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- ItemAnisotropy in wavelet based phase field models(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Korzec, Maciek; Münch, Andreas; Süli, Endre; Wagner, BarbaraAnisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature
- ItemPotentials of Gaussians and approximate wavelets(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Maz'ya, Vladimir; Schmidt, GuntherWe derive new formulas for harmonic, diffraction, elastic, and hydrodynamic potentials acting on anisotropic Gaussians and approximate wavelets. These formulas can be used to construct accurate cubature formulas for these potentials.