Download Acta Numerica 1999 (Volume 8) by Arieh Iserles PDF

By Arieh Iserles

Numerical research, the main zone of utilized arithmetic excited about utilizing pcs in comparing or approximating mathematical types, is essential to all purposes of arithmetic in technological know-how and engineering. Acta Numerica each year surveys crucial advancements in numerical research and clinical computing. The substantive survey articles, selected through a wonderful overseas editorial board, file at the most vital and well timed advances in a fashion available to the broader group of execs drawn to clinical computing.

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Rev. Lett. 76, 4667-4670. A. P. Gentle and W. A. Miller (1998), 'A fully (3+l)-d Regge calculus model of the Kasner cosmology', Class. Quantum Gravit. 15, 389-405. C. Gundlach (1998a), 'Critical phenomena in gravitational collapse', Adv. Theor. Math. Phys. 2, 1-49. C. Gundlach (19986), 'Pseudo-spectral apparent horizon finders: An efficient new algorithm', Phys. Rev. D 57, 863-875. S. W. Hawking and G. F. R. Ellis (1973), The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge, England.

Rev. 48, 73-77. C. R. Evans (1984), 'A method for numerical relativity: Simulation of axisymmetric gravitational collapse and gravitational radiation generation', PhD thesis, University of Texas at Austin. A. E. Fischer and J. E. Marsden (1972), 'The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system, F, Commun. Math. Phys. 28, 1-38. Y. Foures-Bruhat (1952), 'Theorem d'existence pour certain systems d'equations aux derivees partielles non lineaires', Ada. Math.

1995a) and Briigmann (1996). Tests of a more general 3-dimensional implementation of apparent horizon boundary conditions were reported in Cook et al. (1998). The details of this scheme were reported in Scheel, Baumgarte, Cook, Shapiro and Teukolsky (1997). For concreteness, we will describe the NUMERICAL RELATIVITY 31 apparent horizon boundary condition scheme used in Cook et al. 6 The key feature of the causal differencing scheme described in Cook et al. (1998) is that it accommodates excised regions that move through the computational grid.

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