Method of lines solution of axisymmetric problems

Sadiku, Matthew N. O.; Garcia, R.C.

doi:10.1109/secon.2000.845626

Cited by 3 publications

(2 citation statements)

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“…The absorption probability matrix B which describes the probabilities that a randomly walking particle starting at free node i will be absorbed at a fixed node j is given as = B NR (11) The size of matrix B is × f p n n . The matrix B is stochastic and it is given as Finally, the potential at any free node i is given as…”

Section: Absorbing Markov Chainmentioning

confidence: 99%

“…Several methods such as the Method of Lines [11], the Finite Element method [12] [13], Finite difference method [14] and the Boundary Integral Equation methods [15] [16] have all been applied in the modeling and analysis of axisymmetric problems. Since the connection between Brownian motion and the potential theory was established [17] and the application of probabilistic potential theory to electrical engineering related problems [18], several Monte Carlo techniques such as fixed random walk, floating random walk and Exodus method [9] [19]- [26] have evolved dramatically.…”

Section: Introductionmentioning

confidence: 99%

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Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Shadare¹,

Sadiku²,

Musa³

2019

OJMSi

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With increasing complexity of today's electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace's equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

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Section: Absorbing Markov Chainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Shadare¹,

Sadiku²,

Musa³

2019

OJMSi

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A method of lines solution of a cylindrical problem via radial discretization

Nelatury

Sadiku

Proceedings. IEEE SoutheastCon 2001 (Cat. No.01CH37208)

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The method of lines (MOL) is applied to solve for the electrostatic potential in a coaxial trough by discretizing in both the longitudinal and radial directions. The coupled equations are diagonalized by Eigen decomposition with the aid of MATLAB software. The results agree quite well. An attempt is made to do the same exercise in case of a cylindrical region without the inner conductor. While it is straight forward when we discretize along the longitudinal dimension, it is difficult to do the same along the radial dimension. We gave an approximation to the first two terms of the P matrix. In the analytical solution truncating the infinite summation gives rise to Gibb's phenomenon in the form of ripples at the discontinuities. A smoothing window gives potential that is free of overshoots at the discontinuities.

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Determination of Potential Profile In Planar Electronic Structures Using A Semi-Analytical Technique

2010

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In this paper, a semi-analytical technique known as the Method of Lines (MoL) with uniform and non-uniform discretization schemes is developed. The aim is to determine static potential profile in planar electronic structures. Even though this method has been known for some time, there has been reported work on its application to planar semiconductor device analysis for voltage profile determination. Since most current electronic devices are manufactured using planar and quasi-planar technology, the proposed algorithm is well suited for device analysis prior to fabrication. Compared with known popular methods such as Finite Difference and Finite Elements methods, the proposed technique is relatively simple, more accurate and unlike other methods, has no convergence problem. In addition to this, its semi-analytical nature, which consists of reducing one computing dimension, allows saving significant memory and computation time. Typical planar electronic structures are considered to demonstrate their suitability for these devices, and the obtained results are presented and discussed.

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Method of lines solution of axisymmetric problems

Cited by 3 publications

References 10 publications

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

A method of lines solution of a cylindrical problem via radial discretization

Determination of Potential Profile In Planar Electronic Structures Using A Semi-Analytical Technique

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