qotential

tools for high‑order quaternionic product quadratures that resolve singular and nearly singular 3D layer potentials (Laplace, .. ). The implementation follows Ref. 1 and Ref. 2.

Layout

• kernels/: dense Laplace/Stokes kernel evaluation (inspired and partialy copied from https://github.com/ahbarnett/BIE3D), and FMM wrapper with similar interface as the dense kernel evaluation, quaternionic evaluation variants.
• utils/: a few smooth quadrature utilities, harmonic bases, FMM (https://github.com/flatironinstitute/FMM3D), kd‑tree (https://github.com/taiya/kdtree).
• utils/f: source files. lap3ddlp.f implements the original close‑evaluation scheme in Ref. 1; lap3dslp.f implements the correct Laplace SLP formulation in Ref. 2, but not the improved RRQ scheme...

References

1. Hai Zhu, and Shravan Veerapaneni. 2022. “High-Order Close Evaluation of Laplace Layer Potentials: A Differential Geometric Approach.” SIAM Journal on Scientific Computing.
2. Shidong Jiang, and Hai Zhu. 2024. “Recursive reduction quadrature for the evaluation of Laplace layer potentials in three dimensions.” arXiv preprint arXiv:2411.08342.

Please consider citing the above works if this code benefits your research.