No abstract

The field perturbation induced by an elastic or electrical inclusion admits a multipole expansion in terms of the outgoing potential functions. In the classical expansion, basis functions are defined independently of the inclusion. In this paper, we introduce the new concept of the geometric multipole expansion for the two-dimensional conductivity problem (or, equivalently, anti-plane elasticity problem) of which basis functions are associated with the inclusion's geometry; the coefficients of the expansion are denoted by the Faber polynomial polarization tensor (FPT). In the derivation we use the series expansion for the complex logarithm by the Faber polynomials that are associated with the exterior conformal mapping of the inclusion. The virtue of the proposed expansion is that one can express the field perturbation in a simple series form for an inclusion of arbitrary shape. Regarding the computation of the exterior conformal mapping, one can use the integral formula for the conformal mapping coefficients obtained in [22]. As an application, we construct multi-coated neutral inclusions of general smooth shape that have negligible perturbation for low-order polynomial loadings. These neutral inclusions are layered structures composed of level curves of an exterior conformal mapping; material parameters in each layer are determined such that the FPTs vanish or are small for low-order terms. We provide numerical examples to validate the results.

We consider the conductivity problem with a simply connected or multi-coated inclusion in two dimensions. The potential perturbation due to an inclusion admits a classical multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). The GPTs have been fundamental building blocks in conductivity inclusion problems. In this paper, we present a new concept of geometric multipole expansion and its expansion coefficients, named the Faber polynomial polarization tensors (FPTs), using the conformal mapping and the Faber polynomials associated with the inclusion. The proposed expansion leads us to a series solution method for a simply connected or multi-coated inclusion of general shape, while the classical expansion leads us to a series solution only for a single- or multilayer circular inclusion. We also provide matrix expressions for the FPTs using the Grunsky matrix of the inclusion. In particular, for the simply connected inclusion with extreme conductivity, the FPTs admit simple formulas in terms of the conformal mapping associated with the inclusion. As an application of the concept of the FPTs, we construct semi-neutral inclusions of general shape that show relatively negligible field perturbations for low-order polynomial loadings. These inclusions are of the multilayer structure whose material parameters are determined such that some coefficients of geometric multipole expansion vanish.

No abstract

To increase the accuracy of photovoltaic (PV) power prediction, meteorological data measured at a plant’s target location are widely used. If observation data are missing, public data such as automated synoptic observing systems (ASOS) and automatic weather stations (AWS) operated by the government can be effectively utilized. However, if the public weather station is located far from the target location, uncertainty in the prediction is expected to increase owing to the difference in distance. To solve this problem, we propose a power output prediction process based on inverse distance weighting interpolation (IDW), a spatial statistical technique that can estimate the values of unsampled locations. By demonstrating the proposed process, we tried to improve the prediction of photovoltaic power in random locations without data. The forecasting accuracy depends on the power generation forecasting model and proven case, but when forecasting is based on IDW, it is up to 1.4 times more accurate than when using ASOS data. Therefore, if measured data at the target location are not available, it was confirmed that it is more advantageous to use data predicted by IDW as substitute data than public data such as ASOS.