@Article{CiCP-24-1,
author = {},
title = {Efficient Mapping of High Order Basis Sets for Unbounded Domains},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {1},
pages = {69--85},
abstract = {<p style="text-align: justify;">Many physical problems involve unbounded domains where the physical
quantities vanish at infinities. Numerically, this has been handled using different techniques
such as domain truncation, approximations using infinitely extended and vanishing
basis sets, and mapping bounded basis sets using some coordinate transformations.
Each technique has its own advantages and disadvantages. Yet, approximating
simultaneously and efficiently a wide range of decaying rates has persisted as major
challenge. Also, coordinate transformation, if not carefully implemented, can result in
non-orthogonal mapped basis sets. In this work, we revisited this issue with an emphasize
on designing appropriate transformations using sine series as basis set. The
transformations maintain both the orthogonality and the efficiency. Furthermore, using
simple basis set (sine function) help avoid the expensive numerical integrations. In
the calculations, four types of physically recurring decaying behaviors are considered,
which are: non-oscillating and oscillating exponential decays, and non-oscillating and
oscillating algebraic decays. The results and the analyses show that properly designed
high-order mapped basis sets can be efficient tools to handle challenging physical
problems on unbounded domains. Decay rate ranges as large of 6 orders of magnitudes
can be approximated efficiently and concurrently.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0067},
url = {https://global-sci.com/article/79938/efficient-mapping-of-high-order-basis-sets-for-unbounded-domains}
}