A new method for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM

• We present a new indirect regularized boundary element formulation.
• A new distance formula for high-order geometry elements is constructed.
• The exponential transformation is developed to remove the near singularities.
• The efficiency and applicability of the scheme are verified by some examples.

This work presents a new method for numerical computation of the two-dimensional nearly singular integrals by using the eight-node second-order quadrilateral surface elements in 3D BEM. A new indirect regularized boundary element formulation excluding the CPV (Cauchy Principal Value) and HFP (Hadamard-Finite-Part) integrals is proposed. Based on this, a new approximation formula of the distance from the fixed calculation point to a generic point of the aforementioned surface geometry elements is developed firstly, and then the exponential transformation, which has been widely employed in 2D BEM, is extended to 3D BEM to remove the near singularities of integrands for considered integrals. Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme.