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

Vincent, Trevor; Pfeiffer, Harald P.; Fischer, Nils L.

doi:10.1103/PhysRevD.100.084052

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

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Pfeiffer, Harald P.
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Vincent, T., Pfeiffer, H. P., & Fischer, N. L. (2019). hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity. Physical Review D, 100(8): 084052. doi:10.1103/PhysRevD.100.084052.

Cite as: https://hdl.handle.net/21.11116/0000-0004-3A87-3

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.