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Volume 11, Issue 2
Modified Moving Least Square Collocation Method for Solving Wave Equations

Zhentian Huang, Dong Lei & Yuan Wang

Adv. Appl. Math. Mech., 11 (2019), pp. 518-534.

Published online: 2019-01

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  • Abstract

This paper presents a modified moving least square (MMLS) collocation method for solving wave equations. In contrast to the conventional moving least square (CMLS) method, this method modifies how discretization of computational points is done and decreases the number of base functions to simplify shape functions while solving high-dimensional problems. In addition, the proposed method maintains the independence of discretization for different dimensions, which is convenient to deal with computational domains in a simple manner while retaining a local character. The above improvement results in this approximation significantly saving calculation time while preserving accuracy of the solution. The numerical simulations show that MMLS collocation method has good stability and accuracy in analyzing high-dimensional wave propagation.

  • Keywords

MMLS collocation method, wave propagation, base function.

  • AMS Subject Headings

65N80, 65N35, 65N38, 86-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-518, author = {Huang , ZhentianLei , Dong and Wang , Yuan}, title = {Modified Moving Least Square Collocation Method for Solving Wave Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {518--534}, abstract = {

This paper presents a modified moving least square (MMLS) collocation method for solving wave equations. In contrast to the conventional moving least square (CMLS) method, this method modifies how discretization of computational points is done and decreases the number of base functions to simplify shape functions while solving high-dimensional problems. In addition, the proposed method maintains the independence of discretization for different dimensions, which is convenient to deal with computational domains in a simple manner while retaining a local character. The above improvement results in this approximation significantly saving calculation time while preserving accuracy of the solution. The numerical simulations show that MMLS collocation method has good stability and accuracy in analyzing high-dimensional wave propagation.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0029}, url = {http://global-sci.org/intro/article_detail/aamm/12975.html} }
TY - JOUR T1 - Modified Moving Least Square Collocation Method for Solving Wave Equations AU - Huang , Zhentian AU - Lei , Dong AU - Wang , Yuan JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 518 EP - 534 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0029 UR - https://global-sci.org/intro/article_detail/aamm/12975.html KW - MMLS collocation method, wave propagation, base function. AB -

This paper presents a modified moving least square (MMLS) collocation method for solving wave equations. In contrast to the conventional moving least square (CMLS) method, this method modifies how discretization of computational points is done and decreases the number of base functions to simplify shape functions while solving high-dimensional problems. In addition, the proposed method maintains the independence of discretization for different dimensions, which is convenient to deal with computational domains in a simple manner while retaining a local character. The above improvement results in this approximation significantly saving calculation time while preserving accuracy of the solution. The numerical simulations show that MMLS collocation method has good stability and accuracy in analyzing high-dimensional wave propagation.

Zhentian Huang, Dong Lei & Yuan Wang. (2020). Modified Moving Least Square Collocation Method for Solving Wave Equations. Advances in Applied Mathematics and Mechanics. 11 (2). 518-534. doi:10.4208/aamm.OA-2018-0029
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