Rotational quotient procedure: A tracking control continuation method for PDEs on radially symmetric domains

Yueh Cheng Kuo; Shih Feng Shieh; Weichung Wang

doi:10.1016/j.cpc.2012.01.008

Rotational quotient procedure: A tracking control continuation method for PDEs on radially symmetric domains

Yueh Cheng Kuo
, Shih Feng Shieh
, Weichung Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.

Original language	English
Pages (from-to)	998-1001
Number of pages	4
Journal	Computer Physics Communications
Volume	183
Issue number	4
DOIs	https://doi.org/10.1016/j.cpc.2012.01.008
Publication status	Published - 2012 Apr

Keywords

Continuation methods
Radially symmetric domain
Rotation invariant solutions

ASJC Scopus subject areas

Hardware and Architecture
General Physics and Astronomy

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10.1016/j.cpc.2012.01.008

Cite this

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title = "Rotational quotient procedure: A tracking control continuation method for PDEs on radially symmetric domains",

abstract = "Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schr{\"o}dinger equation on a disk domain to demonstrate the functionality of the proposed method.",

keywords = "Continuation methods, Radially symmetric domain, Rotation invariant solutions",

author = "Kuo, \{Yueh Cheng\} and Shieh, \{Shih Feng\} and Weichung Wang",

note = "Funding Information: The authors are grateful to the anonymous referees for their comments and suggestions. This work is partially supported by the National Science Council , the National Center for Theoretical Sciences , and the Taida Institute of Mathematical Sciences in Taiwan .",

year = "2012",

month = apr,

doi = "10.1016/j.cpc.2012.01.008",

language = "English",

volume = "183",

pages = "998--1001",

journal = "Computer Physics Communications",

issn = "0010-4655",

publisher = "Elsevier BV",

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TY - JOUR

T1 - Rotational quotient procedure

T2 - A tracking control continuation method for PDEs on radially symmetric domains

AU - Kuo, Yueh Cheng

AU - Shieh, Shih Feng

AU - Wang, Weichung

N1 - Funding Information: The authors are grateful to the anonymous referees for their comments and suggestions. This work is partially supported by the National Science Council , the National Center for Theoretical Sciences , and the Taida Institute of Mathematical Sciences in Taiwan .

PY - 2012/4

Y1 - 2012/4

N2 - Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.

AB - Continuation methods are capable of finding multiform solutions by tracking solution curves. However, these methods may fail to track some desired solution curves due to the interference of the rotational equivalent solutions on a radially symmetric domain. We propose a rotational quotient procedure that applies extra constraints to standard continuation which overcomes this difficulty. We solve a time-independent nonlinear Schrödinger equation on a disk domain to demonstrate the functionality of the proposed method.

KW - Continuation methods

KW - Radially symmetric domain

KW - Rotation invariant solutions

UR - https://www.scopus.com/pages/publications/84862814791

UR - https://www.scopus.com/pages/publications/84862814791#tab=citedBy

U2 - 10.1016/j.cpc.2012.01.008

DO - 10.1016/j.cpc.2012.01.008

M3 - Article

AN - SCOPUS:84862814791

SN - 0010-4655

VL - 183

SP - 998

EP - 1001

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 4

ER -

Rotational quotient procedure: A tracking control continuation method for PDEs on radially symmetric domains

Abstract

Keywords

ASJC Scopus subject areas

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