spectrum to a desired color by the use of different photoactive materials. [2][3][4][5][6] These characteristics enable the production of power generating smart windows, awnings, building facades etc. [7][8][9] Still, semitransparent solar cells show lower effi ciencies than their opaque counterparts due to the inherent tradeoff between transmission and absorption. To overcome this problem different light trapping approaches such as microcavities, dielectric scatters, microlenses, and wavelength selective mirrors have been investigated. [10][11][12][13][14][15][16][17][18][19] Particularly the last approach allows to precisely adjust the transparency as well as the color of a device. Wavelength selective fi lters are also known as 1D photonic crystals, Bragg mirrors or dielectric mirrors (DMs). The working principle of DMs relies on constructive or destructive interference of thin layers. For this purpose, a high refractive index (HRI) and a low refractive index (LRI) material have to be arranged alternatingly and fulfi ll the equation 4 HRI HRI LRI LRI 0 n d n d λ = = , with n being the refractive index (RI), d being the layer thickness, and λ 0 being the wavelength with maximum refl ection at perpendicular incidence. An high RI contrast is desirable as this leads to a broad stopband with a large refl ection at λ 0 . [ 20 ] The production of a DM, however, is challenging as only slight variations in layer thicknesses cause a shift in λ 0 (see Figure S1, Supporting Information). Conventional techniques for DM fabrication are evaporation of inorganic materials under high vacuum conditions, electron beam evaporation, and magnetron sputtering. [ 15,16,[21][22][23] However, polymers or organic-inorganic nanocomposites are much more promising because they allow a controlled variation of n , better processability, and highly fl exible fi lms. [24][25][26] Methods such as spin coating or dip coating can be carried out with these ink-based materials. [ 17,24,[27][28][29][30] However, while these techniques allow precise settings in layer thickness, they only offer limited potential with respect to commercial and largearea processing as they are cost-intensive and diffi cult in terms of upscaling. In addition, DMs directly processed on the top of solar cells further complicate the whole device structure. For example, up to 16 additional layers are necessary to increase the short-circuit current ( J sc ) by ≈20% compared to a device without DM. [ 31 ] Building integrated semitransparent thin-fi lm solar cells is a strategy for future eco-friendly power generation. Organic photovoltaics in combination with dielectric mirrors (DMs) are a potential candidate as they promise high effi ciencies in parallel to the possibility to adjust the color and thus the transparency of the whole device. A fully solution processed and printable DM with an easily adjustable refl ection maximum is presented that can be facilely attached to solar cells. The DM is optimized via optical simulations to the particular needs of the device with regar...

The combination technique is a method to reduce the computational time in the numerical approximation of partial differential equations. In this paper, we present a new technique to analyze the convergence rate of the combination technique. This technique is applied to general second order elliptic differential equations in two dimensions. Furthermore, it is proved that the combination technique for Poisson's equation convergences in arbitrary dimensions.

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A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles in x -and y-direction. A suitable discretization provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order O(1) for the multilevel algorithm.