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Geometrical validity of curvilinear pyramidal finite elements Johnen, Amaury ; Geuzaine, Christophe in Journal of Computational Physics (2015), 299 Detailed reference viewed: 19 (3 ULg)A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations ; ; et al in Journal of Computational Physics (2015), 294 Detailed reference viewed: 26 (4 ULg)Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem Vion, Alexandre ; Geuzaine, Christophe in Journal of Computational Physics (2014), 266 Detailed reference viewed: 31 (8 ULg)Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations ; ; Geuzaine, Christophe in Journal of Computational Physics (2014), 279(15), 241-260 Detailed reference viewed: 15 (1 ULg)Geometrical validity of curvilinear finite elements Johnen, Amaury ; ; Geuzaine, Christophe 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 ▲] Detailed reference viewed: 94 (32 ULg)Robust untangling of curvilinear meshes ; Geuzaine, Christophe ; et al in Journal of Computational Physics (2013), 254 Detailed reference viewed: 9 (1 ULg)A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation ; ; Geuzaine, Christophe in Journal of Computational Physics (2012), 231(2), 262-280 Detailed reference viewed: 28 (6 ULg)Identification of Bayesian posteriors for coefficients of chaos expansions Arnst, Maarten ; ; 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 ▲] Detailed reference viewed: 31 (7 ULg)Phase Reduction Models for Improving the Accuracy of the Finite Element Solution of Time-Harmonic Scattering Problems I: General Approach and Low-Order Models ; Geuzaine, Christophe in Journal of Computational Physics (2009), 228 Detailed reference viewed: 61 (12 ULg)On destabilizing implicit factors in discrete advection-diffusion equations Beckers, Jean-Marie 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 ▲] Detailed reference viewed: 34 (5 ULg)Stability of a FBTCS Scheme Applied to the Propagation of Shallow-Water Inertia-Gravity Waves on Various Space Grids Beckers, Jean-Marie ; 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 ▲] Detailed reference viewed: 42 (12 ULg) |
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