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Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems
Joint Authors
Xu, Zhiyu
Tan, Yonghua
Li, Xiaoming
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-03-09
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Adaptive wavelet collocation methods use wavelet transform and filtering to generate adaptive grids.
However, if the boundary moves, the grid becomes aberrant.
It baffles wavelet transform and makes the adaptive wavelet methods lose advantages on computational efficiency.
This paper develops a series of methods or skills to effectively perform wavelet transform and to generate adaptive grids for one-dimensional movable boundary problems.
The methods remain the original inner grid points and keep the grid in the original-nested structure, in order to remain scanty during the whole computing process.
For boundary extending, the adaptive wavelet program begins to run on the very new grid beyond the original boundary once it reaches a nested structure, which is called the Intermittent Adaptive Method as a consequence.
If the boundary extends tremendously, the new nested grids can be combined to a greater nested grid for further efficiency, which is named the Grid Combine Method.
While for boundary contracting, a fictitious boundary is addressed to replace the original boundary that will recede, so wavelet transform can be successfully performed on the original nested grid.
Finally, two numerical tests, local features moving and gas gun, were resolved and discussed to show the evolution process of the adaptive grids with the boundaries moving.
For boundary contracting, the valid points decrease because the computation domain recedes; while for boundary extending, the valid point numbers vary between a range that almost remains unchanged.
American Psychological Association (APA)
Xu, Zhiyu& Tan, Yonghua& Li, Xiaoming. 2020. Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1193926
Modern Language Association (MLA)
Xu, Zhiyu…[et al.]. Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems. Mathematical Problems in Engineering No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1193926
American Medical Association (AMA)
Xu, Zhiyu& Tan, Yonghua& Li, Xiaoming. Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1193926
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193926