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Journal articles on the topic 'Formulation implicite'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

MACDONALD, Roderick A. "Pour la reconnaissance d’une normativité juridique implicite et « inférentielle »." Sociologie et sociétés 18, no. 1 (September 30, 2002): 47–58. http://dx.doi.org/10.7202/001460ar.

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Résumé L'auteur s'interroge sur l'importance des normes non formalisées dans les systèmes normatifs institutionnalisés. Il conteste l'approche réductrice du positivisme institutionnel, qui distingue le droit du non juridique par le critère de la source et qui privilégie en fait un modèle particulier de norme: la proposition formalisée émanant d'un organe législatif. L'auteur propose plutôt une typologie combinant le mode d'élaboration des normes et la manière dont on en extrait la signification. Dans cette optique plus sociologique, la question de la source du droit devient un problème d'argument et la fonction d'une norme n'apparaît plus fondamentalement affectée par sa formulation explicite dans une loi. S'il est vrai que la naissance d'institutions spécifiquement chargées d'appliquer la loi oriente la recherche normative vers les normes explicites formulées par ces institutions, il reste que, d'un point de vue dynamique, seules les nonnes implicites et "inférentielles" sont réellement normatives.

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2

Gaudreau, Louis. "Espace, temps et théorie du capital chez Henri Lefebvre et Marx." Cahiers de recherche sociologique, no. 55 (December 3, 2014): 155–76. http://dx.doi.org/10.7202/1027685ar.

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Ce texte propose une réflexion sur la production capitaliste de l’espace. Il présente la théorie d’Henri Lefebvre sur l’espace et tente de mettre en lumière la contribution originale de cet auteur à la compréhension du rapport entre temps et espace dans la reproduction du capitalisme. L’analyse porte plus particulièrement sur le concept d’espace abstrait développé par Lefebvre, dont on retrouve une formulation implicite dans les travaux de Marx, et qui révèle le rôle actif joué par la spatialité dans le procès de valorisation capitaliste. Le concept lefebvrien d’espace abstrait jette ainsi les bases d’une remise en question du primat accordé au temps dans la tradition d’analyse critique du capitalisme. Le texte se conclut par de brèves réflexions sur l’actualité d’une telle conception de l’espace pour saisir la récente financiarisation du capital.

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Hurley, Robert. "De la violence divine à l’obéissance esclave, le Père et le Fils renoncent au pouvoir en Ph 2." Dossier 67, no. 1 (August 9, 2011): 87–110. http://dx.doi.org/10.7202/1005568ar.

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L’acte de kénose décrit dans le Carmen Christi (Ph 2,6-11) a été maintes fois et correctement présenté comme une attitude ou une disposition spirituelle assumée par Jésus Christ quand il a accepté de mourir plutôt que d’avoir recours à la violence. De ces exégètes qui ont récemment attiré l’attention sur le caractère politique du langage de l’hymne, au moins deux (Oakes en 2005 et Heen, en 2004) détectent dans sa formulation une critique implicite du pouvoir violent qui fondait et soutenait l’Empire romain. L’auteur du présent article s’inscrit sur cette même trajectoire : il propose une interprétation de Ph 2,6-11 comme l’expression de la théopolitique qui informait la vie commune des ekklēsiai qui déclaraient que Jésus était seigneur. Dans ce passage, l’Église naissante projette une utopie féconde qui prévoit pour le faible un monde formé à l’image de celui qui renonçait aux honneurs divins si convoités de l’élite romaine. Tout en reconnaissant les implications politiques (sociales et matérielles) du message symbolique véhiculé en Ph 2, l’auteur soutient que l’Église qui chantait cet hymne devait voir son destin non seulement dans un monde (terrestre) plus juste, mais ultimement dans un royaume céleste où le Christ régnerait comme un seigneur au service de tous.

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Gardner, David J., Jorge E. Guerra, François P. Hamon, Daniel R. Reynolds, Paul A. Ullrich, and Carol S. Woodward. "Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models." Geoscientific Model Development 11, no. 4 (April 17, 2018): 1497–515. http://dx.doi.org/10.5194/gmd-11-1497-2018.

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Abstract. The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.

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Kanno, Yoshihiro. "AN IMPLICIT FORMULATION OF MATHEMATICAL PROGRAM WITH COMPLEMENTARITY CONSTRAINTS FOR APPLICATION TO ROBUST STRUCTURAL OPTIMIZATION." Journal of the Operations Research Society of Japan 54, no. 2-3 (2011): 65–85. http://dx.doi.org/10.15807/jorsj.54.65.

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6

Moosavian, Naser. "Pipe network modeling for analysis of flow in porous media." Canadian Journal of Civil Engineering 46, no. 12 (December 2019): 1151–59. http://dx.doi.org/10.1139/cjce-2018-0786.

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In this paper, a new matrix framework has been developed for the simulation of flow and pressure in porous media. In this framework, the pressure gradient formulation in Darcy’s law is considered as the head-loss equation in pipe network modeling. Then, an artificial pipe network has been constructed to find the pressure head profile in porous media. Two explicit and implicit formulations have been advanced for linear and nonlinear analysis, which the latter is an implementation of the Newton–Raphson algorithm. Both formulations iteratively solve a linear system of equations for calculating the nodal heads and apply a matrix multiplication for updating the flow vector. While the explicit method needs few iterations, the implicit method requires at least 20 iterations to converge with acceptable accuracy. For testing these formulations, four different types of network configurations were tested. The analysis of three laboratory tests showed that the application of the implicit method provides reliable and accurate results.

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7

GRAO, Frédéric, and Nicole RAMOGNINO. "Les matérialités sociales et leurs observations." Sociologie et sociétés 29, no. 2 (September 30, 2002): 103–19. http://dx.doi.org/10.7202/001309ar.

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Résumé La réception de Maurice Halbwachs peut être explicite dans les publications diverses ou encore dans des programmes de recherche en cours, et implicite dans des travaux de recherche publiés. Notre réception de l'œuvre est d'abord méthodique, alors même, comme nous le pensons, que ces considérations peuvent déplacer, élargir ou gauchir (selon le point de vue) le cadre de la théorie sociale. Les travaux de Maurice Halbwachs nous ont intéressés par leurs entrées méthodiques dans l'appréhension du social, ce que nous appelons les " matérialités du social " : espace, temps et information des faits sociaux dont la matérialité observable est essentiellement le langage. Ces " matérialités " relèvent d'une morphologie sociale, si l'on donne à ce terme son sens premier de délimitation de la forme des phénomènes sociaux qui permet et conditionne les opérations de découpage de discontinuités visibles dans la continuité du mouvement de la vie sociale, opérations que le sociologue effectue explicitement ou implicitement pour pouvoir envisager la description du social. Ces entrées ne sont pas spécifiques à la sociologie et demandent une construction sociologique. À cet égard, M. Halbwachs ouvre la voie en modalisant ces entrées selon le point de vue du groupe social : l'on peut voir, notamment lorsqu'il analyse la mémoire individuelle, à quel point le recours à la notion de groupe social lui apparaît pertinente et, lorsqu'il analyse les statistiques, l'approche relationnelle qu'il en fait. Nous avons voulu montrer la fécondité de cette approche méthodique, notamment en sociologie urbaine à partir de l'entrée spatio-temporelle, et pour ce faire, nous avons utilisé les travaux de G. Granai sur le développement de la ville d'Aix-en-Provence. Pour la troisième entrée que nous présentons, la matérialité langagière, nous avons sélectionné les recherches que nous menons dans le domaine de la sociologie de la réception littéraire, ceci autour d'une discussion sur la notion de " lecteur virtuel ", développée et déclinée de différentes manières depuis sa formulation par Gérard Genette, et d'un programme de recherche en cours sur la réception de la littérature de science-fiction.

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8

Benson, David J. "An implicit multi-material Eulerian formulation." International Journal for Numerical Methods in Engineering 48, no. 4 (June 10, 2000): 475–99. http://dx.doi.org/10.1002/(sici)1097-0207(20000610)48:4<475::aid-nme881>3.0.co;2-u.

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9

Bertei, Antonio, Andrea Lamorgese, and Roberto Mauri. "Constitutive Relations of Thermal and Mass Diffusion." Journal of Non-Equilibrium Thermodynamics 45, no. 1 (January 28, 2020): 27–38. http://dx.doi.org/10.1515/jnet-2019-0055.

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AbstractNon-equilibrium thermodynamics provides a general framework for the description of mass and thermal diffusion, thereby including also cross-thermal and material diffusion effects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass flux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefficients are not uniquely defined, though, as they can be derived by adopting one of the several constitutive relations satisfying the principles of non-equilibrium thermodynamics. Therefore, mass diffusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, predicted even in the absence of coupling terms. This study presents a critical analysis of different formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the different formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass diffusion allows for the implicit thermo-diffusion effect to be strictly absent while the resulting Dufour effect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling effects are predicted only if explicitly introduced via Onsager coupling coefficients.

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BOFFI, DANIELE, LUCIA GASTALDI, and LUCA HELTAI. "NUMERICAL STABILITY OF THE FINITE ELEMENT IMMERSED BOUNDARY METHOD." Mathematical Models and Methods in Applied Sciences 17, no. 10 (October 2007): 1479–505. http://dx.doi.org/10.1142/s0218202507002352.

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The immersed boundary method is both a mathematical formulation and a numerical method. In its continuous version it is a fully nonlinearly coupled formulation for the study of fluid structure interactions. Many numerical methods have been introduced to reduce the difficulties related to the nonlinear coupling between the structure and the fluid evolution. However numerical instabilities arise when explicit or semi-implicit methods are considered. In this work we present a stability analysis based on energy estimates of the variational formulation of the immersed boundary method. A two-dimensional incompressible fluid and a boundary in the form of a simple closed curve are considered. We use a linearization of the Navier–Stokes equations and a linear elasticity model to prove the unconditional stability of the fully implicit discretization, achieved with the use of a backward Euler method for both the fluid and the structure evolution, and a CFL condition for the semi-implicit method where the fluid terms are treated implicitly while the structure is treated explicitly. We present some numerical tests that show good accordance between the observed stability behavior and the one predicted by our results.

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Motamedian, Hamid Reza, and Artem Kulachenko. "Rotational Constraint between Beams in 3-D Space." Mechanical Sciences 9, no. 2 (November 16, 2018): 373–87. http://dx.doi.org/10.5194/ms-9-373-2018.

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Abstract. In this paper, we develop two alternative formulations for the rotational constraint between the tangents to connected beams with large deformations in 3-D space. Such a formulation is useful for modeling bonded/welded connections between beams. The first formulation is derived by consistently linearizing the variation of the strain energy and by assuming linear shape functions for the beam elements. This formulation can be used with both the Lagrange multiplier and the penalty stiffness method. The second non-consistent formulation assumes that the contact normal is independent of the nodal displacements at each iteration, and is updated consistently between iterations. In other words, we ignore the contribution due to the change of the contact normal in the linearization of the contact gap function. This assumption yields simpler equations and requires no specific assumption regarding the shape functions for the underlying beam elements. However, it is limited to the penalty method. We demonstrate the performance of the presented formulations in solving problems using implicit time integration. We also present a case showing the implications of ignoring this rotational constraint in modeling a network of beams.

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Hustad, Odd Steve, and David John Browning. "A Fully Coupled Three-Phase Model for Capillary Pressure and Relative Permeability for Implicit Compositional Reservoir Simulation." SPE Journal 15, no. 04 (July 27, 2010): 1003–19. http://dx.doi.org/10.2118/125429-pa.

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Summary A coupled formulation for three-phase capillary pressure and relative permeability for implicit compositional reservoir simulation is presented. The formulation incorporates primary, secondary, and tertiary saturation functions. Hysteresis and miscibility are applied simultaneously to both capillary pressure and relative permeability. Two alternative three-phase capillary pressure formulations are presented: the first as described by Hustad (2002) and the second that incorporates six representative two-phase capillary pressures in a saturation-weighting scheme. Consistency is ensured for all three two-phase boundary conditions through the application of two-phase data and normalized saturations. Simulation examples of water-alternating-gas (WAG) injection are presented for water-wet and mixed-wet saturation functions. 1D homogeneous and 2D and 3D heterogeneous examples are employed to demonstrate some model features and performance.

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Peer, Andreas, Markus Ihmsen, Jens Cornelis, and Matthias Teschner. "An implicit viscosity formulation for SPH fluids." ACM Transactions on Graphics 34, no. 4 (July 27, 2015): 1–10. http://dx.doi.org/10.1145/2766925.

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Takahashi, Tetsuya, Yoshinori Dobashi, Issei Fujishiro, Tomoyuki Nishita, and Ming C. Lin. "Implicit Formulation for SPH-based Viscous Fluids." Computer Graphics Forum 34, no. 2 (May 2015): 493–502. http://dx.doi.org/10.1111/cgf.12578.

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Abdel-Malek, K., J. Yang, and D. Blackmore. "On swept volume formulations: implicit surfaces." Computer-Aided Design 33, no. 1 (January 2001): 113–21. http://dx.doi.org/10.1016/s0010-4485(00)00065-8.

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Raymond, William H. "Recursive filters determined from implicit formulations." Communications in Applied Numerical Methods 8, no. 11 (November 1992): 801–9. http://dx.doi.org/10.1002/cnm.1630081103.

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Kang, K. S., and D. E. Keyes. "Implicit symmetrized streamfunction formulations of magnetohydrodynamics." International Journal for Numerical Methods in Fluids 58, no. 11 (December 20, 2008): 1201–22. http://dx.doi.org/10.1002/fld.1755.

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18

Asai, Mitsuteru, Abdelraheem M. Aly, Yoshimi Sonoda, and Yuzuru Sakai. "A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition." Journal of Applied Mathematics 2012 (2012): 1–24. http://dx.doi.org/10.1155/2012/139583.

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A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

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ASTLEY, R. J., and J. A. HAMILTON. "NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION." Journal of Computational Acoustics 08, no. 01 (March 2000): 1–24. http://dx.doi.org/10.1142/s0218396x00000029.

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Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley–Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.

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Navia-Vázquez, A., and A. R. Figueiras-Vidal. "Efficient Block Training of Multilayer Perceptrons." Neural Computation 12, no. 6 (June 1, 2000): 1429–47. http://dx.doi.org/10.1162/089976600300015448.

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The attractive possibility of applying layerwise block training algorithms to multilayer perceptrons MLP, which offers initial advantages in computational effort, is refined in this article by means of introducing a sensitivity correction factor in the formulation. This results in a clear performance advantage, which we verify in several applications. The reasons for this advantage are discussed and related to implicit relations with second-order techniques, natural gradient formulations through Fisher's information matrix, and sample selection. Extensions to recurrent networks and other research lines are suggested at the close of the article.

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Knechtges, Philipp, Marek Behr, and Stefanie Elgeti. "Fully-implicit log-conformation formulation of constitutive laws." Journal of Non-Newtonian Fluid Mechanics 214 (December 2014): 78–87. http://dx.doi.org/10.1016/j.jnnfm.2014.09.018.

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22

Branco, Celso M., and Fernando Rodriguez. "A Semi-Implicit Formulation for Compositional Reservoir Simulation." SPE Advanced Technology Series 4, no. 01 (May 1, 1996): 171–77. http://dx.doi.org/10.2118/27053-pa.

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23

Qin, Hao, Lars-Erik Lindgren, Wing Kam Liu, and Jacob Smith. "Implicit finite element formulation of multiresolution continuum theory." Computer Methods in Applied Mechanics and Engineering 293 (August 2015): 114–30. http://dx.doi.org/10.1016/j.cma.2015.04.009.

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Sudersan, S., U. Saravanan, and A. Arockiarajan. "Finite element formulation for implicit magnetostrictive constitutive relations." Computational Mechanics 66, no. 6 (September 15, 2020): 1497–514. http://dx.doi.org/10.1007/s00466-020-01914-1.

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Soto, O., R. Löhner, J. Cebral, and F. Camelli. "A stabilized edge-based implicit incompressible flow formulation." Computer Methods in Applied Mechanics and Engineering 193, no. 23-26 (June 2004): 2139–54. http://dx.doi.org/10.1016/j.cma.2004.01.018.

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Noronha, Santosh, Günter Gruhn, and Zdravko Kravanja. "Handling implicit model formulations in MINLP optimization." Computers & Chemical Engineering 21 (May 1997): S499—S504. http://dx.doi.org/10.1016/s0098-1354(97)87551-5.

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Noronha, S. "Handling Implicit Model Formulations in MINLP Optimization." Computers & Chemical Engineering 21, no. 1-2 (1997): S499—S504. http://dx.doi.org/10.1016/s0098-1354(97)00098-7.

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Cihan, Mertcan, Blaž Hudobivnik, Fadi Aldakheel, and Peter Wriggers. "3D mixed virtual element formulation for dynamic elasto-plastic analysis." Computational Mechanics 68, no. 3 (April 15, 2021): 1–18. http://dx.doi.org/10.1007/s00466-021-02010-8.

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AbstractThe virtual element method (VEM) for dynamic analyses of nonlinear elasto-plastic problems undergoing large deformations is outlined within this work. VEM has been applied to various problems in engineering, considering elasto-plasticity, multiphysics, damage, elastodynamics, contact- and fracture mechanics. This work focuses on the extension of VEM formulations towards dynamic elasto-plastic applications. Hereby low-order ansatz functions are employed in three dimensions with elements having arbitrary convex or concave polygonal shapes. The formulations presented in this study are based on minimization of potential function for both the static as well as the dynamic behavior. Additionally, to overcome the volumetric locking phenomena due to elastic and plastic incompressibility conditions, a mixed formulation based on a Hu-Washizu functional is adopted. For the implicit time integration scheme, Newmark method is used. To show the model performance, various numerical examples in 3D are presented.

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Kadapa, Chennakesava. "A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids." Acta Mechanica 232, no. 6 (March 1, 2021): 2135–63. http://dx.doi.org/10.1007/s00707-020-02883-5.

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AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

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Antunes, A. R. E., P. R. M. Lyra, R. B. Willmersdorf, and S. M. A. Bastos. "An implicit monolithic formulation based on finite element formulation for incompressible Navier–Stokes equations." Journal of the Brazilian Society of Mechanical Sciences and Engineering 37, no. 1 (March 18, 2014): 199–210. http://dx.doi.org/10.1007/s40430-014-0155-x.

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Beljaars, Anton, Emanuel Dutra, Gianpaolo Balsamo, and Florian Lemarié. "On the numerical stability of surface–atmosphere coupling in weather and climate models." Geoscientific Model Development 10, no. 2 (February 27, 2017): 977–89. http://dx.doi.org/10.5194/gmd-10-977-2017.

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Abstract. Coupling the atmosphere with the underlying surface presents numerical stability challenges in cost-effective model integrations used for operational weather prediction or climate simulations. These are due to the choice of large integration time steps compared to the physical timescale of the problem, aiming at reducing computational burden, and to an explicit flux coupling formulation, often preferred for its simplicity and modularity. Atmospheric models therefore use the surface-layer temperatures (representative of the uppermost soil, snow, ice, water, etc.) at the previous integration time step in all surface–atmosphere heat-flux calculations and prescribe fluxes to be used in the surface model integrations. Although both models may use implicit formulations for the time steps, the explicit flux coupling can still lead to instabilities.In this study, idealized simulations with a fully coupled implicit system are performed to derive an empirical relation between surface heat flux and surface temperature at the new time level. Such a relation mimics the fully implicit formulation by allowing one to estimate the surface temperature at the new time level without solving the surface heat diffusion problem. It is based on similarity reasoning and applies to any medium with constant heat diffusion and heat capacity parameters. The advantage is that modularity of the code is maintained and that the heat flux can be computed in the atmospheric model in such a way that instabilities in the snow or ice code are avoided. Applicability to snow–ice–soil models with variable density is discussed, and the loss of accuracy turns out to be small. A formal stability analysis confirms that the parametrized implicit-flux coupling is unconditionally stable.

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Enenajor, Gilbert. "Kant’s Implicit Suggestion of the Negative Formulation of Duty." International Journal of Undergraduate Research and Creative Activities 4, no. 1 (June 19, 2013): 16. http://dx.doi.org/10.7710/2155-4838.1086.

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Asada, Takashi, and Nobutada Ohno. "Implicit Formulation of Homogenization Method for Periodic Elastoplastic Solids." Key Engineering Materials 340-341 (June 2007): 1055–60. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1055.

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In this study, to determine incremental, perturbed displacement fields in periodic elastoplastic solids, an incremental homogenization problem is fully implicitly formulated, and an algorithm is developed to solve the homogenization problem. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to previous studies. The homogenization algorithm developed is then examined by analyzing a holed plate, with an elastoplastic micro-structure, subjected to tensile loading. It is thus demonstrated that the convergence in iteratively solving the homogenization problem strongly depends on the initial setting of strain increments in unit cells, and that quick convergences can be attained if the initial setting of strain increments is appropriate.

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Andersson, H. "An implicit formulation of the Bodner–Partom constitutive equations." Computers & Structures 81, no. 13 (May 2003): 1405–14. http://dx.doi.org/10.1016/s0045-7949(03)00019-1.

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Peer, Andreas, Christoph Gissler, Stefan Band, and Matthias Teschner. "An Implicit SPH Formulation for Incompressible Linearly Elastic Solids." Computer Graphics Forum 37, no. 6 (December 14, 2017): 135–48. http://dx.doi.org/10.1111/cgf.13317.

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Wang, W. M., and L. J. Sluys. "Formulation of an implicit algorithm for finite deformation viscoplasticity." International Journal of Solids and Structures 37, no. 48-50 (November 2000): 7329–48. http://dx.doi.org/10.1016/s0020-7683(00)00201-8.

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Date, A. W. "NOVEL STRONGLY IMPLICIT ENTHALPY FORMULATION FOR MULTIDIMENSIONAL STEFAN PROBLEMS." Numerical Heat Transfer, Part B: Fundamentals 21, no. 2 (March 1992): 231–51. http://dx.doi.org/10.1080/10407799208944918.

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Jakimow, Georges, Evhen Yakimiw, and André Robert. "An Implicit Formulation for Horizontal Diffusion in Gridpoint Models." Monthly Weather Review 120, no. 1 (January 1992): 124–30. http://dx.doi.org/10.1175/1520-0493(1992)120<0124:aiffhd>2.0.co;2.

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Legat, Vincent, and Jean-Marie Marchal. "Die design: An implicit formulation for the inverse problem." International Journal for Numerical Methods in Fluids 16, no. 1 (January 15, 1993): 29–42. http://dx.doi.org/10.1002/fld.1650160103.

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Zreid, Imadeddin, and Michael Kaliske. "An implicit gradient formulation for microplane Drucker-Prager plasticity." International Journal of Plasticity 83 (August 2016): 252–72. http://dx.doi.org/10.1016/j.ijplas.2016.04.013.

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Wang, Xingshi, Chu Wang, and Lucy T. Zhang. "Semi-implicit formulation of the immersed finite element method." Computational Mechanics 49, no. 4 (October 29, 2011): 421–30. http://dx.doi.org/10.1007/s00466-011-0652-z.

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Lapenta, Giovanni. "Exactly energy conserving semi-implicit particle in cell formulation." Journal of Computational Physics 334 (April 2017): 349–66. http://dx.doi.org/10.1016/j.jcp.2017.01.002.

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Tanveer, M., and K. Shubham. "Smooth twin support vector machines via unconstrained convex minimization." Filomat 31, no. 8 (2017): 2195–210. http://dx.doi.org/10.2298/fil1708195t.

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Twin support vector machine (TWSVM) exhibits fast training speed with better classification abilities compared with standard SVM. However, it suffers the following drawbacks: (i) the objective functions of TWSVM are comprised of empirical risk and thus may suffer from overfitting and suboptimal solution in some cases. (ii) a convex quadratic programming problems (QPPs) need to be solve, which is relatively complex to implement. To address these problems, we proposed two smoothing approaches for an implicit Lagrangian TWSVM classifiers by formulating a pair of unconstrained minimization problems in dual variables whose solutions will be obtained by solving two systems of linear equations rather than solving two QPPs in TWSVM. Our proposed formulation introduces regularization terms to each objective function with the idea of maximizing the margin. In addition, our proposed formulation becomes well-posed model due to this term, which introduces invertibility in the dual formulation. Moreover, the structural risk minimization principle is implemented in our formulation which embodies the essence of statistical learning theory. The experimental results on several benchmark datasets show better performance of the proposed approach over existing approaches in terms of estimation accuracy with less training time.

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Kühnlein, Christian, Willem Deconinck, Rupert Klein, Sylvie Malardel, Zbigniew P. Piotrowski, Piotr K. Smolarkiewicz, Joanna Szmelter, and Nils P. Wedi. "FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS." Geoscientific Model Development 12, no. 2 (February 13, 2019): 651–76. http://dx.doi.org/10.5194/gmd-12-651-2019.

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Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

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Giustolisi, O., L. Berardi, and T. M. Walski. "Some explicit formulations of Colebrook–White friction factor considering accuracy vs. computational speed." Journal of Hydroinformatics 13, no. 3 (October 26, 2010): 401–18. http://dx.doi.org/10.2166/hydro.2010.098.

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The Colebrook–White formulation of the friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations to efficiently calculate the Colebrook–White friction factor are presented herein. The aim of this investigation is twofold: (i) to preserve the accuracy of estimates while (ii) reducing the computational burden (i.e. speed). On the one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large-size water distribution networks (WDN) in optimization problems, flooding software, etc.) is required together with its derivative. On the other hand, the accuracy of the developing formula should be realistically chosen considering the remaining uncertainties surrounding the model where the friction factor is used. In the following, three strategies for friction factor mapping are proposed which were achieved by using the Evolutionary Polynomial Regression (EPR). The result is the encapsulation of some pieces of the friction factor implicit formulae within pseudo-polynomial structures.

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Weller, Hilary, and Ava Shahrokhi. "Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves." Monthly Weather Review 142, no. 12 (December 1, 2014): 4439–57. http://dx.doi.org/10.1175/mwr-d-14-00054.1.

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Abstract Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modeling flow over orography is introduced that guarantees curl-free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain-following grids. Curl-free gradients are achieved by using the covariant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with NΔt up to at least 10 (where N is the Brunt–Väisälä frequency). A warm bubble rising over orography is simulated and the curl-free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

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Greco, Francesco, Domenico Umbrello, Serena Di Renzo, Luigino Filice, I. Alfaro, and E. Cueto. "Application of the Nodal Integrated Finite Element Method to Cutting: a Preliminary Comparison with the “Traditional” FEM Approach." Advanced Materials Research 223 (April 2011): 172–81. http://dx.doi.org/10.4028/www.scientific.net/amr.223.172.

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FEM implicit formulation shows specific limitations in processes such as cutting, where large deformation results in a heavy mesh distortion. Powerful rezoning-remeshing algorithms strongly reduce the effects of such a limitation but the computational times are significantly increased and additional errors are introduced. Nodal Integration is a recently introduced technique that allows finite element method to provide more reliable results when mesh becomes distorted in traditional FEMs. Furthermore, volumetric locking phenomenon seems to be avoided by using this integration technique instead of other methods, such as the coupled formulations. In this paper, a comparison between a “classical” FEM simulation and the Nodal Integration one is carried out taking into account a simple orthogonal cutting process.

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Lee, Joon-Seong, Ho-Jeong Lee, and Tomonari Furukawa. "Formulation of the Neural Network for Implicit Constitutive Model (I) : Application to Implicit Vioscoplastic Model." International Journal of Fuzzy Logic and Intelligent Systems 9, no. 3 (September 1, 2009): 191–97. http://dx.doi.org/10.5391/ijfis.2009.9.3.191.

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Hajibeygi, H., and H. A. A. Tchelepi. "Compositional Multiscale Finite-Volume Formulation." SPE Journal 19, no. 02 (November 20, 2013): 316–26. http://dx.doi.org/10.2118/163664-pa.

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Summary The multiscale finite-volume (MSFV) method is extended to include compositional processes in heterogeneous porous media, which require accurate modeling of the mass transfer and associated phase behaviors. A sequential-implicit strategy is used to deal with the coupling of the flow (pressure) and transport (component overall concentration) problems. In this compositional formulation, the overall continuity equation is used to formulate the pressure equation. The resulting pressure equation conserves total mass by construction and depends weakly on the distributions of the phase compositions. The transport equations are expressed in terms of the overall composition; hence, phase-appearance and -disappearance effects do not appear explicitly in these expressions. The details of the MSFV strategy for the pressure equation are described. The only source of error in this MSFV framework is the localization assumption. No additional assumptions related to the complex physics are used. For 1D problems, the sequential strategy is validated against solutions obtained by a fully implicit simulator. The accuracy of the MSFV method for compositional simulations is then illustrated for different test cases.

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Ramadan, Omar. "Unified integro-differential equation for efficient dispersive FDTD simulations." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 4 (July 3, 2017): 1089–105. http://dx.doi.org/10.1108/compel-10-2016-0471.

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Purpose The purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations. Design/methodology/approach In this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed. Findings It is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation. Research limitations/implications The stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit. Practical implications Based on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function. Originality/value The proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

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