Seminar on Numerical Analysis and Applied Mathematics at Valparaíso

Join us on Fridays at 12:20 hrs. (GMT-4) in room IMA 2-3 (IMA-PUCV) or by clicking on the following link https://shorturl.at/fSZ28.

 Upcoming Seminar

• August 25, 2023, 11:00 hrs.,  Andrea Trucchia, CIMA Research Foundation, Italy.

Contact

Prof. Paulina Sepúlveda y Prof. Ignacio Muga  

email:       paulina.sepulveda@pucv.cl,  o ignacio.muga@pucv.cl
website:   http://ima.ucv.cl/seminarios-permanentes/caleta-numerica

Calendario 2023

Calendario 2022

Calendario 2021

Calendario 2020

Calendario 2019

Calendario 2018

Calendario 2017

Calendario 2016

Calendario 2015

Calendario 2014

Calendario 2013

Next Seminars

• August 25. Andrea Trucchia. PROPAGATOR, stochastic cellular automaton for wildfires: from response to planning. CIMA Research Foundation, Italy.

Previous Seminars

• July 7. Nicolás Barnafi. Matemática computacional para tejidos blando. Pontificia Universidad Católica de Chile, Chile.

• June 30. Manuel Sánchez. Reflectionless Discrete Analytic Perfectly Matched Layers for Higher-Order Finite Difference Schemes. Pontificia Universidad Católica de Chile, Chile.

• April 14. Luis Contreras. Sobre métodos multiescala generalizados para flujo en medios porosos complejos y sus aplicaciones. Universidad Nacional de Colombia, Colombia.

• March 24. Paweł Maczuga. Graph-grammar based algorithm for asteroid tsunami simulations. AGH University of Science and Technology, Poland.

Seminars 2022

• December 16. Otilio Rojas. A pseudo-spectral time-domain method for acoustic wave propagation in dispersive and power-law dissipative media. Barcelona Supercomputing Center, Spain.

• November 11. Carlos Uriarte. A deep double Ritz method for solving partial
  differential equations. BCAM and UPV/EHU, Spain.

• September 30. Marcin Łoś. Space-time residual minimization with efficient linear solver based on matrix compression. AGH University of Science and Technology, Poland.

• May 25. Argenis Méndez. On Kato’s smoothing effect for a n-dimensional extension of the Zakharov-Kuznetsov equation, Pontificia Universidad Católica de Vaparaíso, Chile.

• April 1. Pablo Venegas. Numerical approximation of the axisymmetric acoustic vibration problem, Universidad del BioBio, Chile.

• March 18. Marcin Łoś. Splitting for non-stationary Maxwell equations with absorbing boundary conditions. AGH University of Science and Technology, Poland.

• March 11. Maciej Woźniak. Concurrent algorithms for integrating three-dimensional B-spline functions into machines with shared memory such as GPU. AGH University of Science and Technology, Poland.

Seminars 2021

• November 12, Natasha S. Sarma. First-Order Time Stepping schemes for sixth-order Cahn-Hilliard type equations modeling microemulsions, University of Texas at El Paso, USA.

• October 1st, 15:00 hrs. Judit Muñoz-Matute,
  

  Time marching DPG scheme and adaptivity for transient partial differential equations

  , The University of Texas at Austin, USA.

•  September 24, 15:00, Thomas Führer, Descomposiciones y normas multilevel en espacios de Sobolev de órdenes negativos. Pontificia Universidad Católica de Chile, Chile.
• August 20 15:00, Federico Fuentes, Estabilidad global de flujo de Couette en 2D por encima del límite de estabilidad energético, Pontificia Universidad Católica de Chile, Chile.
• June 18, 15:00, Sarah Roggenforf. The Non-Linear Petrov-Galerkin Method for the Convection-Diffusion Equation. Pontificia Universidad Católica de Chile, Chile.

• May 14, 15:00, Jaime Mora, El método DPG para elementos poliedrales y aplicaciones en problemas lineales y no lineales, University of Texas at Austin.

• May 7, 15:00, Jeffrey Ovall, An approach for investigating eigenvector localization, Portland State University, USA.

• April 30, Maciej Paszynski, Deep neural network driven self-adaptive hp finite element method,  Department of Computer Sciences, AGH University of Science and Technology, Krakow, Poland.
• April 16, 15:00, Daniel García, Refined Isogeometric Analysis: A solver-based discretization, Institute of Environmental Assessment and Water Research (IDAEA-CSIC), Spain.

• April 9, 2021.  Patrick Vega, Frequency-explicit a posteriori error estimates for finite element discretizations of Maxwell’s equations. Inria Sophia Antipolis – Méditerranée Research Centre, Valbonne, France. (LINK)

• March 26, 15:00, Carlos Uriarte, A finite element based Deep Learning solver for parametric PDEs, BCAM, Spain.

• March 19, 15:00, Francisca Álvarez Toledo, Un método DPG para la ecuación de onda. Universidad Técnica Federico Santa María, Chile.

• March 12, 15:00, Elisabete Alberdi, The use of Genetic Algorithms and Multi-Objective Evolutionary Algorithms in real problems. University of the Basque Country, Bilbao, Spain. 

Seminars 2020

Seminars 2019

isogeometric Residual Minimization Method (iGRM)

Seminars 2018

Diciembre 13, 2018, 12:00, Elisabete Alberdi, Universidad del País Vasco, España.

Diciembre 6, 2018, 12:00, Andreas Meister, Universidad de Kassel, Alemania.

Noviembre 30, 2018, 15:45, Juan Carlos Muñoz, Universidad del Valle, Cali, Colombia.

Octubre 19, 2018, 16:00, Roberto C. Cabrales, Universidad de La Serena

Seminars 2017

Agosto 11, 15:30, Ernesto Castillo, Universidad de Santiago de Chile

Seminars 2016

Noviembre 25, 15:40, Norbert Heuer, Pontificia Universidad Católica de Chile

Noviembre 18, Erwin Hernández, Universidad Técnica Federico Santa María

Noviembre 11, Dae-Jin Lee, Basque Center for Applied Mathematics (BCAM)

Septiembre 30, Diego Paredes, IMA-PUCV

Septiembre 23, Jorge Clarke, Universidad Santa María

Septiembre 9, Gino Montecinos, CMM, Universidad de Chile

Agosto 19, Elisabete Alberdi, Universidad del Pais Vasco

Designing techniques to find Symmetric Composition Methods of Symmetric Integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on symmetric composition methods involving some basic second order symmetric integrator with different step sizes [1]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [2], methods of order 8 and 15 stages were given in [3, 5, 6], 10-order methods of 31, 33 and 35 stages have been also found [2, 4]. In this work a technique that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) is explained. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Mayo 13, Michael Karkulik, Universidad Santa María

Space-time least squares methods for evolution equations

We consider two types of evolution equations: (i) linear second-order parabolic problems (e.g., the heat equation), and (ii), linear first-order hyperbolic systems (e.g., the wave equation). Classical numerical schemes for such equations discretize first in space and use ODE-techniques to advance in time. In our talk, we present variational formulations in space-time. This means that we do not treat the time as an extra dimension, but discretize and solve in the whole space-time cylinder. Our variational formulations are of least-squares type. We show existence and uniqueness of conforming finite element solutions and a-priori error estimates. This is joint work with Jay Gopalakrishnan, Martin Neumueller, and Panayot Vassilevski.

Mayo 6, Vincent Darrigrand, Universidad del Pais Vasco & INIRIA-Magique 3D Université de Pau

Marzo 11, Gabriel Barrenecha, University of Strathclyde

A unified analysis of algebraic flux-correction schemes

In this talk I will review recent results on the mathematical analysis of algebraic flux-correction (AFC) schemes. The schemes are designed mainly to preserve a discrete version of the maximum principle, and, unlike usual staibilised finite element schemes, AFC schemes do not start from a weak formulation, but rather they only “see” the linear system resulting from the discretisation. This lack of weak formulation is one of the main issues that have prevented from providing a mathematical analysis for this class of schemes. Then, the first step is to to write this scheme in a weak form, and then obtain stability results. Positivity of the scheme is proved under some approriate conditions on the mesh, and convergence results are proved.

Seminars 2015

Agosto 7, Nicole Spillane, Centro de Modelamiento Matemático

Achieving Robustness in Domain Decomposition

Domain Decomposition methods are a family of solvers that aim to solver very large linear systems on parallel architectures. They proceed by splitting the computational domain into subdomains and then approximating the inverse of the original problem by a sum of local inverses in the subdomains. I will present a classical domain decomposition method and show that for realistic simulations (with heterogeneous materials for instance) convergence can become very slow. Then I will explain how this can be fixed by using either a coarse space (this is also known as deflation) or multiple search directions within the conjugate gradient algorithm.

Julio 10, K.G. van de Zee, The University of Nottingham

Fundamentals of goal-oriented error estimation and adaptivity

Goal-oriented computational methodologies are extremely useful in the numerical solution of partial differential equations (PDEs) in the engineering and applied sciences. The idea of a goal oriented computation embraces the notion that a numerical simulation is generally done to study specific features of the solution, instead of the solution itself. These features are the so-called quantities of interest or target outputs, which are, therefore, the true goals of the simulation.

In this talk I will focus on the adaptive approximation of PDEs using goal-oriented (or adjoint-based, or duality-based) error estimates. I will start by recalling fundamental theory of goal-oriented a posteriori error estimation, and subsequently present a recent abstract convergence analysis of an optimal goal oriented adaptive finite element method.

Julio 3, Antônio Gomes (Laboratório Nacional de Computação Científica – BRASIL)

Experiments with Multi-Language Approaches to Implementing Scalable FEM/FVM solvers

In this talk we discuss about approaches to the development of scalable FEM/FVM solvers based on multiple programming languages. The aim of this type of “multi-language approach” is to cater for different software quality attributes (performance, fault tolerance, configurability, maintainability) by adequately exploring the features of different programming languages. Such an approach has been used elsewhere (e.g. the FENICS project) and has been also explored in a joint project involving PUCV, LNCC (Brazil) and INRIA (France). In this project we have progressed work on the implementation of a solver specifically crafted for a new family of FE methods called Multiscale Hybrid-Mixed (MHM). The MHM method allows solving (global) problems on coarse meshes while providing solutions with high-order precision by exploring the loosely-coupled strategy of embedding independent (local) subproblems in the upscaling procedure. Sticking to the idea of multi-language approaches, we’ve adopted Erlang as the base implementation for the communicating processes of the new solver. In this talk we present the advantages of adopting Erlang for such processes in terms of high productivity, good scalability, and support to fault tolerance. We show how the Erlang processes are loosely integrated with numerical computing processes (implemented in C++) that ultimately solve the global and local problems, thus indicating the potential of the Erlang implementation in being adopted in other contexts, e.g. for scalable FVM solvers. We present a preliminary performance evaluation of the overall (Erlang plus C++) implementation, taking into account its speed-up and load balancing properties. We then conclude the talk by pointing out the intended future work.

Junio 12, Thomas Führer (Pontificia Universidad Católica)

A wirebasket preconditioner for the mortar boundary element method

We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of freedom. The corresponding wirebasket type space decomposition is stable up to logarithmic terms. For the blocks that correspond to the inner degrees of freedom standard preconditioners for the hypersingular integral operator on open boundaries can be used. For the boundary and interface parts as well as the Lagrangian multiplier space, simple diagonal preconditioners are optimal. Our technique applies to quasi-uniform and non-uniform meshes of shape-regular elements. Numerical experiments on triangular and quadrilateral meshes confirm theoretical bounds for condition and MINRES iteration numbers.

Junio 5, Michael Karkulik (Pontificia Universidad Católica)

DPG method with optimal test functions for a transmission problem

We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultraweak finite element formulation on the interior. To be precise, it is a nonsymmetric coupling as developed in [3], but with an ultraweak finite element part as used in [1]. To guarantee the discrete inf-sup condition, we discretize the whole system with optimal test functions. In this way, we obtain quasi-optimality of the method in the so-called energy norm. In order to relate the energy norm to usual Sobolev norms, we use recent results regarding the nonsymmetric coupling of finite elements and boundary elements on polygonal interfaces, cf. [2, 4].

[1] L. Demkowicz and J. Gopalakrishnan. Analysis of the DPG method for the Poisson equation. SIAM J. Numer. Anal., 49(5):1788–1809, 2011.

[2] G. N. Gatica, G. C. Hsiao, and F.-J. Sayas. Relaxing the hypotheses of Bielak-MacCamy’s BEM-FEM coupling. Numer. Math., 120(3):465–487, 2012.

[3] C. Johnson and J.-C. Nédélec. On the coupling of boundary integral and finite element methods. Math. Comp., 35(152):1063–1079, 1980.

[4] F.-J. Sayas. The validity of Johnson-Nédélec’s BEM-FEM coupling on polygonal interfaces. SIAM Rev., 55(1):131–146, 2013

Mayo 29, Jessika Camaño (Universidad Católica de la Santísima Concepción)

A new augmented mixed finite element method for the Navier-Stokes problem

Abstract

Mayo 4, Maciej Paszynski (AGH University of Science and Technology, Krakow, Poland)

Parallel alternating direction preconditioner for isogeometric simulations of explicit dynamics

Abstract

Abril 17, Gabriel Barrenechea (University of Strathclyde)

Stabilising some inf-sup stable pairs on anisotropic quadrilateral meshes

Abstract

Abril 10, Claudio Torres (Universidad Técnica Federico Santa María)

An extension of a simple vertex model for mathematical modeling of grain growth in polycrystalline materials

Abstract

Marzo 13, Ivan Graham (University of Bath)

On domain decomposition preconditioners for finite element approximations of the Helmholtz equation using absorption

Abstract

Seminars 2014

Diciembre 12, Felipe Lepe (Universidad de Concepción)

Finite Element Analysis for a Bending Moment Formulation for the Vibration Problem of a Non-homogeneous Timoshenko Beam

Abstract

Noviembre 21, Manuel Solano (Universidad de Concepción)

Hybridizable discontinuous Galerkin method on general domains

Abstract

Noviembre 14, Raúl Fierro (IMA-PUCV)

Approximation of Some Discrete-Time Stochastic Processes by Differential Equations

Abstract

Noviembre 7, Karin Saavedra (Universidad de Talca)

Nuevas contribuciones a una estrategia multiescala de descomposición de dominios para la simulación de materiales compuestos laminados

Resumen

Octubre 24, Kris van der Zee (The University of Nottingham)

Diffuse-interface tumour growth modelling, analysis and simulation

Abstract

In this talk I will consider a class of nonlinear PDEs relevant to the growth of cancerous tumours, described with so-called diffuse interfaces. Its thermomechanical foundations will be discussed, as well as its sharp-interface limit. I will furthermore illuminate the underlying gradient-flow structure, which is important for the design of stable time-stepping schemes. Numerical examples will be presented for a recently proposed 2nd-order stabilised convex-splitting scheme.

Octubre 17, Tomás Barrios (Universidad Católica de la Santísima Concepción)

Esquemas numericos de orden bajo para las ecuaciones de Reissner-Mindlin

Resumen

En esta charla se presentarán nuevos esquemas estabilizados que permiten aproximar las ecuaciones de Reissner-Mindlin. A modo de motivación, previa a la presentacion de los esquemas, utilizamos las ecuaciones de la elasticidad lineal para materiales isotrópicos, a fin de describir algunos clásicos fenómenos de bloqueo numérico, además de explicar una forma de evitarlos. Esta descripción nos sirvió de motivación para iniciar nuestro estudio a las ecuaciones de Reissner-Mindlin, con lo cual pensamos que es el medio con el cual mejor se presentan los nuevos resultados.

Octubre 10, Ricardo Oyarzúa (Universidad del Bio Bio)

A priori and a posteriori error analysis for a vorticity-based mixed formulation of the Brinkman problem

Abstact

This work deals with the analysis of new mixed finite element methods for the generalized Stokes problem formulated in terms of velocity, vorticity and pressure, with non-standard boundary conditions. By employing an extension of the Babuška-Brezzi theory, it is proved that the resulting continuous and discrete variational formulations are well-posed. In particular, on the one hand we show that Raviart-Thomas elements of order k >= 0 for the approximation of the velocity field, piecewise continuous polynomials of degree k+1 for the vorticity, and piecewise polynomials of degree k for the pressure, yield unique solvability of the discrete problem. On the other hand, we also show that families of finite elements based on Brezzi-Douglas-Marini elements of order k+1 for the approximation of velocity, piecewise continuous polynomials of degree k+2 for the vorticity, and piecewise polynomials of degree k for the pressure ensure the well-posedness of the associated Galerkin scheme. We note that these families provide exactly divergence-free approximations of the velocity field. We establish a priori error estimates in the natural norms and we carry out the reliability and efficiency analysis of a residual-based a posteriori error estimator. Finally, we report several numerical experiments illustrating the behavior of the proposed schemes and confirming our theoretical results on unstructured meshes. Additional examples of cases not covered by our theory are also presented.

Septiembre 26, Richard Rankin (Universidad Técnica Federico Santa María)

Abstract

Agosto 22, Diego Paredes (IMA-PUCV)

Abstract

Junio 20, Jay Gopalakrishnan (Portland State University)

Abstract

Mayo 02, Karina Vilches Ponce (DIM-Universidad de Chile)

Abstact

Abril 04, Felipe Millar (Universidad del Bío-Bío, Chile)

Un método de elementos finitos para el problema de pandeo de placas Kirchhoff simplemente apoyada

Abstact

El método de elementos finitos para la aproximación de problemas de valores propios es un objeto de gran interés tanto desde el punto de vista teórico como práctico. El presente trabajo tiene relación con la estabilidad elástica de placas, en particular el llamado problema de pandeo, el cual frecuentemente aparece en problemas de ingeniería asociados a puentes, naves y diseño aeroespacial. Dicho problema puede ser formulado como un problema espectral cuya solución está relacionada con el límite de la estabilidad elástica de la placa. El método propuesto está basado en una formulación introducida por Ciarlet y Raviart, y consiste en la introducción de una nueva variable σ = ∆u (donde u representa el desplazamiento transversal de la superficie media). Para el análisis de este problema a nivel continuo, se introduce un operador llamado solución que tiene directa relación con los valores propios asociados al problema de pandeo. Luego, a través del uso de la teoría de Babuska-Osborn, intentaremos caracterizar la convergencia de los valores propios y las autofunciones asociadas, mostrando una convergencia optimal.

Marzo 28, Paulina Sepúlveda Salas (Fariborz Maseeh Department of Mathematics + Statistics, Portland State University, Oregon, USA.)

Solución de problemas de propagación de ondas sísmicas utilizando CLAWPACK

Abstact

Este trabajo se basa en el modelamiento de fenómenos de propagación de ondas sísmicas a través de diferentes materiales. Usando las ecuaciones de la elastodinámica y el métodos de volúmenes finitos, se obtiene una solución numérica al problema de propagación de ondas elásticas considerando discontinuidades en los parámetros de Lamé.

La implementación de algoritmos para encontrar estas soluciones pueden ser halladas en el paquete de sofware Clawpack. En esta presentación, tomando como base la teoría, incluiré el funcionamiento y utilización de Clawpack como una herramienta para obtenerlas.

Muchos de los fenómenos de interés práctico involucran geometrías irregulares, por lo que a partir del procedimiento aplicado en mallados uniformes, se pueden obtener resultados a problemas en mallados de tipo no uniformes.

Seminars 2013

November 22, Luis Briceño (Departamento de Matemáticas – UTFSM, Chile)

A Monotone[latex]+[/latex]Skew Splitting Model for Composite Monotone Inclusions in Duality

Abstract

October 25, Joaquín Mura (Ingeniería Civil -PUCV, Chile)

Estimación de la Porosidad en un Medio Incompresible con Microburbujas a través de Mediciones No-Invasivas.

En el presente trabajo, nos interesamos en materiales compuestos por un medio elástico incompresible e inclusiones gaseosas confinadas en pequeñas burbujas. Este modelo puede representar la dinámica de tejidos blandos, como por ejemplo el pulmonar. Para visualizar el campo de porosidad en el medio nos apoyamos en técnicas de elastografía por resonancia magnética, de donde se puede obtener información acerca del estado de deformaciones del espécimen en estudio. Considerando un modelo efectivo obtenido mediante homogeneización periódica propuesto por Baffico et Al. (2008) y, extendiéndolo al caso armónico en tiempo, nos encontramos con aproximaciones explícitas de la interacción entre la microgeometría y la macroestructura. Esto nos permite concebir un problema inverso, bajo ciertas hipótesis, para estimar el tamaño de los poros en distintas regiones del espécimen.

October 11, Sebastián Ossandón (IMA-PUCV, Chile)

Modelación de la Corrosión Atmosférica de Metales y Aleaciones Utilizando Redes Neuronales

Abstract: En este trabajo se presentan modelos de entrada-salida para estimar y predecir la velocidad de corrosión del acero y del cobre en diferentes estaciones de experimentación. Los modelos desarrollados se basan en el entrenamiento de una Red Neuronal Artificial (RNA) de base radial para ajustar de manera precisa los datos conocidos u observados. Una vez que se han ajustado los valores de los pesos, en base al entrenamiento antes mencionado, es posible estimar y/o predecir valores para la velocidad de corrosión del acero y del cobre en función de las variables de entrada.

September 27, Loredana Smaranda (Universidad de Pitesti, Rumania)

Convergence of the Lagrange-Galerkin method for fluid-structure interaction problems

We focus on a numerical method for the discretization of an initial and boundary value problem that models the self–propelled motion of one deformable solid in a bidimensional viscous incompressible fluid. In the model, we suppose that the solid is subjected to a known deformation field representing the action of the aquatic organism muscles. The governing equations consist of the Navier-Stokes equations for the fluid, coupled to Newton’s laws for the solid. The numerical method we propose is based on a global weak formulation, where the nonlinear term in the Navier–Stokes model is discretized using the characteristic function. Since the formulation is global in space, this characteristic function is extended in an appropriated manner inside of the creature, taking into account its deformation. In this talk, we concentrate our attention in the semi-discretization in time and we prove the stability and the convergence of the numerical scheme. The numerical method is consistent enough with the motion of the creature and for this reason, the discretization in space variable is successfully implemented using finite element method.

Abstract_LoredanaSmaranda

September 13, David Pardo (Universidad del País Vasco & Ikerbasque)

FAST INVERSION OF LOGGING-WHILE-DRILLING (LWD) RESISTIVITY MEASUREMENTS FOR THE CHARACTERIZATION OF HYDROCARBON-BEARING FORMATIONS

A number of three-dimensional (3D) simulators of borehole logging measurements have been developed during the last two decades for oil-industry applications. These simulators have been successfully used to study and quantify different physical effects occurring in 3D geometries. Despite such recent advances, there are still many 3D effects for which reliable simulations are not available. Furthermore, in most of the existing results only partial validations have been reported, typically obtained by comparing solutions of simplified model problems against the corresponding solutions calculated with a lower dimensional (2D).