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The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is...
We consider a domain decomposition method for some unsteady
heat conduction problem in composite structures.
This linear model problem is obtained by homogenization of thin layers
of fibres embedded into some standard material.
For ease of presentation we consider the case of two space dimensions only.
The set of finite element equations obtained by the backward Euler scheme
is parallelized in a problem-oriented fashion by some noniterative overlapping
domain splitting method,
eventually enhanced...
We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...
In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation [Achdou and Nataf,
C. R. Acad. Sci. Paris Sér. I325 (1997) 1211–1216]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into 2 sub-domains,...
We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...
The paper deals with the application of a non-conforming domain
decomposition method
to the problem of the computation of induced currents in electric engines
with moving conductors.
The eddy currents model is considered as a quasi-static
approximation of Maxwell
equations and we study its two-dimensional formulation with either the
modified magnetic vector potential or the magnetic field as primary variable.
Two discretizations are proposed, the first one based on curved finite
elements
and the...
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
In this article we introduce an adaptive multi-level
method in space and time for convection diffusion problems. The scheme
is based on a multi-level spatial splitting and the use of different
time-steps. The temporal discretization relies on the characteristics method.
We derive an a posteriori error estimate and design a corresponding
adaptive algorithm.
The efficiency of the multi-level method is illustrated by numerical experiments,
in particular for a convection-dominated problem.
We present an asynchronous multi-domain time integration algorithm with a dual domain decomposition method for the initial boundary-value problems for a parabolic equation. For efficient parallel computing, we apply the three-field domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. The implicit method for time discretization and the multi-domain spatial decomposition enable us to use different time steps...
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
Here, we prove the uniform observability of a two-grid method
for the semi-discretization of the 1D-wave equation for a time ;
this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418].
Our proof follows an Ingham type approach.
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