Modeling chatter in peripheral milling using the Semi Discretization Method
CIRP Journal of Manufacturing Science and Technology, 2012Abstract In this paper the Semi Discretization Method, SDM, is employed to model chatter in peripheral milling using cutters with helical teeth. The process damping is included in the model using the equivalent viscous damper approach. The development is demonstrated first in straight cutting of plain surfaces.
K. Ahmadi, F. Ismail
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Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model
Computational Methods in Applied Mathematics, 2017AbstractIn this paper, a semi-discrete Galerkin finite element method is applied to the two-dimensional diffusive Peterlin viscoelastic model which can describe the unsteady behavior of some incompressible ploymeric fluids. For the derived semi-discrete finite element spatial discretization scheme, the a priori bounds are given that does not rely on ...
Jiang, Yao-Lin, Yang, Yun-Bo
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Semi-discrete method for generalized Schrödinger-type equations
Mathematics and Computers in Simulation, 1997Abstract In this article, a semi-discrete method for solving a class of generalized Schrodinger-type equations is presented. By discretization of the spatial variables, the initial-boundary value problem for partial differential equations can be reduced to the initial value problem for ordinary differential systems.
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Band algorithm for unsymmetric matrices in finite element and semi‐discrete methods
International Journal for Numerical Methods in Engineering, 1982AbstractA compact FORTRAN subroutine for reducing unsymmetric band matrices (in‐core solution) is presented. As usual, the zeros inside the band are skipped during the Gauss elimination. However, the theme of the paper is centred on a new approach in applying the above‐mentioned band solver to transient problems.
Gopalakrishnan, T. C. +1 more
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Updated semi‐discretization method for periodic delay‐differential equations with discrete delay
International Journal for Numerical Methods in Engineering, 2004AbstractAn updated version of the semi‐discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined.
Insperger, Tamás, Stépán, Gábor
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Semi‐discretization method for the heat equation with non‐local boundary conditions
Communications in Numerical Methods in Engineering, 1994AbstractSemi‐discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute the spatial derivative by finite differences.
Araújo, A. L., Oliveira, F. Aleixo
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Numerical integration scheme–based semi-discretization methods for stability prediction in milling
The International Journal of Advanced Manufacturing Technology, 2021Chatter is not conducive to machining efficiency and surface quality. One of the essential types of chatter in the machining process is regenerative chatter. This study presents the numerical integration scheme–based semi-discretization methods (NISDMs) for milling stability prediction.
Changfu Zhang +2 more
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An extrapolated splitting method for solving semi-discretized parabolic differential equations
International Journal of Computer Mathematics, 2014An extrapolated Peaceman–Rachford–Strang splitting method is designed and examined in application to semi-discretized parabolic partial differential equations. A multi-product expansion method is implemented to improve the order of accuracy beyond second order in time.
Matthew Beauregard, Jürgen Geiser
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A discrete method for the initialization of semi-discrete optimal transport problem
Knowledge-Based Systems, 2021Abstract Semi-discrete optimal transport setting is a very important formulation in the computation of Wasserstein distance, as it is an approximation form of the continuous setting of optimal transport. However, initialization process of dual weight vector for the dual problem in this setting is required for the computation of the first and second ...
Judy Yangjun Lin +4 more
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The methods discussed so far have all been fully discrete methods, discretized in both space and time. At times it is useful to consider the discretization process in two stages, first discretizing only in space, leaving the problem continuous in time.
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