Peizhu Ding

A linear spline approximation for radiative transfer problems in slab medium

Abstract A spline approximation algorithm is adopted to solve radiative transfer problems in a slab medium with an amsotropic scattering. By using the algorithm, the radiative transfer problem is separated into a system of linear algebraic equations and the matrix of coefficients of the system is a band matrix. So the algorithm is very simple to evaluate on a computer and very easy to master for experimentalists. An example is evaluated and it is shown that the algorithm is precise and effective.

A spline approximation of the Abel transformation for use in optically-thick, cylindrically-symmetric plasmas☆

Abstract A spline approximation to obtain the radial emission coefficient for optically-thick, cylindrically-symmetric plasmas is proposed and an explicit formula to evaluate the values of the coefficient at nodes is deduced. Using the formula, the work to find approximate values of the coefficient is simplified very much. An example is evaluated using present spline approximation. It is shown that the spline approximation is precise and much easier to apply than both the Youngs iteration and the block-bi-quadratic interpolation.

The Symplectic Algorithm for Use in A Model of Laser Field

Using the asymptotic boundary condition the time‐dependent Schrodinger equations with initial conditions in the infinite space can be transformed into the problem with initial and boundary conditions, and it can further be discrected into the inhomogeneous canonic equations. The symplectic algorithms to solve the inhomogeneous canonic equations have been developed and adopted to compute the high‐order harmonics of one‐dimensional Hydrogen in the laser field. We noticed that there is saturation intensity for generating high‐order harmonics, which are agree with previous results, and there is a relationship between harmonics and bound state probabilities.

An improved block-bi-quadric interpolation of the abel transformation for use in optically-thick, cylindrically-symmetric plasmas☆

Abstract An improved block-bi-quadric interpolation (BBQI) to obtain the radial emission coefficient for optically-thick, cylindrically-symmetric plasmas is proposed and an example is evaluated using our improved BBQI. It is shown that the BBQI is improved greatly: the relative errors at the nodes near the centre are decreased about 5 ~ 50 times and the advantage of the BBQI is preserved.

Gauss numerical inversion for use in computing the radiation field from a cylindrically symmetric radiation source

Abstract Abel inversion of a cylindrically symmetric radiation source involves the solution of the generalized Abel equations. In this paper, by using the Gauss numerical integral (GNI), the Abel equation can be separated into a system of linear algebraic equations, whose coefficient matrix is an upper triangle matrix and can be easily solved explicitly. Its numerical solution can achieve second-order accuracy. Three examples are evaluated using the present GNI. It is shown that the high accuracy is achieved and the computed values converge to the exact solutions with an increase in the number of nodes. This method is simple and requires less computer time, thus the experimenters can apply this method easily.