References of "Journal of Computational Physics"
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See detailA coupled electro-thermal Discontinuous Galerkin method
Homsi, Lina ULiege; Geuzaine, Christophe ULiege; Noels, Ludovic ULiege

in Journal of Computational Physics (2017), 348

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental ... [more ▼]

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree. [less ▲]

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See detailWaveform relaxation for the computational homogenization of multiscale magnetoquasistatic problems
Niyonzima, Innocent; Geuzaine, Christophe ULiege; Schöps, Sebastian

in Journal of Computational Physics (2016), 327

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See detailGeometrical validity of curvilinear pyramidal finite elements
Johnen, Amaury ULiege; Geuzaine, Christophe ULiege

in Journal of Computational Physics (2015), 299

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See detailA quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations
El Bouajaji, Mohamed; Thierry, Bertrand; Antoine, Xavier et al

in Journal of Computational Physics (2015), 294

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See detailDouble sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
Vion, Alexandre ULiege; Geuzaine, Christophe ULiege

in Journal of Computational Physics (2014), 266

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See detailApproximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations
Bouajaji, M. El; Antoine, X.; Geuzaine, Christophe ULiege

in Journal of Computational Physics (2014), 279(15), 241-260

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See detailGeometrical validity of curvilinear finite elements
Johnen, Amaury ULiege; Remacle, J.-F.; Geuzaine, Christophe ULiege

in Journal of Computational Physics (2013), 233

In this paper, we describe a way to compute accurate bounds on Jacobian determinants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i ... [more ▼]

In this paper, we describe a way to compute accurate bounds on Jacobian determinants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the distortion of curvilinear elements. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

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See detailRobust untangling of curvilinear meshes
Toulorge, Thomas; Geuzaine, Christophe ULiege; Remacle, Jean-François et al

in Journal of Computational Physics (2013), 254

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See detailA Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation
Boubendir, Y.; Antoine, X.; Geuzaine, Christophe ULiege

in Journal of Computational Physics (2012), 231(2), 262-280

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See detailIdentification of Bayesian posteriors for coefficients of chaos expansions
Arnst, Maarten ULiege; Ghanem, Roger; Soize, Christian

in Journal of Computational Physics (2010), 229(9), 3134-3154

This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of ... [more ▼]

This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology. [less ▲]

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See detailOn destabilizing implicit factors in discrete advection-diffusion equations
Beckers, Jean-Marie ULiege

in Journal of Computational Physics (1994), 111(2), 260-265

In the present paper, we find necessary and sufficient stability conditions for a simple one-time step finite difference discretization of an N-dimensional advection-diffusion equation. Furthermore, it is ... [more ▼]

In the present paper, we find necessary and sufficient stability conditions for a simple one-time step finite difference discretization of an N-dimensional advection-diffusion equation. Furthermore, it is shown that when the implicit factors differ in each direction, a strange behavior occurs: By increasing one implicit factor in only one direction, a stable scheme can become unstable. It is thus suggested to use a single implicit direction (for efficient computing), or the same implicit factor in each direction. (C) 1994 Academic Press, Inc. [less ▲]

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See detailStability of a FBTCS Scheme Applied to the Propagation of Shallow-Water Inertia-Gravity Waves on Various Space Grids
Beckers, Jean-Marie ULiege; Deleersnijder, Eric

in Journal of Computational Physics (1993), 108(1), 94-104

The equations governing the propagation of inertia-gravity waves in geophysical fluid flows are discretized on the A, B, C, and D grids according to the classical forward-backward on time and centered on ... [more ▼]

The equations governing the propagation of inertia-gravity waves in geophysical fluid flows are discretized on the A, B, C, and D grids according to the classical forward-backward on time and centered on space (FBTCS) numerical scheme. The von Neumann stability analysis is performed and it is shown that the stability condition of the inertia-gravity waves scheme is more restrictive, at least by a factor of , than that concerning pure gravity waves, whatever the magnitude of the Coriolis parameter. Finally, the general necessary and sufficient stability condition is derived for the A, B and C grids, while, on the D grid, the stability condition has been obtained only in particular cases. [less ▲]

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