An analysis of HDG methods for convection-dominated diffusion problems

Fu, Guosheng; Qiu, Weifeng; Zhang, Wujun

doi:10.1051/m2an/2014032

Cited by 61 publications

(71 citation statements)

References 41 publications

(88 reference statements)

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“…These boundary conditions were derived after assuming the region L w < z < L d to be uncharged and at local quasi-thermal equilibrium [18]; furthermore, a bias voltage V ext was applied at the plane z = L d . Solution of this system of equations was undertaken using the HDG scheme [46,25,45], in which all the z-dependent variables have to be discretized using discontinuous finite elements in a space of piecewise polynomials of a fixed degree. The full discretized system was solved for n(z), p(z), and φ(z), using the Newton-Raphson method [43].…”

Section: Electrical Theorymentioning

confidence: 99%

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading

et al. 2019

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The power conversion efficiency of an ultrathin CuIn 1−ξ Ga ξ Se2 (CIGS) solar cell was maximized using a coupled optoelectronic model to determine the optimal bandgap grading of the nonhomogeneous CIGS layer in the thickness direction. The bandgap of the CIGS layer was either sinusoidally or linearly graded, and the solar cell was modeled to have a metallic backreflector corrugated periodically along a fixed direction in the plane. The model predicts that specially tailored bandgap grading can significantly improve the efficiency, with much smaller improvements due to the periodic corrugations. An efficiency of 27.7% with the conventional 2200-nm-thick CIGS layer is predicted with sinusoidal bandgap grading, in comparison to 22% efficiency obtained experimentally with homogeneous bandgap. Furthermore, the inclusion of sinusoidal grading increases the predicted efficiency to 22.89% with just a 600-nm-thick CIGS layer. These high efficiencies arise due to a large electron-hole-pair generation rate in the narrow-bandgap regions and the elevation of the open-circuit voltage due to a wider bandgap in the region toward the front surface of the CIGS layer. Thus, bandgap nonhomogeneity, in conjunction with periodic corrugation of the backreflector, can be effective in realizing ultrathin CIGS solar cells that can help overcome the scarcity of indium.

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Section: Electrical Theorymentioning

confidence: 99%

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading

et al. 2019

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“…The nonlinear Shockley-Read-Hall, Auger, and radiative terms are included to model electron-hole recombination [1,2]. A hybridizable discontinuous Galerkin (HDG) method [10,11,12,13] is developed, and the Newton-Raphson method [14] is used to find a solution of the resulting nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

Coupled optoelectronic simulation and optimization of thin-film photovoltaic solar cells

Anderson

Civiletti

Monk

et al. 2020

Journal of Computational Physics

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A design tool was formulated for optimizing the efficiency of inorganic, thin-film, photovoltaic solar cells. The solar cell can have multiple semiconductor layers in addition to antireflection coatings, passivation layers, and buffer layers. The solar cell is backed by a metallic grating which is periodic along a fixed direction. The rigorous coupled-wave approach is used to calculate the electron-hole-pair generation rate. The hybridizable discontinuous Galerkin method is used to solve the drift-diffusion equations that govern charge-carrier transport in the semiconductor layers. The chief output is the solar-cell efficiency which is maximized using the differential evolution algorithm to determine the optimal dimensions and bandgaps of the semiconductor layers.

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“…By a similar argument used in this paper, we can show that the HDG method for the convection dominated diffusion equation (1.5) is well defined for any > 0. Under the same assumption of β in [10], it can be shown that u h − u ≤ Ch k+1/2 u k+2, , where the constant C is independent of .…”

Section: Introductionmentioning

confidence: 98%

“…Namely, we can decompose the stabilization function used in the numerical flux (1.3e) into diffusion τ D h K (P M u h − u h ) and convection τ C (u h − u h ) parts. In particular, we adapt the technique used in the elasticity problem in [13] and the standard up-winding scheme similar to that in [4,[9][10][11] in the diffusion and convection parts, respectively. It is also worth to mention that we can choose τ C to be any function which satisfies τ C ≥ 1 2 β · n. With the new design of numerical flux (1.3e), we show that the global L 2 -norm of the error of u converges with order k + 2 while that of q converges with order k + 1.…”

Section: Introductionmentioning

confidence: 99%

An HDG Method for Convection Diffusion Equation

Qiu

Shi

2015

J Sci Comput

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We present a new hybridizable discontinuous Galerkin (HDG) method for the convection diffusion problem on general polyhedral meshes. This new HDG method is a generalization of HDG methods for linear elasticity introduced in Qiu and Shi (2013) to problems with convection term. For arbitrary polyhedral elements, we use polynomials of degree k + 1 and k ≥ 0 to approximate the scalar variable and its gradient, respectively. In contrast, we only use polynomials of degree k to approximate the numerical trace of the scalar variable on the faces which allows for a very efficient implementation of the method, since the numerical trace of the scalar variable is the only globally coupled unknown. The global L 2 -norm of the error of the scalar variable converges with the order of k + 2 while that of its gradient converges with order k + 1. From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this method achieves superconvergence for the scalar variable without postprocessing. A key inequality relevant to the discrete Poincaré inequality is a novel theoretical contribution. This inequality is useful to deal with convection term in this paper and is essential to error analysis of HDG methods for the Navier-Stokes equations and other nonlinear problems.

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An analysis of HDG methods for convection-dominated diffusion problems

Cited by 61 publications

References 41 publications

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading

Coupled optoelectronic simulation and optimization of thin-film photovoltaic solar cells

An HDG Method for Convection Diffusion Equation

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