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An extension ofA-stability to alternating direction implicit methods
BIT, 1979Completely implicit, noniterative, finite-difference schemes have recently been developed by several authors for nonlinear, multidimensional systems of hyperbolic and mixed hyperbolic-parabolic partial differential equations. The method of Douglas and Gunn or the method of approximate factorization can be used to reduce the computational problem to a ...
Warming, R. F., Beam, Richard M.
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Optimal Alternating Direction Implicit Preconditioners for Conjugate Gradient methods
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Apostolos Hadjidimos, M. Lapidakis
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Alternating Direction Implicit Methods
1962Publisher Summary Alternating direction implicit methods, or ADI methods as they are called for short, constitute powerful techniques for solving elliptic and parabolic partial difference equations. However, in contrast with systematic overrelaxation methods, their effectiveness is hard to explain rigorously with any generality.
Garrett Birkhoff +2 more
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EFFICIENT ABC FOR THE FREQUENCY DEPENDENT ALTERNATING DIRECTION-IMPLICIT FDTD METHOD
International Journal on Wireless & Optical Communications, 2007Ultra WideBand (UWB) signals have a high potential for a wide range of applications. The Finite-Difference Time-Domain (FDTD) method is widely used in the development of UWB technology but has still two main limitations. One is that material parameters are constant over the whole frequency range.
Arnaud Thiry +2 more
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Alternating direction implicit methods for the Navier-Stokes equations
AIAA Journal, 1992The ADI method is extended to solve the Navier-Stokes equations. Attention is focused on methods of adding the viscous contributions in a way that does not disturb the overall stability and efficiency of the implicit scheme. No attempt is made here to incorporate a turbulence model, so the discussion will be limited to laminar flows.
Tysinger, T. L., Caughey, D. A.
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Electrostatic Potential Distribution by Numerical Method Alternating Direction Implicit Method
2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), 2021Charge free electrostatic potential has been calculated from Laplace equation with specific boundaries. Laplace equation is second-order partial differential equation (PDE) widely useful in physics because its solutions occur in problems of electrical, magnetic, and gravitational potentials, of steady-state temperatures, of hydrodynamics and of stress ...
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Extrapolated alternating direction implicit iterative methods
BIT, 1970This paper describes a new generalised (extrapolated) A.D.I. method for the solution of Laplace's equation. This method uses (i) a fixed acceleration parameter and (ii) the set of acceleration parameters of Douglas. The theory is applied to the 2-dimensional case and optimum numerical results are obtained.
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Parallelization of Alternating Direction Implicit Methods for Three-Dimensional Domains
2003The method of domain decomposition using a three-dimensional analogue of the Peaceman-Rachford algorithm is considered. In the proposed method, solution of a three-dimensional boundary value problem is performed with the use of iterations, each including two half-steps: at the first step “two-dimensional” problems are solved by the classical Peaceman ...
Valeri P. Il'in +2 more
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Alternating-Direction Implicit Iterative Methods
2009In the previous chapter, we considered various block iterative methods, such as the line and 2-line successive overrelaxation iterative methods, which as pratical methods involved the direct (or implicit) solution of particular lower-order matrix equations.
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A new FDTD algorithm based on alternating-direction implicit method
IEEE Transactions on Microwave Theory and Techniques, 1999In 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 ...
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