The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes
Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-bel...
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| Autor*in: |
Yang, Junxiang [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature B.V. 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of engineering mathematics - Springer Netherlands, 1967, 129(2021), 1 vom: Aug. |
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volume:129 ; year:2021 ; number:1 ; month:08 |
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| DOI / URN: |
10.1007/s10665-021-10155-x |
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| 520 | |a Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. | ||
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10.1007/s10665-021-10155-x doi (DE-627)OLC2127115120 (DE-He213)s10665-021-10155-x-p DE-627 ger DE-627 rakwb eng 510 VZ Yang, Junxiang verfasserin aut The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. Energy stability Gradient flows S-TSAV approach Stabilization technique Kim, Junseok (orcid)0000-0002-0484-9189 aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 129(2021), 1 vom: Aug. (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:129 year:2021 number:1 month:08 https://doi.org/10.1007/s10665-021-10155-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 129 2021 1 08 |
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10.1007/s10665-021-10155-x doi (DE-627)OLC2127115120 (DE-He213)s10665-021-10155-x-p DE-627 ger DE-627 rakwb eng 510 VZ Yang, Junxiang verfasserin aut The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. Energy stability Gradient flows S-TSAV approach Stabilization technique Kim, Junseok (orcid)0000-0002-0484-9189 aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 129(2021), 1 vom: Aug. (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:129 year:2021 number:1 month:08 https://doi.org/10.1007/s10665-021-10155-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 129 2021 1 08 |
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10.1007/s10665-021-10155-x doi (DE-627)OLC2127115120 (DE-He213)s10665-021-10155-x-p DE-627 ger DE-627 rakwb eng 510 VZ Yang, Junxiang verfasserin aut The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. Energy stability Gradient flows S-TSAV approach Stabilization technique Kim, Junseok (orcid)0000-0002-0484-9189 aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 129(2021), 1 vom: Aug. (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:129 year:2021 number:1 month:08 https://doi.org/10.1007/s10665-021-10155-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 129 2021 1 08 |
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10.1007/s10665-021-10155-x doi (DE-627)OLC2127115120 (DE-He213)s10665-021-10155-x-p DE-627 ger DE-627 rakwb eng 510 VZ Yang, Junxiang verfasserin aut The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. Energy stability Gradient flows S-TSAV approach Stabilization technique Kim, Junseok (orcid)0000-0002-0484-9189 aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 129(2021), 1 vom: Aug. (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:129 year:2021 number:1 month:08 https://doi.org/10.1007/s10665-021-10155-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 129 2021 1 08 |
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10.1007/s10665-021-10155-x doi (DE-627)OLC2127115120 (DE-He213)s10665-021-10155-x-p DE-627 ger DE-627 rakwb eng 510 VZ Yang, Junxiang verfasserin aut The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2021 Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. Energy stability Gradient flows S-TSAV approach Stabilization technique Kim, Junseok (orcid)0000-0002-0484-9189 aut Enthalten in Journal of engineering mathematics Springer Netherlands, 1967 129(2021), 1 vom: Aug. (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:129 year:2021 number:1 month:08 https://doi.org/10.1007/s10665-021-10155-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 129 2021 1 08 |
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Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. © The Author(s), under exclusive licence to Springer Nature B.V. 2021 |
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Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. © The Author(s), under exclusive licence to Springer Nature B.V. 2021 |
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Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability. © The Author(s), under exclusive licence to Springer Nature B.V. 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2127115120</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505130357.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10665-021-10155-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2127115120</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10665-021-10155-x-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yang, Junxiang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature B.V. 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be satisfied. Furthermore, the phase-field variables and auxiliary variable r can be treated in a totally decoupled manner, which simplifies the algorithm. A practical stabilization method is employed to suppress the effect of an explicit nonlinear term. Using our proposed approach, temporally first-order and second-order methods are easily constructed. We prove analytically the discrete energy dissipation laws of the first- and second-order schemes. Furthermore, we propose a multiple TSAV approach for complex systems with multiple components. A comparison of stabilized-SAV (S-SAV) and stabilized-TSAV (S-TSAV) approaches is performed to show their efficiency. Two-dimensional numerical experiments demonstrated the desired accuracy and energy stability.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Energy stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gradient flows</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">S-TSAV approach</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stabilization technique</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kim, Junseok</subfield><subfield code="0">(orcid)0000-0002-0484-9189</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of engineering mathematics</subfield><subfield code="d">Springer Netherlands, 1967</subfield><subfield code="g">129(2021), 1 vom: Aug.</subfield><subfield code="w">(DE-627)129595748</subfield><subfield code="w">(DE-600)240689-5</subfield><subfield code="w">(DE-576)015088766</subfield><subfield code="x">0022-0833</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:129</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:1</subfield><subfield code="g">month:08</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10665-021-10155-x</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">129</subfield><subfield code="j">2021</subfield><subfield code="e">1</subfield><subfield code="c">08</subfield></datafield></record></collection>
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