Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

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A. E. Shadare
M. N. O. Sadiku
S. M. Musa

Abstract

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.     

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How to Cite
Shadare, A., Sadiku, M., & Musa, S. (2019). Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions. Advanced Electromagnetics, 8(5), 29-36. https://doi.org/10.7716/aem.v8i5.1255
Section
Research Articles
Author Biographies

A. E. Shadare, Prairie View A&M University

Adebowale E. Shadare received the B.Sc. degree in electronic and electrical engineering in 2009 from the Obafemi Awolowo University, Ile-Ife, Nigeria. In 2015, he received the M.S. degree in electrical engineering from Prairie View A&M University, Texas. He has just completed his doctoral program in Electrical Engineering at Prairie View A&M University, Texas. He is a student member of IEEE and the author of several papers. He was the recipient of the Roy G. Perry College of Engineering (Electrical & Computer Engineering) Outstanding PhD Student of the Year Award (2018). His research interests include computational electromagnetics and electromagnetic compatibility.             

M. N. O. Sadiku, Prairie View A&M University

Matthew N. O. Sadiku received his B. Sc. degree in 1978 from Ahmadu Bello University, Zaria, Nigeria and his M.Sc. and Ph.D. degrees from Tennessee Technological University, Cookeville, TN in 1982 and 1984, respectively.  From 1984 to 1988, he was an assistant professor at Florida Atlantic University, Boca Raton, FL, where he did graduate work in computer science.  From 1988 to 2000, he was at Temple University, Philadelphia, PA, where he became a full professor.    From 2000 to 2002, he was with Lucent/Avaya, Holmdel, NJ as a system engineer and with Boeing Satellite Systems, Los Angeles, CA as a senior scientist.   He is presently a professor of electrical and computer engineering at Prairie View A&M University, Prairie View, TX.

He is the author of over 330 professional papers and  over 70  books including “Elements of  Electromagnetics” (Oxford University Press, 7th ed., 2018), “Fundamentals of Electric Circuits” (McGraw-Hill, 6th ed.,2017, with C.  Alexander), “Computational Electromagnetics with MATLAB” (CRC, 4th ed., 2018), “Metropolitan Area Networks” (CRC Press, 1995), and “Principles of Modern Communication Systems” (Cambridge University Press, 2017, with S. O. Agbo). In addition to the engineering books, he has written several Christian books. Some of his books have been translated into French, Korean, Chinese (and Chinese Long Form in Taiwan), Italian, Portuguese, and Spanish.   He was the recipient of the 2000 McGraw-Hill/Jacob Millman Award for outstanding contributions in the field of electrical engineering.  He was also the recipient of Regents Professor award for 2012-2013 by the Texas A&M University System. He is a registered professional engineer and a Fellow of IEEE. His current research interests are in the areas of computational electromagnetics, computer networks, and engineering education.

S. M. Musa, Prairie View A&M University

Sarhan M. Musa is a professor in the Department of Engineering Technology at Prairie View A&M University, Texas. He received his Ph.D. in Electrical Engineering from the City University of New York in 2001. Professor Musa has been the founder and director of Prairie View Networking Academy, Texas, since 2004. He is LTD Sprint and Boeing Welliver Fellow. Professor Musa is an author of several books in mathematics and engineering. His current research interests include electromagnetic computation, smart grid, imaging and spectroscopy, computational nanotechnology, cybersecurity, and computer networks.   

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