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Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method

Ivo Babuška, Xu Huang, Robert Lipton (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A multiscale spectral generalized finite element method (MS-GFEM) is presented for the solution of large two and three dimensional stress analysis problems inside heterogeneous media. It can be employed to solve problems too large to be solved directly with FE techniques and is designed for implementation on massively parallel machines. The method is multiscale in nature and uses an optimal family of spectrally defined local basis functions over a coarse grid. It is proved that the method has an...

Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes

A. Caboussat (2011)

Mathematical Modelling of Natural Phenomena

Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol...

Mathematical modeling of time-harmonic aeroacoustics with a generalized impedance boundary condition

Eric Luneville, Jean-Francois Mercier (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the time-harmonic acoustic scattering in a duct in presence of a flow and of a discontinuous impedance boundary condition. Unlike a continuous impedance, a discontinuous one leads to still open modeling questions, as in particular the singularity of the solution at the abrupt transition and the choice of the right unknown to formulate the scattering problem. To address these questions we propose a mathematical approach based on variational formulations set in weighted Sobolev spaces. Considering...

Mathematical modelling of rock bolt reinforcement

Runt, David, Novotný, Jaroslav, Pruška, Jan (2017)

Programs and Algorithms of Numerical Mathematics

Rock bolts as construction elements are often used in underground civil engineering projects. This work deals with their numerical modelling. Aydan special finite elements for the description of rock bolts and hexahedral quadratic finite elements for the description of rock massif were used. A code for the computation of stiffness matrices and right hand sides of these elements was developed. The code was tested on several simple test examples and their results were compared with the analytical...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Mesh Refinement For Stabilized Convection Diffusion Equations

B. Achchab, M. El Fatini, A. Souissi (2010)

Mathematical Modelling of Natural Phenomena

We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.

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