The recent discovery of gravitational waves by Advanced LIGO ushered in a new kind of astronomy, one potentially integrating its findings with those obtained from electromagnetic and/or neutrino observations. Multi-messenger astronomy promises to revolutionize our understanding of the universe by providing dramatically contrasting views of the same objects. To understand this unprecedented wealth of observational evidence, theoretical calculations are required in order to link data with underlying physics. However, these demand the creation of new computational tools that can handle an increasingly wide range of physical treatments, characteristic scales, and levels of complexity. The main thrust of this project is to develop some of these tools.
The principal goals supported by this award are to introduce two new techniques into the repertory of physicists and astrophysicists studying strong-field gravity: multipatch methods and regularized spherical coordinates. The former is an infrastructure to permit efficient computation of heterogeneous systems involving multiple kinds of physics, multiple length scales, and multiple reference frames. The latter is a way to systematically remove from partial differential equations the singularity ordinarily arising at the polar axis. We expect both will be of great value to studies of astrophysical objects in dynamical spacetimes. To make this introduction, we will generalize our multipatch infrastructure to make it freely compatible with many codes, including Athena++, The Einstein Toolkit, and Harm3D; we will introduce regularized spherical coordinates into the numerical relativity and MHD solvers of both the Einstein Toolkit and the widely used relativistic magnetohydrodynamics code Harm3D; and we will demonstrate the results on selected science problems. With Advanced LIGO now fully operational and the detection of additional gravitational wave events imminent, we expect that there will be a surge in the number of researchers interested in performing simulations of compact binary mergers. Our new curvilinear and multipatch frameworks will greatly improve the efficiency and ease with which such simulations may be carried out, thereby improving the accuracy of the predictions made for all the messengers---gravitational waves, photons, and neutrinos---of multi-messenger astronomy.