Topic
Alternating direction implicit method
About: Alternating direction implicit method is a research topic. Over the lifetime, 2327 publications have been published within this topic receiving 46616 citations.
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3,125 citations
01 Sep 1976
TL;DR: In this article, an implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation law form, which is second-order time-accurate, noniterative, and in a spatially factored form.
Abstract: Abstract An implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation law form. The algorithm is second-order time-accurate, noniterative, and in a spatially factored form. Second- or fourth-order central and second-order one-sided spatial differencing are accommodated within the solution of a block tridiagonal system of equations. Significant conceptual and computational simplifications are made for systems whose flux vectors are homogeneous functions (of degree one), e.g., the Eulerian gasdynamic equations. Conservative hybrid schemes, which switch from central to one-sided spatial differencing whenever the local characteristic speeds are of the same sign, are constructed to improve the resolution of weak solutions. Numerical solutions are presented for a nonlinear scalar model equation and the two-dimensional Eulerian gasdynamic equations.
1,050 citations
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TL;DR: In this article, an implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation-law form, which is second-order time-accurate, noniterative, and in a spatially factored form.
1,036 citations
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TL;DR: In this article, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint.
Abstract: In this paper, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on an alternating-direction implicit method. It is shown that the new algorithm is quite stable both analytically and numerically even when the CFL condition is not satisfied. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than conventional FDTD schemes in terms of computer resources such as central-processing-unit time. Numerical formulations are presented and simulation results are compared to those using the conventional FDTD method.
926 citations
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TL;DR: A new iterative method for the solution of systems of linear equations has been recently proposed by Meijerink and van der Vorst and has been applied to real laser fusion problems taken from typical runs of the laser fusion simulation code LASNEX.
908 citations