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International Journal of Applied Mechanics, 2021
This paper proposes the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on the nonsingular weight function for three-dimensional (3D) potential problems. The core of the IIDSEFG method is to transform the 3D problem domain into a series of two-dimensional (2D) problem subdomains along the splitting direction ...
Zhijuan Meng +3 more
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This paper proposes the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on the nonsingular weight function for three-dimensional (3D) potential problems. The core of the IIDSEFG method is to transform the 3D problem domain into a series of two-dimensional (2D) problem subdomains along the splitting direction ...
Zhijuan Meng +3 more
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The Dimension Splitting Interpolating Element-Free Galerkin Method for Solving 3D Wave Equations
International Journal of Applied Mechanics, 2022Based on the idea of dimension splitting method, a dimension splitting interpolating element-free Galerkin (DSIEFG) method for 3D wave propagation problems is proposed. In the splitting direction, the 3D domain of a problem is divided into a series of related 2D subdomains. Using the improved interpolating moving least-squares (IMLS) method to acquire
Shihan Wang, Miaojuan Peng
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Dimension splitting method for the three dimensional rotating Navier-Stokes equations
Acta Mathematicae Applicatae Sinica, English Series, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Kai-tai +3 more
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Engineering Analysis With Boundary Elements, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yumin Cheng
exaly +3 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yumin Cheng
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The dimension splitting element-free Galerkin method for 3D transient heat conduction problems
Science China: Physics, Mechanics and Astronomy, 2018By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin (DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin (IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction ...
Zhijuan Meng, Heng Cheng, Yumin Cheng
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The Journal of the Acoustical Society of America, 2023
The parabolic-equation (PE) method is a popular technique in underwater acoustics for obtaining 2D and 3D acoustic-field predictions in spatially-dependent environments. Tangent linear models for these PE solutions relate perturbations in the environmental properties (inputs) to corresponding changes in the acoustic field-solutions (outputs), enabling ...
Brandon M. Lee, David R. Dowling
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The parabolic-equation (PE) method is a popular technique in underwater acoustics for obtaining 2D and 3D acoustic-field predictions in spatially-dependent environments. Tangent linear models for these PE solutions relate perturbations in the environmental properties (inputs) to corresponding changes in the acoustic field-solutions (outputs), enabling ...
Brandon M. Lee, David R. Dowling
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IMA Journal of Numerical Analysis, 2014
Splitting methods constitute a well-established class of numerical schemes for the solution of evolution equations. Their efficient application, however, requires spatial smoothness of the underlying exact solution. If smoothness is lacking, the methods usually react with order reduction.
Tobias Hell +2 more
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Splitting methods constitute a well-established class of numerical schemes for the solution of evolution equations. Their efficient application, however, requires spatial smoothness of the underlying exact solution. If smoothness is lacking, the methods usually react with order reduction.
Tobias Hell +2 more
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International Journal for Numerical Methods in Engineering, 2018
SummaryIn this paper, by combining the dimension splitting method and the improved complex variable element‐free Galerkin method, the dimension splitting and improved complex variable element‐free Galerkin (DS‐ICVEFG) method is presented for 3‐dimensional (3D) transient heat conduction problems. Using the dimension splitting method, a 3D transient heat
Yumin Cheng
exaly +3 more sources
SummaryIn this paper, by combining the dimension splitting method and the improved complex variable element‐free Galerkin method, the dimension splitting and improved complex variable element‐free Galerkin (DS‐ICVEFG) method is presented for 3‐dimensional (3D) transient heat conduction problems. Using the dimension splitting method, a 3D transient heat
Yumin Cheng
exaly +3 more sources
The dimension split element-free Galerkin method for three-dimensional potential problems
Acta Mechanica Sinica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Meng, Z. J. +3 more
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State-space-split method for some generalized Fokker-Planck-Kolmogorov equations in high dimensions
Physical Review E, 2012The state-space-split method for solving the Fokker-Planck-Kolmogorov equations in high dimensions is extended to solving the generalized Fokker-Planck-Kolmogorov equations in high dimensions for stochastic dynamical systems with a polynomial type of nonlinearity and excited by Poissonian white noise.
Guo-Kang, Er, Vai Pan, Iu
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