Numerical simulations have been critical in the recent rapid developments of advanced accelerator concepts. Among the various available numerical techniques, the ParticleIn-Cell (PIC) approach is the method of choice for self-consistent simulations from first principles, and although the fundamentals of the PIC method were established decades ago, improvements or variations still continue to ar...

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials ar...

An implicit non-linear lower-upper symmetric Gauss-Seidel (LU-SGS) solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids. The non-linear LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with a LU decomposition approach. The large sparse Jacobian matrix is computed nu...

This paper presents a new dynamic classifier selection approach for hyperspectral image classification, in which both spatial and spectral information are used to determine a pixel’s label once the remaining classified pixels’ neighborhood meets the threshold. For volumetric texture feature extraction, a volumetric gray level co-occurrence matrix is used; for spectral feature extraction, a mini...

An implicit non-linear lower-upper symmetric Gauss-Seidel (LU-SGS) solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids. The non-linear LU-SGS solver is preconditioned by a block element matrix, and the system of equations is then solved with the LU decomposition approach. The large sparse Jacobian matrix is computed nu...

It is shown that a N ×N real symmetric [complex hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n) [ SU(m,n)], for any choice of partition N = m+n. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson’s theorem which states that if N is e...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...