Discontinuous collocation methods and gravitational self-force applications

Numerical simulations of extereme mass ratio inspirals, the mostimportant sources for LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations self-force acting on point particles orbiting supermassive holes. Such are distributionally sourced, standard numerical methods, such as finite-difference or spectral difficulties associated with approximating discontinuous functions. However, problem we typically have access full a-priori information about local structure discontinuity at particle. Using this information, show that high-order accuracy can be recovered by adding Lagrange interpolation formula linear combination certain jump amplitudes. construct spatial temporal discretizations operating corrected formula. In method-of-lines framework, provides simple efficient method solving time-dependent equations, without loss near moving singularities discontinuities. This is well-suited time-domain reconstruction metric via Teukolsky Regge-Wheeler-Zerilli formalisms. Parallel implementations modern CPU GPU architectures discussed.