences, to discuss and share ideas, experiences and knowledge for a joint attempt to design novel methodologies for effective sampling.
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MS25 - Advanced multilevel Monte Carlo methods
Håkon Hoel, Kody Law, Raul Tempone
Abstract
For weak approximations of stochastic problems that require numerical
pproximation, the computational cost to obtain a given level of accuracy
by a plain vanilla Monte Carlo approach can be very high. The multilevel
Monte Carlo approach consists of introducing a telescopic sum of different
resolution, coupled numerical approximations with decreasing variance,
such that the number of necessary samples is progressively reduced for
the more expensive fine resolution samples. This can considerably reduce
the total cost of obtaining a given accuracy. There has been a lot of research
activity recently in extending the plain vanilla Monte Carlo to more advanced
multilevel Monte Carlo methods involving higher dimensional PDEs and inference
in static and sequential contexts. This minisymposium aims to bring together
experts in the field to share their most recent advances.
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MS26 - Computational and stochastic methods in inverse problems
Jana de Wiljes, Sebastian Reich
Abstract
The emphasis of this minisymposium within the area of inverse problems will be on computational and stochastic methods applied to problems involving partial differential equations.
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MS27 - Advances in Bayesian computation for large-scale differential equation models
Youssef Marzouk
Abstract
The application of Bayesian inference to systems described by ordinary and partial differential equations raises several distinctive computational challenges. Nonlinear differential equation models may produce complex posterior distributions, with strong variations in local geometry. The targets of inference may be high dimensional or, in the case of PDEs, infinite-dimensional. Direct and repeated evaluation of likelihood functions containing differential equations can quickly become computationally intractable. And approximations of differential equation models, even standard numerical approximations, lead to errors in the sampled posterior that should be understood and controlled.
This minisymposium will highlight recent methodological advances aimed at many of these challenges. Topics of particular interest will include posterior sampling schemes with discretization-invariant performance; posterior exploration schemes that exploit geometric information from the posterior---including not only Markov chain and sequential Monte Carlo, but also schemes based on optimal transportation and on sparse quadrature; and approximation or model reduction methods tailored to the context of Bayesian inference, including schemes for exact sampling with approximate models.
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MS28 - Molecular dynamics
Carsten Hartmann, Robert Skeel
Abstract
Molecular dynamics is an the essential algorithmic technology of modern scientic computing.
It provides a rich source of challenging problems which are amenable to mathematical
study, with the best methods drawing on concepts and ideas from dynamical systems,
numerical analysis, and applied probability.
Our double-length minisymposium, that is likely to be related to the addresses of several
of the plenary speakers at SCICADE 2015 (e.g. Lelievre, Klein), will address a number of
dierent interconnected topics arising in connection with molecular dynamics:
equilibrium sampling methods (typically using SDE paths)
dynamical Monte-Carlo methods
control theoretic approaches
methods for nonequilibrium simulation
multiscale techniques
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MS29 - Mathematical models and numerical methods for image processing
Adérito Araújo, Sílvia Barbeiro, Eduardo Cuesta
Abstract
The purpose of this mini symposium is the theoretical and numerical analysis of different problems in Image Processing. It intends to be a forum to share recent results on modelling, theory and numerical approximation.
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MS30 - Surface matching for image processing tasks
Thomas Batard, Marcelo Bertalmio
Abstract
Surface, and more generally manifold,
matching techniques are a very powerful tool in computer vision and they have
been widely employed over the last decade. The application of surface matching
techniques in the context of image processing is more recent, but the results
demonstrate its efficiency, and the aim of this mini-symposium is to present
some of the most recent results.
There exist several techniques to perform surface matching, e.g. minimization
of an elastic energy, optimal transport, and Gromov-Haussdorff distance
framework to name a few, and our proposal for this workshop is that each of
the four speakers will present a different technique, both from the theoretical
and computational viewpoint, and an application of that technique to image
processing.
We expect this workshop to be an opportunity to emphasize the connections
and differences between these different approaches for surface matching, as well
as point out the range of image processing tasks that can performed through
surface matching.
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MS31 - New aspects and applications of structure preserving numerical methods
Takaharu Yaguchi
Abstract
The purpose of this minisymposium is to present recent
research on structure-preserving numerical methods.
The focus is particularly on newly discovered aspects
of these methods. Examples are reinterpretation and
reformulation of classical results and new applications
of the structure-preserving methods.
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MS32 - Optimal transport in image and shape analysis
Jan Lellmann, Carola Schönlieb
Abstract
The Wasserstein distances have a long history in feature matching and
recognition, image and shape analysis, as well as computer vision. More
recently numerical and computational advances have made it possible to
apply these techniques to large-scale problems. In this mini-symposium we
will focus on recent developments, including shape analysis and interpolation,
registration, and variational models based on Optimal Transport.
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MS33 - Mathematical modelling in pharmacology and drug development
Wilhelm Huisinga
Abstract
Mathematical and statistical modelling approaches are increasingly used in drug development and therapeutic use to get insight into the processes governing drug pharmacokinetics, i.e., absorption, distribution, metabolism and excretion, as well as the desired and undesired drug effects. In many cases, deterministic models are used that describe the most relevant physiological processes and are parameterized in terms of species- and drug-specific parameters. Typical problems include the optimization of drug therapy (in particular, when drug combinations are administered), the characterization of variability in drug pharmacokinetics and response (potentially necessitating individual dose adjustments), or the identification of population characteristics and individual parameters (which in the light of restricted measurements poses questions of parameter identifiability). In addition, with increasing complexity, questions of model validation and verification become increasingly relevant. The talks of the minisymposium illustrate the mathematical challenges and give successful applications.
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MS34 - Parametric Model Order Reduction: Challenges and Solutions
Christian Himpe, Ulrike Baur
Abstract
Many real-life applications are built upon models that are based on (partial) differential equations,
such us biological or chemical systems, micro-electro-mechanical systems, circuit systems or fluid dynamics.
Accuracy requirements lead to high-dimensional systems of differential equations which are
difficult to evaluate due to long computational times and high memory consumption. For an efficient
numerical simulation of such complex system it is necessary to reduce the dimension by a reliable
model order reduction method.
To allow more flexibility in the simulation, the systems often include parameters (describing, e.g.,
material properties, system geometry, initial or boundary conditions). The parameters should be
preserved in the reduced-order system; a task that motivated the development of new methods for
model order reduction called parametric model order reduction (pMOR). Reduced-order, parameterized
systems are especially helpful in design, control, optimization and inverse problems where many system
evaluations are required.
Nowadays, pMOR methods face two major challenges. First, the high-dimensional systems are
getting more and more complex. They include nonlinearities, uncertainties, time-delays or highdimensional
parameter spaces. This makes the computation of the reduced-order, parameterized model
much harder. Second, the technical environment available for the computation and evaluation of the
reduced-order model is composed of multiple nodes where each node may provide multiple or even
many cores. The next generation of pMOR algorithms needs to take this computational architecture
into account and should enable parallelization in this context.
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MS35 - Numerical multiscale methods for oscillatory problems
Richard Tsai, Gil Ariel
Abstact
This mini-symposium will host talks on modern numerical multiscale methods for oscillatory problems.
We shall aim at inviting (young) researchers who develop the relevant numerical methods using a variety of techniques,
including robust numerical averaging, efficient sampling, and sparsity seeking strategies.
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