Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
We propose and analyze a class of temporal up to fourth-order unconditionally structure-preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first revisit some up to second-order exponential time different Runge–Kutta (ETDRK) schemes, and provide unified proofs for t...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/164165 |
| _version_ | 1811695042979430400 |
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| author | Zhang, Hong Yan, Jingye Qian, Xu ong, Songhe |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Zhang, Hong Yan, Jingye Qian, Xu ong, Songhe |
| author_sort | Zhang, Hong |
| collection | NTU |
| description | We propose and analyze a class of temporal up to fourth-order unconditionally structure-preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first revisit some up to second-order exponential time different Runge–Kutta (ETDRK) schemes, and provide unified proofs for the unconditionally maximum-principle-preserving and mass-conserving properties. Noting that the stabilized ETDRK schemes belong to a special class of parametric Runge–Kutta schemes, we introduce the stabilized integrating factor Runge–Kutta (sIFRK) formulation to construct new high-order parametric single-step methods, and propose two strategies to eliminate the exponential effects of sIFRK: (1) a recursive approximation; (2) a combination of exponential and linear functions. Together with the nonnegativity of coefficients and non-decreasing of abscissas, the resulting two families of improved stabilized integrating factor Runge–Kutta (isIFRK) schemes can unconditionally preserve the maximum-principle and conserve the mass. The order conditions, linear stability and convergence in the l∞-norm are analyzed rigorously. We demonstrate that the proposed framework, which is explicit and free of limiters or cut-off post-processing, offers a simple, practical, and effective approach to developing high-order unconditionally structure-preserving algorithms. Comparisons with traditional schemes demonstrate the necessity of developing high-order unconditionally structure-preserving schemes. A series of numerical experiments verify theoretical results of proposed isIFRK schemes. |
| first_indexed | 2024-10-01T07:17:11Z |
| format | Journal Article |
| id | ntu-10356/164165 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:17:11Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1641652023-01-06T08:19:33Z Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations Zhang, Hong Yan, Jingye Qian, Xu ong, Songhe School of Physical and Mathematical Sciences Science::Mathematics Semilinear Parabolic Equations Conservative Allen–Cahn Equations We propose and analyze a class of temporal up to fourth-order unconditionally structure-preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first revisit some up to second-order exponential time different Runge–Kutta (ETDRK) schemes, and provide unified proofs for the unconditionally maximum-principle-preserving and mass-conserving properties. Noting that the stabilized ETDRK schemes belong to a special class of parametric Runge–Kutta schemes, we introduce the stabilized integrating factor Runge–Kutta (sIFRK) formulation to construct new high-order parametric single-step methods, and propose two strategies to eliminate the exponential effects of sIFRK: (1) a recursive approximation; (2) a combination of exponential and linear functions. Together with the nonnegativity of coefficients and non-decreasing of abscissas, the resulting two families of improved stabilized integrating factor Runge–Kutta (isIFRK) schemes can unconditionally preserve the maximum-principle and conserve the mass. The order conditions, linear stability and convergence in the l∞-norm are analyzed rigorously. We demonstrate that the proposed framework, which is explicit and free of limiters or cut-off post-processing, offers a simple, practical, and effective approach to developing high-order unconditionally structure-preserving algorithms. Comparisons with traditional schemes demonstrate the necessity of developing high-order unconditionally structure-preserving schemes. A series of numerical experiments verify theoretical results of proposed isIFRK schemes. This work was supported by the Natural Science Foundation of China (No. 11901577, 11971481, 12071481), Natural Science Foundation of Hunan (No. 2020JJ5652), Defense Science Foundation of China (No. 2021-JCJQ-JJ0523), National Key R&D Program of China (No. SQ2020YFA0709803), National Key Project (No. GJXM92579) and Research Fund of National University of Defense Technology (No. ZK19-37, ZZKY-JJ-21-01). 2023-01-06T08:19:33Z 2023-01-06T08:19:33Z 2022 Journal Article Zhang, H., Yan, J., Qian, X. & ong, S. (2022). Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations. Computer Methods in Applied Mechanics and Engineering, 393, 114817-. https://dx.doi.org/10.1016/j.cma.2022.114817 0045-7825 https://hdl.handle.net/10356/164165 10.1016/j.cma.2022.114817 2-s2.0-85126541664 393 114817 en Computer Methods in Applied Mechanics and Engineering © 2022 Elsevier B.V. All rights reserved. |
| spellingShingle | Science::Mathematics Semilinear Parabolic Equations Conservative Allen–Cahn Equations Zhang, Hong Yan, Jingye Qian, Xu ong, Songhe Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title | Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title_full | Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title_fullStr | Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title_full_unstemmed | Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title_short | Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations |
| title_sort | up to fourth order unconditionally structure preserving parametric single step methods for semilinear parabolic equations |
| topic | Science::Mathematics Semilinear Parabolic Equations Conservative Allen–Cahn Equations |
| url | https://hdl.handle.net/10356/164165 |
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