A hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity

Abstract: A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other discontinuities. This paper investigates discontinuous Galerkin methods for the solution of elliptic problems in numerical relativity. We present a novel hp-adaptive numerical scheme for curvilinear and non-conforming meshes. It uses a multigrid preconditioner with a Chebyshev or Schwarz smoother to create a very scalable discontinuous Galerkin code on generic domains. The code employs compactification to move the outer boundary near spatial infinity. We explore the properties of the code on some test problems, including one mimicking Neutron stars with phase transitions. We also apply it to construct initial data for two or three black holes.