Revisit of logarithmic capacity of line segments and double-degeneracy of BEM/BIEM

Chen, Jeng‐Tzong; Kuo, Shyh‐Rong; Huang, Yu‐Te; Kao, Shing‐Kai

doi:10.1016/j.enganabound.2020.08.003

Cited by 5 publications

(1 citation statement)

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“…Chen et al [12] linked the logarithmic capacity in the potential theory and the degenerate scale in the BEM for the two tangent discs. Even the logarithmic capacity of line segment as well as the double degeneracy in the BIEM/BEM was studied by Chen et al [13]. Due to the use of two-dimensional fundamental solution in the BIEM, the solution space is limited and sometimes the corresponding matrix is rank deficient in the BEM.…”

Section: Introductionmentioning

confidence: 99%

On the solution arising in two-cylinders electrostatics

Chen

Kao

Chou

et al. 2022

Preprint

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The electrostatics of two cylinders charged to the symmetrical or anti-symmetrical potential is studied by using the null-field boundary integral equation (BIE) in conjunction with the degenerate kernel in terms of bipolar coordinates. The undetermined coefficient is obtained according to the Fredholm alternative theorem. Uniqueness of solution, infinite solution and no solution is therein discussed. A single cylinder case (circle or ellipse) is also provided for comparison. The link to the general solution space is also done. The condition at infinity is also correspondingly examined. The flux equilibrium along the circular boundaries and the infinite boundary is also checked as well as the contribution of the boundary integral (single and double layer potential) along the infinite boundary in the BIE is addressed. The ordinary and degenerate scales in the BIE are both investigated. Solution space limited by the BIE is also explained after comparing with the general solution. Identities between the present result and those in the literature of Darevski and Lekner results in Russia and NewZealand, respectively, is also constructed.

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Section: Introductionmentioning

confidence: 99%