A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as $1/|r{|}^{\alpha }$ with α close to 1, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

给出了求解Fredholm 二类边界积分方程的数值方案，该方程的右手边在有限的边界点集上是奇异的。边界本身可能是不平滑的。该方案建立在递归压缩逆预处理 (RCIP) 之上，是通用的，因为它与奇点的性质无关。强右侧奇点，例如$1/|r{|}^{\alpha }$与α接近于1，可以在完整的机器的精度来进行处理。自适应细化仅用于预处理器的递归构造，从而在求解阶段获得最佳数量的离散化点和卓越的稳定性。该方案的性能通过几个数值例子来说明，包括对从稳态 Couette 流的线性化 BGKW 动力学方程导出的积分方程的应用。