References of "Journal of Computational Physics"
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See detailGeometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, J.-F.; Geuzaine, Christophe ULg

in Journal of Computational Physics (2013), 233

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

In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants 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 B ́ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

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

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 ULg; 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 ULg

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 ULg; 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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