28 Luglio, 2015 14:30

MOX Seminar

A Nitsche-XFEM method and splitting schemes for the simulation of thin-walled structures immersed in an incompressible fluid

Benoit Fabrèges, Inria Paris-Rocquencour

Aula Saleri- Sesto Piano

abstract

abstract

The use of fictitious domain/immersed boundary methods for the numerical simulation of fluid-structure interaction problems has recently seen a surge of interest.
In this work we consider the extension of the Nitsche-XFEM method to fluid-structure interaction problems involving a thin-walled elastic structure (Lagrangian formalism) immersed in an incompressible fluid (Eulerian formalism). The fluid domain is discretized with an unstructured mesh not fitted to the solid one. Weak and strong discontinuities across the interface are allowed for the velocity and pressure respectively. The kinematic/kinetic fluid-solid coupling is enforced consistently using a variant of Nitsche’s method involving cut elements. Robustness with respect to arbitrary interface/element intersections is guaranteed through a ghost penalty stabilization.
For the temporal discretization, several coupling schemes with different degrees of fluid-solid splitting (implicit, semi-implicit and explicit) are investigated.
The stability and convergence properties of the methods proposed are rigorously analyzed in a representative linear setting.
Several numerical examples, involving static and moving interfaces, illustrate the performance of the methods.

contact: luca.formaggia@polimi.it

22 Luglio, 2015 11:00

MOX Seminar

Structure preserving discretizations in isogeometric analysis: B-splines and hierarchical splines

Rafael Vazquez, IMATI CNR - Pavia

Aula Saleri VI piano - MOX Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Isogeometric analysis is an emerging technology that intends to advance towards the integration of CAD and CAE technologies. The idea is, invoking the isoparametric concept, to use the same kind of basis functions for the geometry description given by CAD and the test and trial spaces in the discrete problem to be solved by CAE. The functions most commonly used up to now are (rational) B-splines and their non-tensor-product generalizations, such as hierarchical splines. These are a set of splines with multi-level structure, that provide a very promising framework for adaptive simulation, due to their simple construction and their capability to deal with complicated geometries. By abandoning the isoparametric concept, it is possible to extend isogeometric analysis to the definition of discrete differential forms based on spline spaces. This kind of discrete spaces are useful for the construction of structure-preserving discretizations, with applications in computational electromagnetics and fluid mechanics, for instance. In some sense, they can be seen as a generalization of edge and face elements with higher continuity. In the first part of this talk I will review the definition and properties of isogeometric differential forms based on tensor-product B-splines. In the second part, I will extend their construction to multi-level hierarchical splines. In this case, simple numerical tests show that not all the hierarchical meshes guarantee the structure-preserving property. Using cohomology theory, I will provide sufficient and necessary conditions on the hierarchical mesh that ensure that the structure-preserving property is satisfied. This presentation is from joint works with Annalisa Buffa, John Evans, Giancarlo Sangalli, Michael Scott and Derek Thomas.

contact: carlo.defalco@polimi.it

15 Luglio, 2015 12:00 in punto

Sezione di Finanza Quantitativa

Measures of Systemic Risk

Birgit Rudloff, Princeton University

Aula Seminari III piano

abstract

abstract

Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of this type of risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions.
We propose a novel approach to measuring systemic risk. Key to our construction is a rigorous derivation of systemic risk measures from the structure of the underlying system and the objectives of a financial regulator. Systemic risk is measured by the set of allocations of additional capital that lead to acceptable outcomes.
We explain the conceptual framework and the definition of systemic risk measures, provide an algorithm for their computation, and illustrate their application in numerical case studies. We apply our methodology to systemic risk aggregation extending Chen, Iyengar & Moallemi (2013) to allow for feedback effect the capital regulation has on the system, and to network models as suggested in the seminal paper of Eisenberg & Noe (2001) and their generalizations as in Cifuentes, Shin & Ferrucci (2005). This is joint work with Zach Feinstein and Stefan Weber.

9 Luglio, 2015 14:00

MOX Seminar

Simulation of power devices: Applications of Numerical Modeling in R&D

Marco Bellini, ABB Corporate Research, Baden Dättwill

Aula Seminari MOX

abstract

abstract

Contact: carlo.defalco@polimi.it

8 Luglio, 2015 12:00 in punto

Sezione di Finanza Quantitativa

Risk measurement under dependence uncertainty

Valeria Bignozzi, Università degli Studi di Roma "La Sapienza"

Aula Seminari III piano

Contact: carlo.defalco@polimi.it

8 Luglio, 2015 14:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Carleson measures in strongly pseudoconvex domains

Alberto Saracco, Università di Parma

Aula Seminari del terzo piano

abstract

abstract

Since 1962 Carleson measures were introduced to solve the corona problem, they have been both an important tool and an interesting mathematical object to study per se.

In this talk I will review some important characterizations of Carleson measures for Hardy or Bergman spaces of function in the unit disc or the unit ball, due to several authors.

Then I will expose our recent intrinsic characterization of Carleson measures for Bergman spaces in strongly pseudoconvex domains of C^n and related results.
(joint works with Marco Abate and Jasmin Raissy)

1 Luglio, 2015 14:00 in punto

Sezione di Finanza Quantitativa

Arbitrage Theory without a Reference Probability: challenges of the model-free approach

Marco Maggis, Università degli Studi di Milano

Aula Saleri (VI piano)

abstract

abstract

In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets, The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities.
Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

30 Giugno, 2015 16:30

Seminario Matematico e Fisico di Milano

Billiards and Moduli Spaces

Curtis T.McMullen, Harvard University

Dipartimento di Matematica, Via Saldini, Aula Chisini

In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets, The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities.
Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

25 Giugno, 2015 14:00 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Hyperbolic traveling fronts: the bistable equation with relaxation

Corrado Mascia, Universita' di Roma "La Sapienza"

Aula Seminari III Piano

abstract

abstract

The main concern of the talk is to discuss a class of hyperbolic equation
in the presence of a reaction term of Allen-Cahn type, motivated by
the assumption that the alignment of the flux term with the gradient of the unknown function is not istantaneous but delayed by the presence of a relaxation time.
After a brief overview on the derivation of such class of equations
starting from some appropriate modelling assumptions, emphasis will be given to the topic of front propagation in one dimension.
Rigorous results concerning existence and stability of planar fronts will be presented, comparing it with the corresponding results for the
standard parabolic Allen--Cahn equation.

(joint collaboration with C.Lattanzio, R.G.Plaza, C.Simeoni)

24 Giugno, 2015 11:00

MOX Seminar

Modeling kinetic interface-sensitive (KIS) tracers for the optimization of supercritical carbon dioxide injection into deep saline aquifers

Alexandru Tatomir, Department of Applied Geology, Geoscience Centre of the University of Göttingen-Germany

Aula Seminari III Piano Dipartimento di Matematica - Politecnico di Milano

abstract

abstract

Tracer methods represent techniques commonly used for the characterization and for the monitoring of
transport processes in geo-reservoirs (e.g., CO2 storage, geothermal systems, oil recovery, etc.).
Our current research efforts focus on the development of a new class of reactive tracers, i.e. KIS tracers
useful for the characterization of fluid-fluid interfacial areas during supercritical CO2 injection into deep
saline aquifers. The amount of fluid-fluid interfacial areas is important for the quantification of reactions
at the fluid interface, which can implicitly lead to optimized injection strategies, a better assessment of
the extent of the CO2 plume and of the storage efficiency. The work involves multi-disciplinary
collaboration including laboratory experiments, synthesis of new tracer compounds and numerical
modelling at pore- and continuum-scale.

The presentation focuses on the development of a conceptual, mathematical and numerical model for
the KIS tracers in porous media. The presented modeling approach overcomes the drawback of the
current standard multiphase multicomponent models, which ignore kinetics of mass transfer over the
interfacial area between the CO2 and brine and consider only the volumetric fraction of the fluids or
their mass and molar fractions, respectively. In this model, the concept of a specific interfacial area
obtained from pore network modeling is used to complement the constitutive relationships between
capillary pressure and saturation. It is a two-phase four component flow and transport model with a
kinetic mass transfer of tracers between the two fluids and taking the dissolution of CO2 in brine into
account. The modeling approach uses parameters obtained from experimental lab work. Their
implications are investigated by sensitivity analyses to narrow the physical range of reaction rates for
further experiments and molecular tracer design.

contact: alessio.fumagalli@polimi.it