Dimension reduction with auto-associative models We consider approximation of sets with the purpose of “reducing their dimension”, namely finding low dimensional systems of coordinates, either as an end in itself to search for interpretable structures, or as preliminary to optimisation, probabilistic modelling, or approximation of a function whith functional input…
Title: Finite Element Approximation of Elliptic Homogenization Problems in Nondivergence-Form Abstract: In the first part of the talk, we use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization problems of the form $A(x/\varepsilon) : D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We then propose…
Modeling oscillating polymerization/depolymerization processes The process of protein aggregation and fragmentation is intimately linked to the development of a broad class of neurodegenerative diseases or amyloid disease. More particularly, oscillatory kinetic phenomena are identified in experiments on Prion diseases. As a first step, the analysis of experimental data leads us…
Iterative Refinement in Three Precisions. Support for multiprecision floating point arithmetic is increasingly common in emerging architectures. In an effort to exploit this available hardware, we present a general algorithm for solving an n × n nonsingular linear system Ax = b based on iterative refinement in three precisions, where…
Title : A unified Nitsche approach for fluid-structure interactions with contact (Joint work with E. Burman and M.A. Fernández) In this talk we discuss fluid-structure interaction (FSI) problems with large structural deflections and the transition to contact between parts of the structure and an exterior wall. Several modelling issues arise…
Title : Approximation with tree tensor networks Abstract: Many problems in computational science require the approximation of high-dimensional functions. Examples of such problems can be found in physics, stochastic analysis or statistical learning. Other examples include parametric or uncertainty analyses for parameter-dependent models. The approximation of a high-dimensional function requires…
Stokes-Biot modeling of fluid-poroelastic structure interaction We study mathematical models and their finite element approximations for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic material. Applications of interest include flows in fractured poroelastic media and arterial flows. The free fluid…
Title: The boundary value problem for the multidimensional Camassa-Holm equation: generalized flows and numerical challenges Abstract: In this talk we will consider a multidimensional generalization of the Camassa-Holm equation, describing a shallow-water approximation for ideal fluid flow with a free boundary. Similarly to its one-dimensional counterpart, the multidimensional model has…
Title: A Posteriori Error Control of FEM for the Elliptic Obstacle Problem. Abstract: Elliptic obstacle problem which occurs in contact mechanics is a prototype model for a class of variational inequalities of the first kind. The linear finite element method for the obstacle performs optimally with respect to the uniform…
Title: isogeometric Residual Minimization Method (iGRM) We focus first on stationary advection-diffusion problems [1]. We present a stabilized isogeometric analysis method that exploits the Kronecker product structure of the computational problem. The trial spaces in our solution scheme are maximum continuity B-splines. To accelerate the solution of the algebraic scheme,…
