A new regularized boundary integral equation for three-dimensional potential gradient field

• We present a new regularized boundary integral equation (BIE) method for three-dimensional (3D) potential gradient field.
• Two special tangential vectors are constructed.
• A characteristics theorem and a limit theorem are provided.
• Any potential gradients on the boundary, not limited to normal gradients, can be calculated by the proposed method.

This paper presents a new regularized boundary integral equation (BIE) method for three-dimensional (3D) potential gradient field. For this method, we firstly construct two special tangential vectors, and then provide a characteristics theorem with respect to the contour integrations of normal and tangential gradients of the fundamental solution. Finally, a new regularized boundary integral equation with indirect unknowns is derived by using the characteristics theorem and a limit theorem. Compared with the direct boundary element method (BEM), the proposed method has three new features: (1) the continuity requirements of density functions are reduced from C1, α to C0, α; (2) the BIE does not involve the hypersingular (HFP) integral and thus its numerical evaluation is more easy and precise; (3) any potential gradients on the boundary, not limited to normal gradients, can now be calculated. Numerical results illustrate that the present method is computationally efficient, accurate, and convergent with an increasing number of boundary elements.