CTTK: a new method to solve the initial data constraints in numerical relativity

Eugene Lim; Katy Clough; Josu C. Aurrekoetxea

doi:10.1088/1361-6382/acb883

CTTK: a new method to solve the initial data constraints in numerical relativity

Eugene Lim, Katy Clough, Josu C. Aurrekoetxea

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Abstract

In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields’ configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.

Original language	English
Article number	075003
Journal	Classical and Quantum Gravity
Volume	40
Issue number	7
DOIs	https://doi.org/10.1088/1361-6382/acb883
Publication status	Published - 6 Mar 2023

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10.1088/1361-6382/acb883Licence: CC BY

Aurrekoetxea_2023_Class._Quantum_Grav._40_075003Licence: CC BY

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title = "CTTK: a new method to solve the initial data constraints in numerical relativity",

abstract = "In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields{\textquoteright} configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.",

author = "Eugene Lim and Katy Clough and Aurrekoetxea, {Josu C.}",

note = "Funding Information: We acknowledge useful conversations with David Garfinkle and Mark Hannam. We would also like to thank Francesco Muia for the Gaussian scalar field profiles. This Project has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (Grant Agreement No 693024). JCA acknowledges funding from the Beecroft Trust and The Queen{\textquoteright}s College via an extraordinary Junior Research Fellowship (eJRF). KC acknowledges funding from the ERC, and an STFC Ernest Rutherford Fellowship project reference ST/V003240/1. Funding Information: This work was performed using the Leibnitz Supercomputing Centre SuperMUC-NG under PRACE grant Tier-0 Proposal 2018194669, on the J{\"u}lich Supercomputing Center JUWELS HPC under PRACE grant Tier-0 Proposal 2020225359, COSMA7 in Durham and Leicester DiAL HPC under DiRAC RAC13 Grant ACTP238, and the Cambridge Data Driven CSD3 facility which is operated by the University of Cambridge Research Computing on behalf of the STFC DiRAC HPC Facility. The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1. Publisher Copyright: {\textcopyright} 2023 The Author(s). Published by IOP Publishing Ltd.",

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doi = "10.1088/1361-6382/acb883",

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N1 - Funding Information: We acknowledge useful conversations with David Garfinkle and Mark Hannam. We would also like to thank Francesco Muia for the Gaussian scalar field profiles. This Project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 693024). JCA acknowledges funding from the Beecroft Trust and The Queen’s College via an extraordinary Junior Research Fellowship (eJRF). KC acknowledges funding from the ERC, and an STFC Ernest Rutherford Fellowship project reference ST/V003240/1. Funding Information: This work was performed using the Leibnitz Supercomputing Centre SuperMUC-NG under PRACE grant Tier-0 Proposal 2018194669, on the Jülich Supercomputing Center JUWELS HPC under PRACE grant Tier-0 Proposal 2020225359, COSMA7 in Durham and Leicester DiAL HPC under DiRAC RAC13 Grant ACTP238, and the Cambridge Data Driven CSD3 facility which is operated by the University of Cambridge Research Computing on behalf of the STFC DiRAC HPC Facility. The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1. Publisher Copyright: © 2023 The Author(s). Published by IOP Publishing Ltd.

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N2 - In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields’ configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.

AB - In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields’ configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.

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DO - 10.1088/1361-6382/acb883

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VL - 40

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 7

M1 - 075003

ER -

CTTK: a new method to solve the initial data constraints in numerical relativity

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