Accuracy enhancement of the equivalence principle algorithm based on the meshless spherical surface

Conventional equivalence principle algorithm (EPA) employs cubical boxes to support equivalence sources. However, it introduces strong discontinuities. In this work, a spherical surface is employed as the equivalence surface in EPA to avoid singularities from non-smooth surfaces. Further to achieve high order accuracy, meshless samples are used for the integrals on the spherical surface to avoid the equivalence surface mesh discretization. Theoretically the accuracy of EPA can be significantly improved, which was further benchmarked though numerical examples. Various meshless schemes are also discussed to achieve the optimal solution based on the spherical equivalence surface.