Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new algorithmic process to do this. The construction of invariant schemes consists in parametrizing the sc...

and Applied Analysis 3 on the whole space H, is a bounded operator. Here, I is the identity operator. The following operators D ( I τA τA 2 2 ) , G ( I − τ 2A 2 ) , P ( I τ 2 A ) , R I τB −1, Tτ ( I B−1A ( I τA τ 2 P−2 ) K ( I − R2N−1 ) GKP−2R2N−1 −GKP−2 2I τB R [ n ∑ i 1 αi ( I ( λi − [ λi τ ] τ ) A ) D − λi/τ u0 ])−1

For optical waveguides with high index-contrast and sharp corners, existing full-vectorial mode solvers including those based on boundary integral equations typically have only second or third order of accuracy. In this paper, a new full-vectorial waveguide mode solver is developed based on a new formulation of boundary integral equations and the so-called Neumann-to-Dirichlet operators for sub...

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed. The data structure, the directional refinement and coarsening, including the method for initializing the refined new cells, for the anisotropic adaptive method are described. It provides efficient high resolution of flow features, which are aligned with the original qu...