Solving the gravitational self-force problem with numerical relativity methods

For the upcoming space-based gravitational-wave detector LISA we will need to simulate binary black holes with extreme mass ratios (EMRIs). To achieve the required accuracy for these simulations we will have to compute the gravitational self-force acting on a small body in Kerr spacetime to second order in perturbation theory. In this talk I present a computational approach towards this goal based on numerical solutions of elliptic partial differential equations, which is made feasible using technology developed for large-scale numerical relativity simulations. I demonstrate how we use discontinuous Galerkin methods, task-based parallelism, and the iterative elliptic solver algorithms developed for binary black hole initial data problems to solve for the self-force acting on a scalar charge in Kerr spacetime, and present progress towards solving the gravitational self-force problem with this technology.