We introduce a novel spectral element method based on the ultraspherical and hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations polygonal domains with unstructured quadrilateral or triangular meshes. Properties of lead to almost banded systems, allowing be competitive in high-polynomial regime ($p > 5$). The enables precomputed solution opera...

We study effects of finite height and surrounding material on photonic crystal slabs of oneand two-dimensional photonic crystals with a pseudo-spectral method and finite difference time domain simulation methods. The band gap is shown to be strongly modified by the boundary material. As an application we suggest reflection and guiding of light by patterning the material on top/below the slab.

We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomia...

introduction in recent decades, a large variety of science experts, including geology and mine scientists, have considered remote sensing technology as one of the most important instruments to receive information. access to hyper spectral data is one of the main evolutions in the remote sensing technology. the main feature of the technology is its application in identification of minerals and d...