| Published Date |
2026 / March
|
|---|---|
| Title | General null-field boundary integral formulation for boundary value problems using degenerate kernels of orthogonal curvilinear coordinates |
| Author | |
| Keyword | |
| Download | |
| Pagination | 21-48 |
| Abstract | In this paper, a general null-field boundary integral formulation for boundary value problems is proposed using degenerate kernels in orthogonal curvilinear coordinates. By introducing separable kernels, all singular integrals are handled rigorously, even when the collocation point lies on the real boundary. The polar, elliptical, and bipolar coordinates are employed, and four Jacobians are derived to establish their interrelations. The closed-form fundamental solution $\ln(r)$ is represented in terms of degenerate kernels with harmonic bases in these coordinates. The proposed formulation effectively solves boundary value problems governed by the Laplace operator. Additionally, the unit logarithmic capacity and degenerate scale in boundary integral equations are investigated for circular, elliptical, and infinite plane domains containing two circles. |
| DOI | |
| Received |
2025-01-16
|
Bulletin of the Institute of
Mathematics Academia Sinica
Mathematics Academia Sinica
NEW SERIES
2026 / March Volume 21 No.1
General null-field boundary integral formulation for boundary value problems using degenerate kernels of orthogonal curvilinear coordinates