Electro-thermo-chemical computational models for 3D heterogeneous semiconductor device simulation

Mauri, Aurelio Giancarlo; Sacco, Riccardo; Verri, Maurizio

doi:10.1016/j.apm.2014.12.008

Cited by 20 publications

(9 citation statements)

References 35 publications

(66 reference statements)

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“…In this section we perform a thorough validation of the performance of the proposed method. To this end, we have implemented problem (1) and the DMH-RT0 FEM scheme proposed for its discretization within the computational software MP-FEMOS (Multi-Physics Finite Element Modeling Oriented Simulator) that has been developed by one of the authors [33,32,3,34,47]. MP-FEMOS is a general-purpose modular code based on the Galerkin Finite Element Method that is programmed in a fully 3D framework through shared libraries using an object-oriented language (C++).…”

Section: Numerical Resultsmentioning

confidence: 99%

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A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces

2020

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This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective interface. We propose a novel approach for the numerical approximation of such heterogeneous systems combining, for the first time: (1) a dual mixed hybrid (DMH) finite element method (FEM) based on the lowest order Raviart-Thomas space (RT0);(2) a Three-Field (3F) formulation; and (3) a Streamline Upwind/Petrov-Galerkin (SUPG) stabilization method. Using the abstract theory for generalized saddle-point problems and their approximation, we show that the weak formulation of the proposed method and its numerical counterpart are both uniquely solvable and that the resulting finite element scheme enjoys optimal convergence properties with respect to the discretization parameter. In addition, an efficient implementation of the proposed formulation is presented. The implementation is based on a systematic use of static condensation which reduces the method to a nonconforming finite element approach on a grid made by three-dimensional simplices. Extensive computational tests demonstrate the theoretical conclusions and indicate that the proposed DMH-RT0 FEM scheme is accurate and stable even in the presence of marked interface jump discontinuities in the solution and its associated normal flux. Results also show that in the case of strongly dominating advective terms, the proposed method with the SUPG stabilization is capable of resolving accurately steep boundary and/or interior layers without introducing spurious unphysical oscillations or excessive smearing of the solution front.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Using in (33) the approximation theory for hybrid methods developed in [44] yields the following convergence estimates for the DMH-RT0 FEM.…”

Section: The Dmh Galerkin Finite Element Approximationmentioning

confidence: 99%

A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces

2020

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“…The existence of the required auxiliary concentrations is consequence of Theorem 3.1 and Remark 3.1. In particular, we have 1)[, and the assumptions (15), (16), (19), (22)- (24), and (26)- (27) be fulfilled. Then, the variational problem…”

Section: Existence Of Auxiliary Solutionsmentioning

confidence: 99%

Sufficient conditions for the existence of solutions for a thermoelectrochemical problem

Consiglieri¹

2015

J. Fixed Point Theory Appl.

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Abstract. A mathematical model is introduced for thermoelectrochemical phenomena in an electrolysis cell, and its qualitative analysis is focused on existence of solutions. The model consists of a system of nonlinear parabolic PDEs in conservation form expressing conservation of energy, mass and charge. On the other hand, an integral form of Newton's law is used to describe heat exchange at the electrolyte/electrode interface, a nonlinear radiation condition is enforced on the heat flux at the wall and a nonlinear boundary condition is considered for the electrochemical flux in order to account for Butler-Volmer kinetics. The main objective is the nonconstant character of each parameter, that is, the coefficients are assumed to be dependent on the spatial variable and the temperature. Making recourse of known estimates of solutions for some auxiliary elliptic and parabolic problems, which are explicitly determined by the Gehring-Giaquinta-Modica theory, we find sufficient smallness conditions on the data to guarantee the existence of the original solutions via the Schauder fixed point argument. These conditions may provide useful informations for numerical as well as real applications. We conclude with an example of application, namely the electrolysis of molten sodium chloride.

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“…In this section we provide a short description of the algorithm that is used to numerically solve system (1). We refer to [43] for more details on the stability and convergence analysis of the adopted methods as well as their implementation in the general-purpose C++ modular numerical code MP-FEMOS (Multi-Physics Finite Element Modeling Oriented Simulator) that has been developed by some of the authors [33,32,1].…”

Section: Time Advancing Functional Iteration and Numerical Discretiza...mentioning

confidence: 99%

Medical gallery of Blausen Medical 2014

2014

Wiki J Med

118

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Intraocular pressure, resulting from the balance of aqueous humor (AH) production and drainage, is the only approved treatable risk factor in glaucoma. AH production is determined by the concurrent function of ionic pumps and aquaporins in the ciliary processes but their individual contribution is difficult to characterize experimentally. In this work, we propose a novel unified modeling and computational framework for the finite element simulation of the role of the main ionic pumps involved in AH secretion, namely, the sodium-potassium pump, the calcium-sodium pump, the anion channel and the hydrogenate-sodium pump. The theoretical model is developed at the cellular scale and is based on the coupling between electrochemical and fluid-dynamical transmembrane mechanisms characterized by a novel description of the electric pressure exerted by the ions on the intrachannel fluid that includes electrochemical and osmotic corrections. Considering a realistic geometry of the ionic pumps, the proposed model is demonstrated to correctly predict their functionality as a function of (1) the permanent electric charge density over the channel pump surface; (2) the osmotic gradient coefficient; (3) the stoichiometric ratio between the ionic pump currents enforced at the inlet and outlet sections of the channel. In particular, theoretical predictions of the transepithelial membrane potential for each simulated pump/channel allow us to perform a first significant model comparison with experimental data for monkeys. This is a significant step for future multidisciplinary studies on the action of molecules on AH production.

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Electro-thermo-chemical computational models for 3D heterogeneous semiconductor device simulation

Cited by 20 publications

References 35 publications

A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces

A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces

Sufficient conditions for the existence of solutions for a thermoelectrochemical problem

Medical gallery of Blausen Medical 2014

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