A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions
In this paper, we focus on the numerical solutions of Maxwell’s equations with Dirichlet boundary conditions in rectangular coordinate. A class of explicit methods is derived by using an effective solver for a system of ordinary differential equations which is obtained by approximating on...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9945962/ |
| _version_ | 1811299603418447872 |
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| author | Xianyang Zeng Hongli Yang |
| author_facet | Xianyang Zeng Hongli Yang |
| author_sort | Xianyang Zeng |
| collection | DOAJ |
| description | In this paper, we focus on the numerical solutions of Maxwell’s equations with Dirichlet boundary conditions in rectangular coordinate. A class of explicit methods is derived by using an effective solver for a system of ordinary differential equations which is obtained by approximating on spatial fields. A significant advantage of this class of methods is their simplicity and their ease of implementation. The error estimates presented in this paper show that the numerical solutions obtained by this class of methods is of high-order. The main advantage of this class of methods is that it is divergence-free. |
| first_indexed | 2024-04-13T06:37:17Z |
| format | Article |
| id | doaj.art-300f81776db14295a5c4897215359f74 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-13T06:37:17Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-300f81776db14295a5c4897215359f742022-12-22T02:57:50ZengIEEEIEEE Access2169-35362022-01-011012618812619810.1109/ACCESS.2022.32214119945962A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary ConditionsXianyang Zeng0https://orcid.org/0000-0003-3948-173XHongli Yang1Industrial Center, Nanjing Institute of Technology, Nanjing, ChinaSchool of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, ChinaIn this paper, we focus on the numerical solutions of Maxwell’s equations with Dirichlet boundary conditions in rectangular coordinate. A class of explicit methods is derived by using an effective solver for a system of ordinary differential equations which is obtained by approximating on spatial fields. A significant advantage of this class of methods is their simplicity and their ease of implementation. The error estimates presented in this paper show that the numerical solutions obtained by this class of methods is of high-order. The main advantage of this class of methods is that it is divergence-free.https://ieeexplore.ieee.org/document/9945962/Computation theoryDirichlet boundary value problemdivergence-free methodselectromagnetic propagationMaxwell’s equationstime-domain methods |
| spellingShingle | Xianyang Zeng Hongli Yang A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions IEEE Access Computation theory Dirichlet boundary value problem divergence-free methods electromagnetic propagation Maxwell’s equations time-domain methods |
| title | A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions |
| title_full | A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions |
| title_fullStr | A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions |
| title_full_unstemmed | A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions |
| title_short | A Class of Explicit Divergence-Free Methods for Maxwell’s Equations With Dirichlet Boundary Conditions |
| title_sort | class of explicit divergence free methods for maxwell x2019 s equations with dirichlet boundary conditions |
| topic | Computation theory Dirichlet boundary value problem divergence-free methods electromagnetic propagation Maxwell’s equations time-domain methods |
| url | https://ieeexplore.ieee.org/document/9945962/ |
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