Symmetric finite element computation of convection-diffusion equations on a URR machine
Tóm tắt
We approximate convection-diffusion equations with irrotational flows by a symmetric finite element formulation. Since very large real numbers appear in this formulation, we realize it on a URR (an internal representation method of real numbers) machine where practically no overflow/underflow occurs. Numerical results show that this formulation is applicable for sufficiently high Peclet number problems and is promising in terms of computation time and storage.
Tài liệu tham khảo
P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.
H. Fujimori, Y. Shinoda, K. Shimizu, M. Nakagawa and N. Takahashi, The comparison of floating point arithmetic methods realized on MC68000 — comparison of IEEE and Hamada methods — Proc. of 24th Nat. Conf. of Information Processing Soc., 1982, 935–936 (in Japanese).
H. Hamada, Data length independent real number representation based on double exponential cut. Trans. Inform. Process. Soc. Japan,22 (1981), 521–526 (in Japanese).
H. Hamada, A new real number representation and its operation. Proc. of the 8th Symp. on Computer Arithmetic, IEEE Computer Society Reprint, 1987, 153–157.
A. M. Il'in, Differencing scheme for a differential equation with a small parameter affecting the highest derivative. Math. Notes Acad. Sci. USSR,6 (1969), 596–602.
M. Tabata, Symmetric finite element approximation for convection-diffusion problems. Theoretical and Applied Mechanics, 33, Univ. Tokyo Press, 1985, 445–453.
M. Tabata, A numerical algorithm for an upwind-type finite element method using exponential functions. Theoretical and Applied Mechanics, 34, Univ. Tokyo Press, 1986, 371–376.
M. Tabata, A theoretical and computational study of upwind-type finite element methods. Patterns and Waves, (eds. T. Nishida, M. Mimura and H. Fujii), Kinokuniya/North-Holland, Tokyo, 1986, 319–356.