Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
arXiv:1202.6522 · doi:10.1002/ggge.20071
Abstract
In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library which includes scalar and vector transforms. The main breakthrough is to achieve very efficient on-the-fly computations of the Legendre associated functions, even for very high resolutions, by taking advantage of the specific properties of the SHT and the advanced capabilities of current and future computers. This allows us to simultaneously and significantly reduce memory usage and computation time of the SHT. We measure the performance and accuracy of our algorithms. Even though the complexity of the algorithms implemented in SHTns are in (where N is the maximum harmonic degree of the transform), they perform much better than any third party implementation, including lower complexity algorithms, even for truncations as high as N=1023. SHTns is available at https://bitbucket.org/nschaeff/shtns as open source software.
8 pages
References in corpus (1)
Cited by in corpus (117)
- Turbulent geodynamo simulations: a leap towards Earth's core
- Spherical convective dynamos in the rapidly rotating asymptotic regime
- Scaling regimes in spherical shell rotating convection
- Magnetar formation through a convective dynamo in protoneutron stars
- Convective Lengthscale in Planetary Cores
- Approaching a realistic force balance in geodynamo simulations
- Force balance in numerical geodynamo simulations: a systematic study
- Turbulent Rayleigh-Bénard convection in spherical shells
- Large-Scale Mixing in a Violent Oxygen-Neon Shell Merger Prior to a Core-Collapse Supernova
- Libsharp - spherical harmonic transforms revisited
- Subcritical thermal convection of liquid metals in a rapidly rotating sphere
- Dynamo-based limit to the extent of a stable layer atop Earth's core
- Approaching Earth's core conditions in high-resolution geodynamo simulations
- Precessing spherical shells: flows, dissipation, dynamo and the lunar core
- Magnetic cycles in a dynamo simulation of fully convective M-star Proxima Centauri
- A global model of the magnetorotational instability in protoneutron stars
- Electrical conductivity of the lowermost mantle explains absorption of core torsional waves at the equator
- Active crystals on a sphere
- Stable stratification promotes multiple zonal jets in a turbulent Jovian dynamo model
- The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions
- Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo
- Orientational order on surfaces - the coupling of topology, geometry, and dynamics
- Deep rotating convection generates the polar hexagon on Saturn
- What sets the magnetic field strength and cycle period in solar-type stars?
- MRI-driven dynamos in protoneutron stars
- Geomagnetic semblance and dipolar-multipolar transition in top-heavy double-diffusive geodynamo models
- Three-Dimensional Hydrodynamic Simulations of Convective Nuclear Burning In Massive Stars Near Iron Core Collapse
- Unbiased pseudo-Cl power spectrum estimation with mode projection
- Rotating double-diffusive convection in stably stratified planetary cores
- A highly accurate boundary integral equation method for surfactant-laden drops in 3D
- Deep convection-driven vortex formation on Jupiter and Saturn
- Relating force balances and flow length scales in geodynamo simulations
- Spin-down by dynamo action in simulated radiative stellar layers
- A spectral scheme for Kohn-Sham density functional theory of clusters
- Magnetic fields driven by tidal mixing in radiative stars
- Spatio-angular fluorescence microscopy I. Basic theory
- On The Development of Multidimensional Progenitor Models For Core-collapse Supernovae
- Supergranulation and multiscale flows in the solar photosphere: Global observations vs. a theory of anisotropic turbulent convection
- Efficiency of tidal dissipation in slowly rotating fully convective stars or planets
- Fossil field decay due to nonlinear tides in massive binaries
- Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells
- Identification of inertial modes in the solar convection zone
- Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits
- High-order elastic multipoles as colloidal atoms
- Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment
- The Power of Halometry
- Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone
- The Effects of Robin Boundary Condition on Thermal Convection in a Rotating Spherical Shell
- Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere
- Europa's ocean translates interior tidal heating patterns to the ice-ocean boundary
- Numerical simulations of the Tayler-Spruit dynamo in proto-magnetars
- Mean zonal flows induced by weak mechanical forcings in rotating spheroids
- Transition from multipolar to dipolar dynamos in stratified systems
- Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity
- The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems
- Linking Zonal Winds and Gravity II: explaining the equatorially antisymmetric gravity moments of Jupiter
- Geomagnetic dipole stability and zonal flows controlled by mantle heat flux heterogeneities
- Effects of Emerging Bipolar Magnetic Regions in Mean-field Dynamo Model of Solar Cycles 23 and 24
- Fast computation of spherical phase-space functions of quantum many-body states
- Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability
- A Global Simulation of the Dynamo, Zonal Jets, and Vortices on Saturn
- Dynamic Domains of DTS: Simulations of a Spherical Magnetized Couette Flow
- Multi-Level Spectral Deferred Corrections Scheme for the Shallow Water Equations on the Rotating Sphere
- The Three-Dimensional Collapse of a Rapidly Rotating 16 Star
- Spectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds
- Fingering convection in the stably-stratified layers of planetary cores
- Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars
- Numerical analysis of lognormal diffusions on the sphere
- Moist Shallow Water Response to Tropical Forcing: Initial Value Problems
- On effects of surface bipolar magnetic regions on the convection zone dynamo
- Gravity darkening in late-type stars. The Coriolis effect
- Differentiable and accelerated spherical harmonic and Wigner transforms
- Core-surface kinematic control of polarity reversals in advanced geodynamo simulations
- Global simulations of Tayler instability in stellar interiors: a long-time multi-stage evolution of the magnetic field
- Magnetic induction and diffusion mechanisms in a liquid sodium spherical Couette experiment
- A Parallel Time-Integrator for Solving the Linearized Shallow Water Equations on the Rotating Sphere
- Lorentz force mediation of turbulent dynamo transitions
- Low inertia reversing geodynamos
- Kilohertz quasi-periodic oscillations from neutron star spreading layers
- Can Core Flows inferred from Geomagnetic Field Models explain the Earth's Dynamo?
- Acoustic and inertial modes in planetary-like rotating ellipsoids
- Can one use Earth's magnetic axial dipole field intensity to predict reversals?
- Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification
- Comparison of Quasi-Geostrophic, Hybrid and 3D models of planetary core convection
- Direct driving of simulated planetary jets by upscale energy transfer
- Implicit large eddy simulations of global solar convection: effects of numerical resolution in non-rotating and rotating cases
- Numerical reproduction of the spiral wave visualized experimentally in a wide-gap spherical Couette flow
- Approximation properties of the double Fourier sphere method
- Bifurcation aspect of wide-gap spherical Couette flow emphasizing polygonal coherence and wave numbers observed over transitional Reynolds numbers
- A dynamo simulation generating Saturn-like small magnetic dipole tilts
- On the meaning of the dynamo radius in giant planets with stable layers
- Axisymmetric pulse train solutions in narrow-gap spherical Couette flow
- Global Turbulent Solar Convection: a Numerical Path Investigating Key Force Balances in the context of the Convective Conundrum
- Transition to turbulence in the wide-gap spherical Couette system
- planetMagFields: A Python package for analyzing and plotting planetary magnetic field data
- An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus
- Characterisation of hydromagnetic waves propagating over a steady, non-axisymmetric background magnetic field
- A double Fourier sphere method for -dimensional manifolds
- Active smectics on a sphere
- Revisiting visualization of spiral states in a wide-gap spherical Couette flow
- Westward hotspot offset explained by subcritical dynamo action in an ultra-hot Jupiter atmosphere
- Active waves from non-reciprocity and cytoplasmic exchange
- Observational characterisation of large-scale transport and horizontal turbulent diffusivity in the quiet Sun
- Zonal flows driven by libration in rotating spherical shells: the case of periodic characteristic paths
- Zonal-mean atmospheric dynamics of slowly-rotating terrestrial planets
- Gravity's role in taming the Tayler instability in red giant cores
- Accelerating spherical harmonic transforms for a large number of sky maps
- A thermal convection limit of spiral state in wide-gap spherical Couette flow
- Adjoint-based Control of Three Dimensional Stokes Droplets
- Did lunar tides sustain the early Earth's dynamo?
- An extra-components method for evaluating fast matrix-vector multiplication with special functions
- Non-linear saturation of gravito-inertial modes excited by tidal resonances in binary neutron stars
- Convection in a Rapidly Rotating Spherical Shell: Newton's Method Using Implicit Coriolis Integration
- Large small-scale kinematic dynamo in protoneutron stars
- Influence of Rotation on Fingering Convection in Planetary Cores
- Inferring magnetic helicity spectrum in spherical domains: the method and example applications
- Regime transitions of dynamos driven by fingering double-diffusive convection