A hybrid improved complex variable element-free Galerkin method for three-dimensional advection-diffusion problems
In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin method, a hybrid improved complex variable element-free Galerkin (H-ICVEFG) method is presented for three-dimensional advection-diffusion problems. Using the dimension splitting method, a...
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| Published in | Engineering analysis with boundary elements Vol. 97; pp. 39 - 54 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.12.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0955-7997 1873-197X |
| DOI | 10.1016/j.enganabound.2018.09.007 |
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| Abstract | In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin method, a hybrid improved complex variable element-free Galerkin (H-ICVEFG) method is presented for three-dimensional advection-diffusion problems. Using the dimension splitting method, a three-dimensional advection-diffusion problem is transformed into a series of two-dimensional ones which can be solved with the improved complex variable element-free Galerkin (ICVEFG) method. In the ICVEFG method, the improved complex variable moving least-squares (ICVMLS) approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions. Finite difference method is used in the one-dimensional direction. And Galerkin weak form of three-dimensional advection-diffusion problems is used to obtain the final discretized equations. Then the H-ICVEFG method for three-dimensional advection-diffusion problems is presented. Numerical examples are provided to discuss the influences of the weight functions, the effects of the scale parameter, the penalty factor, the number of nodes, the step number and the time step on the numerical solutions. And the advantages of the H-ICVEFG method with higher computational accuracy and efficiency are shown. |
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| AbstractList | In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin method, a hybrid improved complex variable element-free Galerkin (H-ICVEFG) method is presented for three-dimensional advection-diffusion problems. Using the dimension splitting method, a three-dimensional advection-diffusion problem is transformed into a series of two-dimensional ones which can be solved with the improved complex variable element-free Galerkin (ICVEFG) method. In the ICVEFG method, the improved complex variable moving least-squares (ICVMLS) approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions. Finite difference method is used in the one-dimensional direction. And Galerkin weak form of three-dimensional advection-diffusion problems is used to obtain the final discretized equations. Then the H-ICVEFG method for three-dimensional advection-diffusion problems is presented. Numerical examples are provided to discuss the influences of the weight functions, the effects of the scale parameter, the penalty factor, the number of nodes, the step number and the time step on the numerical solutions. And the advantages of the H-ICVEFG method with higher computational accuracy and efficiency are shown. |
| Author | Peng, M.J. Cheng, H. Cheng, Y.M. |
| Author_xml | – sequence: 1 givenname: H. surname: Cheng fullname: Cheng, H. organization: Department of Civil Engineering, Shanghai University, Shanghai 200444, China – sequence: 2 givenname: M.J. surname: Peng fullname: Peng, M.J. organization: Department of Civil Engineering, Shanghai University, Shanghai 200444, China – sequence: 3 givenname: Y.M. surname: Cheng fullname: Cheng, Y.M. email: ymcheng@shu.edu.cn organization: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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| Keywords | Advection-diffusion problem Improved complex variable element-free Galerkin method Dimension splitting method Improved complex variable moving least-squares approximation Finite difference method Hybrid improved complex variable element-free Galerkin method |
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| SubjectTerms | Advection-diffusion problem Dimension splitting method Finite difference method Hybrid improved complex variable element-free Galerkin method Improved complex variable element-free Galerkin method Improved complex variable moving least-squares approximation |
| Title | A hybrid improved complex variable element-free Galerkin method for three-dimensional advection-diffusion problems |
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