This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient metho...

We have developed a Bayesian model to invert spectral induced-polarization SIP data for Cole-Cole parameters using Markov-chain Monte Carlo MCMC sampling methods. We compared the performance of the MCMC-based stochastic method with an iterative Gauss-Newton-based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton-base...

A novel spectral method with variable transformation, the adaptive Hermite-Gauss decomposition method (A-HGDM), has been developed and applied to the analysis of three-dimensional (3D) dielectric structures. The proposed method includes an optimization strategy to automatically find the quasi-optimum numerical parameters of the variable transformation with low computational effort. The techniqu...

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Se...

A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss– Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are ...

An efficient algorithm for the accurate computation of Gauss–Legendre and Gauss– Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton’s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100.

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical ex...

We study a class of time–domain decomposition based methods for the solution of distributed linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the distributed linear quadratic optimal control problem as a discrete–time optimal control (DTOC) problem in Hilbert space. The optimality conditions for this DTOC problem lead to a linear system wit...

The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, to viscous flows. The high-order spectral diffe...

We present new algorithms for the solution of large structured Markov models whose innnitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuue-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-style m...