The random walk on the boundary method for calculating capacitance

Mascagni, Michael; Simonov, Nikolai A.

doi:10.1016/j.jcp.2003.10.005

Cited by 32 publications

(23 citation statements)

References 21 publications

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“…Since a random walk method uses smaller steps, they have been distributed randomly as well as these methods avoid hidden systematic errors. Similarly, Mascagni and Simonov [18] used Monte Carlo technique for the computation of the capacitance of the unit cube. In order to estimate the computational error; Markov chain version of the central limit theorem was used.…”

Section: Simulation Of Unit Cubementioning

confidence: 99%

“…In this section, the utility of FEM used to calculate the electrical capacitance of T-shaped plate is discussed. Figure 8 shows a T-shaped platewith a dimension of 3.0 m, 1.0 m, and 3.0 m. The model is designed based on three-dimensional modeling using electrostatic environment [18]. T-shaped plate model like 180 domain element of the finite element mesh is shown in Figure 9(a).…”

Section: Simulation Of T-shaped Platementioning

confidence: 99%

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Evaluation of the Capacitance and Charge Distribution for Conducting Bodies by Circuit Modelling

Muneeswaran¹,

Dhanasekaran²

2016

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This paper presents a numerical analysis for computation of free space capacitance of different arbitrarily shaped conducting bodies based on the finite element method with triangular subsection modeling. Evaluation of capacitance of different arbitrary shapes is important for the electrostatic analysis. Capacitance computation is an important step in the prediction of electrostatic discharge which causes electromagnetic interference. We specifically illustrated capacitance computation of electrostatic models like unit cube, rectangular plate, triangular plate, T-shaped plate, sphere and two touching spheres. Numerical data on the capacitance of conducting objects are presented. The results are compared with other available results in the literature. We used the COMSOL Multiphysics software for the simulation. The models are designed in three-dimensional form using electrostatic environment and can be applied to any spacecraft circuit modeling design. The findings of this study show that the finite element method is a more accurate method and can be applied to any circuit modeling design.

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Section: Simulation Of Unit Cubementioning

confidence: 99%

Section: Simulation Of T-shaped Platementioning

confidence: 99%

Evaluation of the Capacitance and Charge Distribution for Conducting Bodies by Circuit Modelling

Muneeswaran¹,

Dhanasekaran²

2016

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“…Problems of this nature are considered to be challenging for any numerical tool and especially so for the BEM approach. In Table 5, we have presented the estimates of the order of singularity at the vertex or the edge as done by methods as diverse as singular perturbation [31], BEM [28], last-passage and walk on spheres [44,45], application of Fichera's theorem [32], singular element approach [33] and the presented approach. From the table, it is clear that there is good agreement among all the methods.…”

Section: Square Plate and Cubementioning

confidence: 99%

“…Both the values compare very well with both old and recent estimates of the order of singularity as shown in Table 5. In Fig.14, we have shown how the slope of the fitted line changes along the edge of a SCM 0.367 [13] Refined SCM 0.3667894 ± 1.1 × 10 −6 0.6606747 ± 5 × 10 −7 and Extrapolation [27] Refined BEM 0.3667874 ± 1 × 10 −7 0.6606785 ± 6 × 10 −7 and Extrapolation [43] Numerical Path 0.36684 0.66069 Integration [23] Random Walk 0.36 ± 0.01 0.6606 ± 1 × 10 −4 [45] Random Walk 0.6606780 ± 2.7 × 10 −7 [33] Singular element 0.6606749 [28] Refined BEM 0.3667896 ± 8 × 10 −7 0.6606767 ± 4 × 10 −6 and Extrapolation [15] Robin Hood 0.6606786 ± 8 × 10 −8 and Extrapolation This work neBEM 0.3667524 0.6606746 Table 4: Comparison of potential at the center and along an edge of a unit cube X Y Z Exact [32] Error in [32] square plate as we move away from a corner of a square plate. From the figure, it is apparent that the change in the singularity index along an edge of a square plate, can be quite significant and only when we are in reality close to the middle of the edge, the analytic value of 0.5 can be used with confidence for the order of singularity.…”

Section: Square Plate and Cubementioning

confidence: 99%

A study of three-dimensional edge and corner problems using the neBEM solver

Mukhopadhyay

Majumdar

2009

Engineering Analysis with Boundary Elements

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The previously reported neBEM solver has been used to solve electrostatic problems having three-dimensional edges and corners in the physical domain. Both rectangular and triangular elements have been used to discretize the geometries under study. In order to maintain very high level of precision, a library of C functions yielding exact values of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed and used. Here we present the exact expressions proposed for computing the influence of uniform singularity distributions on triangular elements and illustrate their accuracy. We then consider several problems of electrostatics containing edges and singularities of various orders including plates and cubes, and L-shaped conductors. We have tried to show that using the approach proposed in the earlier paper on neBEM and its present enhanced (through the inclusion of triangular elements) form, it is possible to obtain accurate estimates of integral features such as the capacitance of a given conductor and detailed ones such as the charge density distribution at the edges / corners without taking resort to any new or special formulation. Results obtained using neBEM have been compared extensively with both existing analytical and numerical results. The comparisons illustrate the accuracy, flexibility and robustness of the new approach quite comprehensively.

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“…For this classical electrostatic problem a very accurate estimate of the normalized capacitance is given by 0.6606780 ± 2.7 × 10 −7 [20], the normalizing value being 4π 0 s. In order to apply the FEM-DBCI method a cube fictitious boundary Γ F is selected homologously to the conductor, placed at a distance of s/2. For symmetry reasons, the analysis is restricted to one octant only, by imposing homogeneous Neumann conditions on the three symmetry planes.…”

Section: Conductor Cubementioning

confidence: 99%