Programa provisional

Programa

A fecha 28 de mayo de 2024

Se adjunta a continuación un breve resumen de los cursos/charlas (en inglés).
 

Curso 1

Luca Bonaventura. Associate Professor, Politecnico di Milano, Department of Mathematics, Italy.
Numerical methods for large systems of ordinary differential equations.

Along with a review of the basic concepts of Runge Kutta methods, I will present introductions to less mainstream topics in ODE methods which are not usually included in elementary courses, but which are of great importance for the practical application of ODE methods to large systems arising from the
spatial discretization of Partial Differential Equations (PDEs).
(volver al programa)

Curso 2

Catalin Turc. Associate Professor, New Jersey Institute of Technology, Department of Mathematical Sciences, USA.
Density Interpolation Methods for the high-order discretization of integral operators

Density Interpolation Method (DIM) produces high-order discretizations of boundary and volumetric potentials associated to Green’s functions of linear constant coefficient PDEs. An attractive feature of DIM algorithms is their capability to handle simultaneously singular (ranging from weakly singular to Hadamard finite parts), near-singular and far interactions needed by the numerical evaluation of layer and volume potentials, independent of the kernel/Green’s functions, and applicable to various types of surface and volumetric meshes produced by existing meshing engines. DIM regularize with the aid of Green’s third identity the kernel singularities present in layer potentials via certain surface/volumetric interpolation problems whereby densities are interpolated to high-order by smooth solutions of the underlying PDE. The mini course on DIM will present the algorithmic details of these methods and various demos will illustrate the performance of these methods for solution of problems of interest.
(volver al programa)

Conferencia 1

David González. Departamento de Ingeniería Mecánica, Universidad de Zaragoza.
Is there a place for AI in numerical simulation?

The development of computers and devices with high computing capacities and the ability to process large amounts of data have not only brought about a revolution in society, where artificial intelligence and its application to a wide range of fields are already considered an everyday fact, but also in science. There is already talk of the arrival of the fourth paradigm: data-driven science. We have moved from an empirical, theoretical and numerical study to a study marked by data that governs certain behaviours or patterns.

Throughout the presentation, advances in numerical simulations applied to situations requiring rapid or real-time responses are reflected. With artificial intelligence as the basis for this constant evolution, model reduction techniques have been used to create haptic simulators and the generation of digital twins. More recently, using machine learning techniques that respect established physical laws, simulation methods have been developed that are distinguished by unprecedented versatility, with promising results that open up wide prospects for their application in the industrial field.
(volver al programa)

Conferencia 2

Tomás Morales. Departamento de Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, Universidad de Málaga.
Modeling and simulation of non-hydrostatic effects in shallow water

The computation of free-surface water flows in environmental hydraulics entails an accurate and efficient modeling of important physical phenomena, including flows over obstacles, tsunami propagation and run-up and dam break waves. In the shallow water framework, the horizontal length scales are generally larger than the vertical ones. The dispersionless nonlinear shallow water equations (SWE), which are derived by assuming vertical hydrostatic pressure distribution and depth-independent horizontal velocity, are often a reasonable choice in such situations.

However, in many applications SWE fall short. For instance, when dealing with tsunami waves that impact a coastal area, it is a known fact that SWE provide accurate inundation maps, but they overestimate the speed of propagation for the waves. In general, simulating the propagation of undular bores in an estuary or the dispersive waves propagating over an obstacle requires to accurately reproduce the vertical acceleration and the pressure distribution. This leads to include dispersive or non-hydrostatic effects into the model.

The vertically-averaged modeling of non-hydrostatic flows has been accomplished traditionally by resorting to two leading families of models: Boussinesq-type models and depth-averaged non-hydrostatic models. The objective of this talk will be to review these two families, starting from the classical system by Boussinesq and continuing to some recent models in non-hydrostatic formulation. In particular, the aim is to include vertical effects that are not present in SWE. This has become of great interest and is currently a very active topic of research. Using recent techniques based on the multilayer approach or the weighted residual method, one can progressively obtain more complex models that provide accurate simulations in an efficient way.
(volver al programa)

Conferencia 3

Laura Saavedra. Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid.
ALE methods for solving compressible multi-material flows

Arbitrary Lagrangian-Eulerian (ALE) techniques blend the advantages of classical methods for hydrodynamics while minimising their drawbacks. We have developed ALE methods to solve systems of hyperbolic equations while keeping the domains invariant. In our ALE methods we use continuous finite elements, an explicit time scheme and a stabilisation based on an artificial viscosity that depends on the states of the neighbouring nodes to a given node ("graph-based viscosity"').

First, we propose a first-order viscosity whose main features are that it does not depend on any ad hoc parameters to be tuned for each simulation and that it satisfies the conservation of invariant domains and entropy inequalities. Secondly, we describe a second-order method that we get to satisfy the same properties of the first-order scheme using a technique that we call convex constraint.

In this talk, I will describe this second-order ALE method for solving the Euler equations, focusing on the most novel aspects of the ALE motion calculation and the convex limiting technique we propose. Subsequently, I will introduce a new purely Lagrangian explicit method we are developing which aims at preserving the mass exactly, as well as preserving the invariant domains. I will numerically illustrate the robustness of these methods for solving multi-material compressible flows with several test problems.
(volver al programa)

Conferencia 4

Enrique Delgado. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla.
An Introduction to Reduced Order Methods. Applications to Fluid Dynamics.

In this talk, we present an introduction to Reduced Order Methods (ROM), in which different approaches are described. On one hand, we present the classical intrusive ROM, for linear and non-linear problems, such as the Proper Orthogonal Decomposition (POD), the Reduced Basis Method (RBM) or the Empirical Interpolation Method (EIM). On the other hand, we present the more novel non-intrusive ROM, based on Artificial Neural Networks (ANN). Moreover, we present some application to Fluid Dynamics in which the reduction of the computational cost is important. Particulary, we present some results of intrusive ROM for turbulent flows and some results for non-intrusive ROM for thermal flows, where we show the fast computation of the reduced order solution.
(volver al programa)

Conferencia 5

Laura Portero. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra.
Space-time parallel iterative solvers for the solution of parabolic problems

Many phenomena in science and engineering are governed by evolutionary partial differential equations. In some cases, as when considering three-dimensional models and/or long-time simulations, the amount of computational work can be a bottleneck to obtain fast and accurate approximations to the solution. In order to take advantage of the computational capabilities of modern parallel clusters, significant research is being conducted in the field of space-time parallel methods. In this talk, we begin by introducing some well-known time-parallel algorithms. Then, we propose to combine the parallel-in-time parareal algorithm with several time-splitting schemes that allow for spatial parallelization. Both dimensional and domain decomposition partitioning strategies will be considered for the solution of parabolic problems. The main theoretical results will be illustrated by a collection of numerical experiments.
(volver al programa)

Conferencia 6

Carmen Rodrigo. Departamento de Matemática Aplicada, Universidad de Zaragoza.
Basics to Multigrid Methods. Application to saddle point problems.

Multigrid methods are among the most efficient methods for the solution of the large sparse linear systems of algebraic equations arising from the discretization of partial differential equations. They achieve asymptotically optimal complexity at least for elliptic problems, that is, the required computational work to solve a discrete problem is of the order of the number of unknowns of the corresponding system. Multigrid methods are mainly based on two ideas: the smoothing and the coarse-grid correction principles, which have to be properly combined by using a hierarchy of levels in order to eliminate all the different components of the error. In this talk, we will explain how these procedures work and their mathematical basis, so that the audience can have a complete understanding of multigrid methods.

The behavior of multigrid methods depends strongly on the choice of their components, which have to be chosen properly depending on the characteristics of the target problem. Due to their indefiniteness and poor spectral properties, saddle point problems represent a significant challenge for solver developers, and therefore, multigrid components have to be carefully designed in order to deal with this type of problems which frequently arise in a wide variety of applications throughout computational science and engineering. Thus the second part of this talk will be devoted to present some ideas about the application of multigrid methods for the solution of saddle point problems.
(volver al programa)

Conferencia 7

Patricia Barral,  Departamento de Matemática Aplicada, Universidad de Santiago de Compostela
Numerical solution of a thermomechanical problem in blast furnaces. 

Steelmaking is mainly carried out from pig iron, which is obtained in metallurgical furnaces, also known as blast furnaces, by reducing the ore. These furnaces operate at high temperature (up to 1500°C), so that the thermal stresses inside the furnace significantly limit the thermal stresses inside the furnace significantly limit the total campaign period of the furnace. In this context, thermomechanical modelling emerges as a fundamental tool to understand the process and try to optimise it.

In this talk, under certain simplifications, we will introduce a system of partial differential equations that allows to model the thermomechanical behaviour of the crucible walls of the blast furnace. We will see that, because of the geometry of the furnace and the characteristics of the forces, the problem can be simplified to a two-dimensional problem.We will approach its numerical solution by means of a finite element method and we will analyse some of the results obtained.
(volver al programa)

Conferencia 8

Inmaculada Higueras. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra.
Strong Stability Preserving Time Integration Methods

The solutions of some initial value systems of ordinary differential equations (ODEs) have relevant qualitative properties (e.g., monotonicity and contractivity in a given norm, semi-norm or convex functional, positivity, boundedness, etc.) that are relevant in the context of the problem due to its physical meaning. Strong Stability Preserving (SSP) time integration methods ensure the numerical preservation of the above qualitative properties under time stepsize restrictions.

In this talk, we will show the most relevant results for SSP Runge-Kutta (RK) and additive Runge-Kutta methods, as well as for other kind of time integration schemes, for different type of problems. Topics like Shu-Osher representations and low-storage implementations of SSP RK methods will also be addressed.

The performance of SSP methods will be illustrated with some numerical experiments. In particular, some PDE models associated with the simulation of stellar convection that appears in the context of astrophysics will be considered.

(volver al programa)

Taller

Alejandro Duque. Basque Center for Applied Mathematics.
Introduction to geometry and mesh generation in Gmsh.

This presentation provides an introductory overview of Gmsh, a specialized software tool focused on mesh generation and postprocessing techniques for Finite Element problems. With a practical approach, attendees will be guided through essential functionalities including geometry creation, exporting procedures, and mesh generation within the Gmsh framework using both the graphical user interface (GUI) and its programming language. Additionally, the session will explore the process of importing geometries from CAD files. By offering insights into key features of Gmsh, this session aims to equip attendees with sufficient knowledge to effectively utilize the tool in their FEM research.
(volver al programa)

Charla de divulgación

Se impartirá en la sede de la Comunidad de las Bardenas Reales en Calle San Marcial, 19.

Érase una vez las matemáticas numéricas.

El objetivo de esta charla es compartir con el auditorio, con las lentes de la divulgación, problemas resueltos con aproximaciones numéricas de las soluciones obtenidas con algoritmos matemáticos precisos. Comenzaremos la historia presentando a los matemáticos gallegos José Rodríguez (1770-1824) y su discípulo Domingo Fontán (1788-1866), que aportaron soluciones al problema de la igualdad, en la definición del metro como unidad de medida, y a un mejor conocimiento del territorio construyendo la Carta Geométrica de Galicia, el primer mapa científico hecho en España. Conectaremos la importancia de la geometría del territorio con algunas de las aportaciones realizadas por la relatora con diferentes investigadoras e investigadores. La motivación de estas aportaciones nace con la necesidad de un mejor conocimiento de la dinámica de las mareas de las rías gallegas a finales de los años ochenta. Continúa gracias a la capacidad de aplicar los métodos desarrollados a otras regiones costeras o interiores, para analizar problemas de inundaciones y de hidráulica fluvial, como por ejemplo el meandro de Ranillas en Zaragoza. Todo este trabajo colectivo ha dado lugar al software IBER. Finalmente, la charla desembocará en la conexión matemática de estos problemas, relacionados con el agua, con otros que nos permiten conocer el movimiento de los gases, la sangre o el tráfico. Los problemas presentados se resuelven empleando herramientas matemáticas de la familia de las compartidas en “Tudela Numérica: Curso y Encuentro de Análisis Numérico Francisco-Javier Sayas”, por lo que, gracias a este encuentro, la historia continuará...

(volver al programa)

Actos Sociales

Visita a las Bardenas reales

Salida, miércoles 12 de junio a las 17:30 desde el campus. 

Visita guiada a Tudela

Jueves 13 de junio, 17:30 (provisional)

Cena: Restaurante Iruña

Jueves 13 de junio, 21:30