An energy-stable convex splitting for the phase-field crystal equation
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conse...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Elsevier Limited
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/51476 |
| _version_ | 1848758707548061696 |
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| author | Vignal, P. Dalcin, L. Brown, D. Collier, N. Calo, Victor |
| author_facet | Vignal, P. Dalcin, L. Brown, D. Collier, N. Calo, Victor |
| author_sort | Vignal, P. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. |
| first_indexed | 2025-11-14T09:48:16Z |
| format | Journal Article |
| id | curtin-20.500.11937-51476 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:16Z |
| publishDate | 2015 |
| publisher | Elsevier Limited |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514762017-09-13T16:09:32Z An energy-stable convex splitting for the phase-field crystal equation Vignal, P. Dalcin, L. Brown, D. Collier, N. Calo, Victor The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. 2015 Journal Article http://hdl.handle.net/20.500.11937/51476 10.1016/j.compstruc.2015.05.029 Elsevier Limited fulltext |
| spellingShingle | Vignal, P. Dalcin, L. Brown, D. Collier, N. Calo, Victor An energy-stable convex splitting for the phase-field crystal equation |
| title | An energy-stable convex splitting for the phase-field crystal equation |
| title_full | An energy-stable convex splitting for the phase-field crystal equation |
| title_fullStr | An energy-stable convex splitting for the phase-field crystal equation |
| title_full_unstemmed | An energy-stable convex splitting for the phase-field crystal equation |
| title_short | An energy-stable convex splitting for the phase-field crystal equation |
| title_sort | energy-stable convex splitting for the phase-field crystal equation |
| url | http://hdl.handle.net/20.500.11937/51476 |