Kerr self-force via elliptic PDEs: Numerical methods (part 2)

          @misc{ pirsa_PIRSA:21060008,
            doi = {10.48660/21060008},
            url = {https://pirsa.org/21060008},
            author = {Osburn, Thomas},
            keywords = {Other},
            language = {en},
            title = {Kerr self-force via elliptic PDEs: Numerical methods (part 2)},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060008 see, \url{https://pirsa.org}}
          }
          

Abstract

I will discuss the numerical methods we use to calculate the self-force on a scalar charge orbiting a Kerr black hole. We apply a 2nd-order finite difference scheme on a rectangular grid in the r*-θ plane. By working in the frequency domain and separating the ϕ variable (but not θ) we encounter elliptic PDEs, which present certain numerical challenges. One challenge is that every grid point is coupled to every other grid point so that a simultaneous solution requires solving a large linear system. Another related challenge involves how imperfect boundary conditions can introduce errors that would inevitably pollute the entire domain. We have applied various techniques to overcome these challenges, such as analyzing the boundary behavior to impose more sophisticated boundary conditions with improved accuracy (for a fixed outer boundary position). Various preliminary self-force results will be presented and discussed.