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 $\alpha$ 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.

翻译：为了解决Fredholm第二类边界组合方程式,提出了一个数字方案,该方程式的右侧面在一定的边界点数上是单数的。边界本身可能是非平稳的。该方程式建立在递归压缩反先决条件(RCIP)的基础上,具有普遍性,因为它独立于奇数的性质。强大的右侧单方方方程式,如1美元/ ⁇ ⁇ ⁇ alpha$,接近1美元/ ⁇ alpha$,可以用完全的机器精确处理。适应性精细只用于前置装置的循环构建,导致解决方案阶段的离散点和超强稳定性达到最佳数量。该方程式的性能通过几个数字示例加以说明,包括用于从线性BGKW动量方程式衍生的组合方程式,用于稳定的库韦特流程。