A boundary-only treatment by singular boundary method for two-dimensional inhomogeneous problems

Abstract

• A boundary-only singular boundary method is proposed for inhomogeneous problems. • The method unifies the MRM and SBM. • The boundary-only merit decreases the quantity of preparing data. • The simple formulas of the origin intensity factors are derived for high-order fundamental solutions. • The MRM–SBM performs well in problems with corner singularities. In this study, an effective singular boundary method (SBM) in conjunction with the recursive multiple reciprocity method (MRM) is developed and validated for inhomogeneous problems. It avoids the inner nodes or domain discretizations to evaluate the particular solution, and preserves the boundary-only property of the SBM. Rather than using only polyharmonic operators in the traditional MRM, a recursive MRM is proposed to annihilate source terms with different partial differential operators recursively. Nevertheless, high-order fundamental solutions are involved in the recursive MRM. The absence of the origin intensity factors of higher order fundamental solutions is a major bottleneck in applying the SBM. In order to remedy this difficulty, the origin intensity factors of higher order fundamental solutions are derived with simple formulas. Numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.