High-accuracy numerical solver for the Eikonal equation
An introduction to the Eikonal equation and its applications in Physics as well as the Earth Sciences is provided, followed by two derivations of the Eikonal equation. Proofs of existence and uniqueness to the Eikonal equation initial value problem are provided. The Fast Sweeping Method (FSM) is the...
| Հիմնական հեղինակ: | |
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| Այլ հեղինակներ: | |
| Ձևաչափ: | Final Year Project (FYP) |
| Լեզու: | English |
| Հրապարակվել է: |
Nanyang Technological University
2021
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| Խորագրեր: | |
| Առցանց հասանելիություն: | https://hdl.handle.net/10356/148484 |
| _version_ | 1826121045753462784 |
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| author | Guo, Jin Long |
| author2 | Tong Ping |
| author_facet | Tong Ping Guo, Jin Long |
| author_sort | Guo, Jin Long |
| collection | NTU |
| description | An introduction to the Eikonal equation and its applications in Physics as well as the Earth Sciences is provided, followed by two derivations of the Eikonal equation. Proofs of existence and uniqueness to the Eikonal equation initial value problem are provided. The Fast Sweeping Method (FSM) is then introduced in detail and run on two dimensional Cartesian coordinates. The numerical results are compared again analytic results and its accuracy is evaluated using percentage relative error. Relative error was found to be reduced by decreasing grid size. The FSM algorithm was also run on three dimensional spherical coordinates as well as Cartesian coordinates using parallel computing techniques. FSM was also implemented on two dimensional Cartesian domain triangulated with acute triangles. In all cases, it was shown that the FSM convergerd quickly after minimal iterations and approximated the actual solution to Eikonal equations to which the analytical solution is known to a high degree of accuracy. Furthermore, it was found that parallel computing techniques greatly improved computing efficiency by reducing convergence time. Some limitations of this project include the type of grid used to discretise the computational domain as well as the type of source used to initialise the Eikonal equation. It is recommended that future projects experiment with adaptive meshes and also possibly linear sources (instead of point sources) which often arise in the field of Seismology. |
| first_indexed | 2024-10-01T05:26:20Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/148484 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:26:20Z |
| publishDate | 2021 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1484842023-02-28T23:14:51Z High-accuracy numerical solver for the Eikonal equation Guo, Jin Long Tong Ping School of Physical and Mathematical Sciences tongping@ntu.edu.sg Science::Mathematics::Applied mathematics An introduction to the Eikonal equation and its applications in Physics as well as the Earth Sciences is provided, followed by two derivations of the Eikonal equation. Proofs of existence and uniqueness to the Eikonal equation initial value problem are provided. The Fast Sweeping Method (FSM) is then introduced in detail and run on two dimensional Cartesian coordinates. The numerical results are compared again analytic results and its accuracy is evaluated using percentage relative error. Relative error was found to be reduced by decreasing grid size. The FSM algorithm was also run on three dimensional spherical coordinates as well as Cartesian coordinates using parallel computing techniques. FSM was also implemented on two dimensional Cartesian domain triangulated with acute triangles. In all cases, it was shown that the FSM convergerd quickly after minimal iterations and approximated the actual solution to Eikonal equations to which the analytical solution is known to a high degree of accuracy. Furthermore, it was found that parallel computing techniques greatly improved computing efficiency by reducing convergence time. Some limitations of this project include the type of grid used to discretise the computational domain as well as the type of source used to initialise the Eikonal equation. It is recommended that future projects experiment with adaptive meshes and also possibly linear sources (instead of point sources) which often arise in the field of Seismology. Bachelor of Science in Mathematical Sciences 2021-04-28T01:55:28Z 2021-04-28T01:55:28Z 2021 Final Year Project (FYP) Guo, J. L. (2021). High-accuracy numerical solver for the Eikonal equation. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/148484 https://hdl.handle.net/10356/148484 en application/pdf Nanyang Technological University |
| spellingShingle | Science::Mathematics::Applied mathematics Guo, Jin Long High-accuracy numerical solver for the Eikonal equation |
| title | High-accuracy numerical solver for the Eikonal equation |
| title_full | High-accuracy numerical solver for the Eikonal equation |
| title_fullStr | High-accuracy numerical solver for the Eikonal equation |
| title_full_unstemmed | High-accuracy numerical solver for the Eikonal equation |
| title_short | High-accuracy numerical solver for the Eikonal equation |
| title_sort | high accuracy numerical solver for the eikonal equation |
| topic | Science::Mathematics::Applied mathematics |
| url | https://hdl.handle.net/10356/148484 |
| work_keys_str_mv | AT guojinlong highaccuracynumericalsolverfortheeikonalequation |