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Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in detail, from which the analysis on the triangle is deduced. The results include cubature formulas and interpolation on(More)
Developing highly scalable algorithms for global atmospheric modeling is becoming increasingly important as scientists inquire to understand behaviors of the global atmosphere at extreme scales. Nowadays, heterogeneous architecture based on both processors and accelerators is becoming an important solution for large-scale computing. However, large-scale(More)
We study a parallel Newton-Krylov-Schwarz (NKS) based algorithm for solving large sparse systems resulting from a fully implicit discretiza-tion of partial differential equations arising from petroleum reservoir simulations. Our NKS algorithm is designed by combining an inexact Newton method with a rank-2 updated quasi-Newton method. In order to improve the(More)
The discrete Fourier analysis on the 30 0 –60 0 –90 0 triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G 2 , which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm–Liouville eigenvalue problem that contains(More)
We present our early performance evaluation results with the NPB benchmark and two scientific computing applications program, i.e., a HFFT package developed by our lab and a CFDO application software, on two 100Teraflops-scale Dawning 5000A and DeepComp 7000. We compared the NPB performance evaluation results of Dawning 5000A and DeepComp 7000, with their(More)