Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions
The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Advanced Electromagnetics
2019-12-01
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| Series: | Advanced Electromagnetics |
| Subjects: | |
| Online Access: | https://aemjournal.org/index.php/AEM/article/view/1255 |
| _version_ | 1818759299427467264 |
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| author | A. E. Shadare M. N. O. Sadiku S. M. Musa |
| author_facet | A. E. Shadare M. N. O. Sadiku S. M. Musa |
| author_sort | A. E. Shadare |
| collection | DOAJ |
| description | The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions. |
| first_indexed | 2024-12-18T06:40:31Z |
| format | Article |
| id | doaj.art-35c0696306524e92b98fbd3f6496e778 |
| institution | Directory Open Access Journal |
| issn | 2119-0275 |
| language | English |
| last_indexed | 2024-12-18T06:40:31Z |
| publishDate | 2019-12-01 |
| publisher | Advanced Electromagnetics |
| record_format | Article |
| series | Advanced Electromagnetics |
| spelling | doaj.art-35c0696306524e92b98fbd3f6496e7782022-12-21T21:17:38ZengAdvanced ElectromagneticsAdvanced Electromagnetics2119-02752019-12-018510.7716/aem.v8i5.1255Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric RegionsA. E. Shadare0M. N. O. Sadiku1S. M. Musa2Prairie View A&M UniversityPrairie View A&M UniversityPrairie View A&M UniversityThe advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.https://aemjournal.org/index.php/AEM/article/view/1255Poisson’s equationsaxisymmetric probleminhomogeneous mediaMarkov Chain Monte Carlo (MCMC) |
| spellingShingle | A. E. Shadare M. N. O. Sadiku S. M. Musa Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions Advanced Electromagnetics Poisson’s equations axisymmetric problem inhomogeneous media Markov Chain Monte Carlo (MCMC) |
| title | Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions |
| title_full | Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions |
| title_fullStr | Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions |
| title_full_unstemmed | Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions |
| title_short | Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions |
| title_sort | markov chain monte carlo solution of poisson s equation in axisymmetric regions |
| topic | Poisson’s equations axisymmetric problem inhomogeneous media Markov Chain Monte Carlo (MCMC) |
| url | https://aemjournal.org/index.php/AEM/article/view/1255 |
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