THE STABILITY AND CONVERGENCE OF THE FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION

In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.

Interference coupling analysis based on a hybrid method: application to a radio telescope system

Working in a way that passively receives electromagnetic radiation from a celestial body, a radio telescope can be easily disturbed by external radio frequency interference as well as electro- magnetic interference generated by electric and electronic components operating at the telescope site. A quantitative analysis of these interferences must be taken into account carefully for further electro- magnetic protection of the radio telescope. In this paper, based on electromagnetic topology theory, a hybrid method that combines the Baum-Liu-Tesche （BLT） equation and transfer function is proposed. In this method, the coupling path of the radio telescope is divided into strong coupling and weak cou- pling sub-paths, and the coupling intensity criterion is proposed by analyzing the conditions in which the BLT equation simplifies to a transfer function. According to the coupling intensity criterion, the topological model of a typical radio telescope system is established. The proposed method is used to solve the interference response of the radio telescope system by analyzing subsystems with different coupling modes separately and then integrating the responses of the subsystems as the response of the entire system. The validity of the proposed method is verified numerically. The results indicate that the proposed method, compared with the direct solving method, reduces the difficulty and improves the efficiency of interference prediction.

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.

Performance analysis of parallel gravitational N-body codes on large GPU clusters

We compare the performance of two very different parallel gravitational N-body codes for astrophysical simulations on large Graphics Processing Unit（GPU） clusters, both of which are pioneers in their own fields as well as on certain mutual scales- NBODY6＋＋ and Bonsai. We carry out benchmarks of the two codes by analyzing their performance, accuracy and efficiency through the modeling of structure decomposition and timing measurements. We find that both codes are heavily optimized to leverage the computational potential of GPUs as their performance has approached half of the maximum single precision performance of the underlying GPU cards. With such performance we predict that a speed-up of200- 300 can be achieved when up to 1k processors and GPUs are employed simultaneously. We discuss the quantitative information about comparisons of the two codes, finding that in the same cases Bonsai adopts larger time steps as well as larger relative energy errors than NBODY6＋＋, typically ranging from10- 50 times larger, depending on the chosen parameters of the codes. Although the two codes are built for different astrophysical applications, in specified conditions they may overlap in performance at certain physical scales, thus allowing the user to choose either one by fine-tuning parameters accordingly.