A Weakly Singular Formulation of Boundary Integral Equations and Field Computation near Boundaries

✍ Scribed by Norio Nakagawa

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 311 KB
• Volume: 122
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1995.1203

✦ Synopsis

Applications of the boundary integral equation method to realworld problems often require that field values should be obtained near boundary surfaces. A numerical difficulty is known to arise in this situation if one attempts to evaluate near-boundary fields via the conventional Green's formula. The present work addresses this particular issue. Namely, a stable computational scheme for both fields and gradients in the near-boundary region has been formulated. This approach starts with the conventional Green and Maue representations of fields and gradients written inside and outside of the defining volume. Then, a new set of integral representations that have weaker kernel singularities is derived by canceling the most singular terms between the conventional formulas of the two sides. The principal contribution of this work is the explicit construction of the improved representations for the fields and gradients. Also presented are several numerical results that demonstrate the superiority of the new representations over the conventional ones. (-) 1995 Academic Press, Inc.