17 Febbraio, 2003 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Applicazioni delle stime a priori nell' ambito della Finanza Matematica

Vincenzo Vespri, Dipartimento di Matematica Università di Firenze

11 Febbraio, 2003 

Sezione di Analisi Numerica

A particular theoretical approach to spline approximation

G. Micula, Università Babes Bolyai Cluj-Napoca

aula seminari

10 Febbraio, 2003 

Sezione di Analisi Numerica

On some spline methods for the numerical solution of delay differential equation problems

G. Micula, Università Babes Bolyai Cluj-Napoca

aula seminari

9 Febbraio, 2003 15:00

Sezione di Analisi

Probabilistic representation of solution to nonlinear parabolic equations

Francois Delarue, Universita di Parigi

Dipartimento di Matematica

29 Gennaio, 2003 11:30

Sezione di Analisi

Parabolic differential-algebraic multiphysics models in electrical network design

Giuseppe Alì, Ist. per le appl. del calcolo M. Picone - Napo

Aula semianri MOX - 6° piano dip. mat.

abstract

abstract

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.
For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.

17 Gennaio, 2003 12:30

Seminari di Cultura Matematica

Frattali

S. Mortola, Dip. di Matematica

aula B 5.4

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.
For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.

13 Gennaio, 2003 15:00

Sezione di Analisi

Problemi di controllo ottimo in economia

Fausto Gozzi, LUISS - Roma

Dipartimento di Matematica

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.
For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.

10 Gennaio, 2003 12:30

Seminari di Cultura Matematica

Buchi neri e singolarità nude

G. Magli, Dip. di Matematica

aula B 5.4

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.
For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.

8 Gennaio, 2003 15:00

Seminari di Cultura Matematica

Reconstruction and classification of distal anastomoses of peripheral by-pass grafts: from Magnetic Resonance Imaging to CFD

Sergio Giordana, Imperial College - London

Aula Seminari MOX - 6° piano - Dip. Matematica

abstract

abstract

Abnormal haemodynamic conditions are implicated in the development of anastomotic myointimal hyperplasia (MIH), which constitutes the main cause of failure of peripheral by-pass grafts. However these conditions are difficult to determine in-vivo, prompting research using ex-vivo idealised models. To relate the understanding gained in idealised geometries to anatomically correct conditions we have investigated an approach to classify in-vivo distal graft anastomoses and their inter-patient variability.

In-vivo distal anastomotic geometries were acquired by magnetic resonance (MR) angiography from 13 patients who had undergone infrageniculate autologous venous bypass surgery. On average, the images were acquired 2 weeks post-operatively. Five patients also underwent repeat examinations 2 to 7 weeks later. For each geometry, the surface of the arterial lumen is reconstructed from MR images using a zero level set of an implicit function constructed from radial basis functions that can be shown to minimise curvature. The final surface representation is a tessellation obtained by the marching cubes algorithm and is the initial support for CFD mesh generation.

The three-dimensional binary image created from the interpolated surface is processed using a skeletonisation algorithm to obtain the centreline of each branch in the geometry. This allows the definition and the computation of the set of parameters that constitute the base of a geometric classification. In this study we have chosen to measure the branching angles between straight line approximations of the centrelines obtained by averaging over a characteristic length of the anastomosis.

7 Gennaio, 2003 15:00

Seminari di Cultura Matematica

Some Remarks on the History and Future of Averaging Techniques in A~Posteriori Finite Element Error Analysis

Carsten Carstensen, Vienna University of Technology

Aula Seminari MOX - 6° piano dipartimento di Matem

abstract

abstract

Given a flux or stress approximation $p_h$ from a low-order finite
element simulation of an elliptic boundary value problem, averaging or
(gradient-) recovery techniques aim the computation of an improved
approximation $Ap_h$ by a (simple) post processing of
$p_h$. For instance, frequently named after Zienkiewicz and Zhu,
$Ap_h$ is the elementwise interpolation of the nodal values
$(Ap_h)(z)$ obtained as the integral mean of $p_h$ on a
neighbourhood of $z$. This paper gives an
overview over old and new arguments in the proof of reliability and
efficiency of the error estimator $ eta_{ cal A}:= |p_h-{A}p_h |$
as an approximation of the error $ |p-p_h |$ in (an energy norm)
$ | cdot |$. High-lighted are the general class of meshes, averaging
operators, or finite elements [conforming, nonconforming, or mixed].
Emphasis is on old and new aspects of superconvergence and arguments
to circumvent superconvergence at all within proofs of a~posteriori
finite element error estimates.