An extended boundary node method for modeling normal derivative discontinuities in potential theory across edges and corners

Telukunta, S.; Mukherjee, Subrata

doi:10.1016/j.enganabound.2004.01.007

Cited by 11 publications

(10 citation statements)

References 30 publications

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“…The new method employs standard Gauss quadrature for the ÿrst term on the right-hand side of (24), together with the method given in Reference [24] for the second term. Care should be taken to avoid a Gauss point atx in Figure 5(a).…”

Section: Proposed New Methods For Evaluating Nearly Log-singular Integmentioning

confidence: 99%

“…The literature contains many methods for accurate evaluation of log-singular integrals. A nice approach for evaluating such integrals, on curved as well as straight lines, is described in Reference [24]. The nearly (also called quasi) log-singular case, along with other nearly singular integrals of various orders, can be e ectively evaluated by employing a cubic polynomial transformation due to Telles [25] and Telles and Oliveira [26].…”

Section: Singular and Nearly Singular Integralsmentioning

confidence: 99%

“…The standard BEM uses strictly quadratic elements. Also, in both versions of the BEM, log-singular integrals are evaluated by the method outlined in Reference [24]. Nearly log-singular integrals appear only in the standard BEM and these, in the interest of 'standardization', are evaluated by usual Gauss quadrature.…”

Section: Comparison Of Thin Beam and Standard Bemmentioning

confidence: 99%

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Electrostatic BEM for MEMS with thin beams

Bao

Mukherjee

2005

Commun. Numer. Meth. Engng.

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SUMMARYMicro-electro-mechanical (MEM) and nano-electro-mechanical (NEM) systems sometimes use beamor plate-shaped conductors that can be very thin-with h=L ≈ O(10 −2 -10 −3 ) (in terms of the thickness h and length L of a beam or the side of a square pate). Conventional boundary element method (BEM) analysis of the electric ÿeld in a region exterior to such thin conductors can become di cult to carry out accurately and e ciently-especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such objects. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with logarithmically singular kernels, results in a powerful technique for the BEM analysis of such problems with thin beams. This new approach, in fact, works best for very thin beams. This thin beam BEM is derived and discussed in this work.

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Section: Proposed New Methods For Evaluating Nearly Log-singular Integmentioning

confidence: 99%

Section: Singular and Nearly Singular Integralsmentioning

confidence: 99%

Section: Comparison Of Thin Beam and Standard Bemmentioning

confidence: 99%

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Electrostatic BEM for MEMS with thin beams

Bao

Mukherjee

2005

Commun. Numer. Meth. Engng.

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“…The variable basis approach [17] (as well as the standard BNM [5]), on the other hand, does not properly model possible discontinuities in the normal derivative of the potential function across edges and corners. Telukunta and Mukherjee [34] have recently tried to combine the advantages of the variable basis approach [16], together with allowing possible discontinuities in the normal derivative of the potential function, across edges and corners, in a new approach called the extended boundary node method (EBNM). A detailed formulation for the EBNM for 2-D potential theory, together with numerical results for selected problems, appear in [34].…”

Section: Outline Of the Present Papermentioning

confidence: 99%

“…Telukunta and Mukherjee [34] have recently tried to combine the advantages of the variable basis approach [16], together with allowing possible discontinuities in the normal derivative of the potential function, across edges and corners, in a new approach called the extended boundary node method (EBNM). A detailed formulation for the EBNM for 2-D potential theory, together with numerical results for selected problems, appear in [34]. The present paper is concerned with far more challenging problems-3-D potential theory.…”

Section: Outline Of the Present Papermentioning

confidence: 99%