Events

Jan 26 - Feb 1, 2025

An introduction to Virtual Elements in 3D

Professor Lourenco Beirao da Veiga, University of Milano-Bicocca

Jan 28, 16:00 - 17:00

B1, L3, R3119

The Virtual Element Method (VEM), is a very recent technology introduced in for the discretization of partial differential equations, that has shared a good success in recent years. The VEM can be interpreted as a generalization of the Finite Element Method that allows to use general polygonal and polyhedral meshes, still keeping the same coding complexity and allowing for arbitrary degree of accuracy. The Virtual Element Method makes use of local functions that are not necessarily polynomials and are defined in an implicit way. Nevertheless, by a wise choice of the degrees of freedom and introducing a novel construction of the associated stiffness matrixes, the VEM avoids the explicit integration of such shape functions.
NumPDE Workshop: Numerical Analysis of PDEs

Jan 26, 08:45 - Jan 28, 15:35

Sunday 26/01 (morning, 8.45-13.30) - Auditorium between Building 2 and Building 3; Sunday 26/01 (afternoon, from 13.45) - Building 9, Room 2322 (Lecture Hall); Monday 27/01 and Tuesday 28/01 - Auditorium between Building 4 and Building 5

PDEs numerical analysis

Explore cutting-edge numerical analysis of PDEs, including Finite Element Methods, Virtual Element Methods, and Isogeometric Analysis, with leading experts.

Apr 28 - May 4, 2024

Non-standard Finite Elements for Eigenvalue Problems

Linda Alzaben, Ph.D. Student, Applied Mathematics and Computational Sciences

May 2, 14:00 - 15:00

B1 L2 R2202

Numerical approximation of partial differential equations involves parameter dependencies from problem formulation and numerical methods. We focus on two areas: least-squares finite element method with linear elasticity, studying its dependence on the Lamé parameter, and the Virtual Element Method, known for handling complex geometries where the stabilization parameter is analyzed.

Mar 10 - Mar 16, 2024

Mathematics and health: a model of the glucose-insulin system for estimating the glycaemic index of food

Fabio Credali, Postdoc at IMATI, Pavia

Mar 12, 14:30 - 15:30

B1 L4 seaside R4214

In 2019, diabetes caused 1.5 million global deaths, with 48% occurring before age 70. While Type 1 diabetes strongly depends on genetic components and is usually diagnosed in childhood, Type 2 diabetes is primarily caused by long term consumption of high calories foods. Lifestyle choices significantly influence the risk of Type 2 diabetes and obesity, including energy intake, diet composition, physical activity, and smoking.

Mar 3 - Mar 9, 2024

WAN Approximation of PDEs: Best Approximation, Stabilization and Boundary Conditions

Prof. Silvia Bertoluzza

Mar 5, 16:00 - 17:00

B2 L5 R5209

WAN PDE approximation Stabilization Boundary Dirichlet

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Dec 3 - Dec 9, 2023

Gradient Estimates for weak solutions of Elliptic PDE's - Seminar

Giuseppe Di Fazio, Professor, Mathematics and Computer Sciences, University of Catania, Italy

Dec 5, 13:00 - 14:00

B1 L4 R4214

Let us consider an elliptic equation of second order in variational form i.e. div(A(x)∇u) = divf in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space.

Nov 26 - Dec 2, 2023

Numerical approximation of PDEs on complex geometries: fluid-structure interaction problems and virtual element methods

Fabio Credali, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

Nov 28, 16:30 - 18:30

KAUST

The studies in numerical approximation of partial differential equations are characterized by the necessity of managing complex geometries and their discretization. We focus our attention on two different fields where complex geometries are very common: the mathematical modeling of fluid-structure interaction problems and the family of virtual element methods.

Nov 12 - Nov 18, 2023

Oct 8 - Oct 14, 2023

Space–Time Multiscale Modeling and Numerics of Sorption Kinetics

Clarissa Astuto, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

Oct 12, 12:00 - 13:00

B9 L2 H2

In this talk we propose and validate a Space Multiscale model for the description of particle diffusion in the presence of trapping boundaries. We start from a drift diffusion equation in which the drift term describes the effect of bubble traps, and it is simulated by the Lennard–Jones potential.
Models and methods for multifluid flow in Lagrangian coordinates

Prof. Giovanni Russo, Full Professor of Numerical Analysis Department of Mathematics and Computer Science, University of Catania, Italy

Oct 10, 14:30 - 15:30

B1 L4 R4102

Abstract Multifluid has attracted a lot of attention in recent years. In particular, stratified fluids composed by a sequence of alternate layers show interesting macroscopic properties, which may be quite different from those of the individual fluids which constitute the stratified system. On a macroscopic scale, such a system can be considered a sort of fluid metamaterial. Several models have been proposed to describe the stratified system as a single effective fluid. After an introduction, we present two homogenized models of the stratified fluid system, which are based on isentropic

Apr 30 - May 6, 2023

Modeling and Simulation of Semiconductor Equations: Insights and Applications

Prof. Nella Rotundo, Department of Mathematics University of Florence, Italy

May 3, 11:00 - 12:00

B1 L4 R4102

Abstract In this talk, we will discuss the modeling and simulation of semiconductor equations using three different formalisms. We will also describe the finite volume method and the Hybridizable Discontinuous Galerkin method as applied to semiconductor equations. These methods have proven to be highly effective in modeling semiconductor behavior, and have been used in a variety of applications such as integrated circuits, solar cells, and transistors. We will provide insights into the fundamental concepts behind these models and demonstrate their effectiveness through numerical simulations

Mar 26 - Apr 1, 2023

Scalable parallel solvers for cardiac reaction-diffusion models and applications

Luca F. Pavarino, Professor, Department of Mathematics, Università degli Studi di Pavia

Mar 28, 16:00 - 17:00

B2 L5 R5220

Applied Partial Differential Equations parallel simulations

After a brief introduction to the field of Computational Cardiology and cardiac reentry, we introduce and study some scalable domain decomposition preconditioners for cardiac reaction-diffusion models, discretized with splitting semi-implicit techniques in time and isoparametric finite elements in space.

Nov 6 - Nov 12, 2022

Parallel multilevel solvers for virtual element discretizations of saddle point problems

Prof. Simone Scacchi, Associate Professor of Numerical Analysis at the Department of Mathematics of the University of Milan

Nov 8, 15:30 - 17:00

B1 L3 R3119

Virtual Element Method

In this seminar, we will present our work on Virtual Element Method (VEM) approximations. The Virtual Element Method is a recent numerical technique for solving partial differential equations on computational grids constituted by polygonal or polyhedral elements of very general shape. This work aims to develop effective linear solvers for general order VEM approximations of three-dimensional scalar elliptic equations in mixed form and Stokes equations. To this end, we consider block algebraic multigrid preconditioners and balancing domain decomposition by constraints (BDDC) preconditioners. The latter allows us to use conjugate gradient iterations, albeit the algebraic linear systems arising from the discretization of the differential problems are indefinite, ill-conditioned, and of saddle point nature.

Oct 16 - Oct 22, 2022

Recent advances in mixed finite element approximation for poroelasticity

Arbaz Khan, Assistant Professor, Department of Mathematics, Indian Institute of Technology (IIT)

Oct 18, 11:00 - 12:00

B1 L3 R3119

parallel computing Numerical Solution of Partial Differential Equations stochastic differential equations

This talk discusses the non-conforming approximation of Biot's consolidation model. In the first part of the talk, we discuss posteriori error estimators for locking-free mixed finite element approximation of Biot’s consolidation model. In the second part of the talk, we discuss a novel locking-free stochastic Galerkin mixed finite element method for the Biot consolidation model with uncertain Young’s modulus and hydraulic conductivity field.

Oct 9 - Oct 15, 2022

Finite element approximation of parameter dependent eigenvalue problems

Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

Oct 11, 12:00 - 13:00

B9 L2 R2322

Finite element approximation of parameter dependent eigenvalue problems

Eigenvalue problems arising from partial differential equations are used to model several applications in science and engineering, ranging from vibrations of structures, industrial microwaves, photonic crystals, and waveguides, to particle accelerators.

Sep 25 - Oct 1, 2022

Modeling and Numerics of Sorption Kinetics

Giovanni Russo, Professor, Department of Mathematics and Computer Science, University of Catania

Sep 27, 15:30 - 17:00

B1 L3 R3119

modeling sorption kinetics

An efficient method is proposed for the numerical solution of the Stokes equations in a domain with a moving bubble and two techniques for the treatment of the boundary conditions are adopted and then compared. The treatment of diffusion of surfactants (anions and cations) in presence of an oscillating bubble is an interesting interdisciplinary problem, with applications to chemistry and biology.

May 8 - May 14, 2022

Non-matching methods for the simulation of multi-dimensional and multi-physics coupled problems

Prof. Luca Heltai, Applied Mathematics, International School for Advanced Studies

May 12, 15:00 - 16:00

B1 L4 R4102

Real life multi-phase and multi-physics problems coupled across different scales present outstanding challenges, whose practical resolution often require unconventional numerical methods.

Apr 3 - Apr 9, 2022

Finite element approximation of Stokes equations with non-smooth data

Lucia Gastaldi, Professor Department of Mathematics, University of Brescia

Apr 6, 16:00 - 17:00

B1 L4 R4102

Finite element methods

Finite element approximation of Stokes equations with non-smooth data

Mar 27 - Apr 2, 2022

Monolithic matrix-free solver for fluid-structure interaction problems

Michał Wichrowski, IWR, University of Heidelberg (Germany)

Mar 28, 16:00 - 17:00

B1 L4 R4214

monolithic

Monolithic matrix-free solver for fluid-structure interaction problems.

Nov 7 - Nov 13, 2021

Compatibility conditions for finite element approximations

Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

Nov 11, 12:00 - 13:00

KAUST

In the classical theory of the finite element approximation of elliptic partial differential equations, based on standard Galerkin schemes, the energy norm of the error decays with the same rate of convergence as the best finite element approximation, without any additional requirements on the involved spaces.

Oct 31 - Nov 6, 2021

High order schemes for hyperbolic balance laws - Topic 3

Giovanni Russo, Full Professor, Mathematics and Computer Science, University of Catania, Italy

Nov 1, 09:00 - 10:00

B1 L4 R4102

Semi-implicit schemes for evolutionary partial differential equations. Topic 3 - construction of more general schemes for evolutionary partial differential equations, in which the stiffness may be of a different type than the one previously considered. Several examples will be given illustrating the general procedure.

Oct 24 - Oct 30, 2021

High order schemes for hyperbolic balance laws - Topic 2

Giovanni Russo,Full Professor,Mathematics and Computer Science, University of Catania, Italy

Oct 28, 09:00 - 10:00

B1 L4 R4102

Implicit-Explicit schemes for hyperbolic systems with stiff relaxation. Topic 2 - hyperbolic relaxation models and to the methods for their numerical solution. After introduction of hyperbolic-hyperbolic and hyperbolic-parabolic type relaxation problem, conservative finite difference space discretization will be introduced.
High order schemes for hyperbolic balance laws - Topic 1

Giovanni Russo, Professor, Mathematics and Computer Science, University of Catania, Italy

Oct 27, 09:00 - 10:00

B1 L4 R4102

Construction of high order finite volume and finite difference shock-capturing schemes for conservation laws. Topic 1 - illustrating how to construct shock capturing schemes for conservation laws. We focus on semi-discrete schemes based on the method of lines.

Sep 5 - Sep 11, 2021

Finite element approximation of fluid-structure interactions: a fictitious domain approach

Lucia Gastaldi, Professor, Numerical Analysis at the University of Brescia, Italy

Sep 7, 15:00 - 16:00

B1 L4 R4102

In this talk I report some results on the approximation of fluid-structure interaction problems using non matching grids. Our formulation originates from the Immersed Boundary Method and then moved toward the Fictitious Domain approach. The advantages of this formulation is that it avoids the difficulties related with mesh generation and it allows the treatment of fluid and solid in their natural Eulerian and Lagrangian framework. I present the well-posedness of our formulation at the continuous level in a simplified setting. Moreover, I shall discuss various time discretizations that provide unconditionally stable schemes and some computational details.

Oct 25 - Oct 31, 2020

On the approximation of the spectrum of differential operators

Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

Oct 29, 12:00 - 13:00

KAUST

Eigenvalue problems associated with partial differential equations are key ingredients for the modeling and simulation of a variety of real world applications, ranging from fluid-dynamics, structural mechanics, acoustics, to electromagnetism and medical problems. We review some properties related to the approximation of eigenvalue problems. Starting from matrix algebraic problems, we present a series of examples and counterexamples showing that even extremely simple situations can produce unexpected results.