Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects

Well-conditioned boundary integral methods for the solution of elliptic value problems (BVPs) are powerful tools static and dynamic physical simulations. When there many close-to-touching boundaries (e.g., in complex fluids) or when is needed bulk, nearly singular integrals must be evaluated at targets. We show that precomputing a linear map from surface density to an effective source representation renders this task highly efficient, common case where each object “simple”, i.e., its smooth needs only moderately nodes. present kernel-independent method needing upsampled quadrature, one dense factorization, distinct shape. No (near-)singular quadrature rules needed. The resulting sources drop-in compatible with fast algorithms, no local corrections nor bookkeeping. Our extensive numerical tests include 2D FMM-based Helmholtz Stokes BVPs up 1000 objects (281000 unknowns), 3D Laplace BVP 10 ellipsoids separated by 1/30 diameter. rigorous analysis analytic data 3D.