A spectral method algorithm for numerical simulations of gravitational fields

Abstract A numerical study of the Einstein field equations, based on 3 + 1 foliation spacetime, is presented. pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely Arnowitt–Deser–Misner (ADM) and conformal Baumgarte–Shapiro–Shibata–Nakamura (BSSN) approach. The code Fourier decomposition, accompanied by filtering techniques. role dealiasing, as well influence filter type, investigated. algorithms have stabilized via a novel procedure that controls self-consistently regularity solutions. accuracy model validated through standard testbeds, revealing filtered among most accurate approaches. Finally, stressed black hole dynamics new strategy, hyperviscous dissipation suppresses spurious boundary problems, proposed. represents valid tool investigation, particularly suitable inspection small scale nonlinear phenomena gravitational dynamics.