SOLVING BOUNDARY AND VOLUME INTEGRAL EQUATIONS WITH INTI.JL

Despite their potential, integral equation methods face under-utilization compared to popular methods like finite elements and finite differences. This is largely attributed to the challenges associated with the discretization of the integral operators—which usually contain singular kernels—and to the difficulties related to the efficient approximation of the dense linear systems that arise. In this paper, we introduce Inti.jl, a Julia package designed to solve volume and boundary integral equations using Nyström methods. Inti.jl provides the fundamental building blocks for discretizing and manipulating various commonly used integral opera- tors appearing in mathematical physics, such as the single- and double-layer operators, as well as volume potentials, for many problems of physical interest. The library is freely available at github.com/IntegralEquations/Inti.jl.