FastEarth3D
A fast, open-source, time-domain spectral–finite-element solid-Earth model
FastEarth3D is a fast, open-source 3D solid-Earth model: a self-gravitating, incompressible, Maxwell-viscoelastic sphere coupled to a self-consistent sea-level equation with migrating coastlines. It is designed as an open-source replacement for VILMA inside the CLIMBER-X Earth system model (Willeit et al. 2022), and more generally as a reusable glacial isostatic adjustment (GIA) engine for ice-sheet and sea-level work.
The numerical method follows the spectral–finite-element, time-domain approach of Martinec (2000): spherical harmonics horizontally, finite elements radially, and an explicit memory-stress integration of the Maxwell rheology in time. The solver is 3D-ready from the start — laterally varying viscosity costs nothing extra — and is validated first in 1D against the published GIA community benchmarks (Spada et al. 2011; Martinec et al. 2018).
Why this method
The structural advantage of this approach is that, with an explicit Maxwell time scheme, the stiffness solve has no angular coupling. Each spherical-harmonic degree \(\ell\) decouples into an independent, small, banded radial system. This makes the solver embarrassingly parallel and cheap, and lateral (3D) viscosity is free: it never couples the harmonics in the solve, entering only through the explicitly-known memory stress. That memory stress is evaluated pointwise on the Gauss–Legendre grid and transformed back to spectral space each step, a pseudo-spectral treatment. The 1D and 3D code paths are therefore the same solver.
| Method family | Examples | 3D viscosity | Speed | Fit for purpose |
|---|---|---|---|---|
| Normal-mode + Love numbers + SLE | SELEN, TABOO, ALMA3 | no (1D only) | fast (1D) | dead end for 3D |
| Time-domain spectral–FE | VILMA (Martinec 2000) | yes | fast | chosen |
| Full 3D FE/FV | CitcomSVE, ASPECT, Elmer | yes | slow, heavy | too complex |
What is in these docs
- Install & run — building with
configme, the&fe3dnamelist, the drivers, and staging runs withrunme. - Physics — the governing equations (momentum, Poisson, incompressibility), the Maxwell rheology and its memory stress, the sea-level equation, and rotational feedback.
- Discretization — the spectral reduction, the P1/P0 radial finite-element operator, the explicit time scheme, and the banded direct solver.
- Benchmarks — a summary table of validation results, with one page per benchmark (Love numbers, the disc-load response, and the sea-level-equation intercomparison).
- Implementation — the libraries the model builds on, and the codebases and datasets that informed the validation.
Status
The full model is implemented. The core includes the spectral–finite-element solver, the viscoelastic time stepping and response operator, the self-consistent migrating-coastline sea-level equation, rotational feedback (polar motion), and laterally varying (3D) viscosity. It also supports restart and spin-up, online remapping of lon-lat forcing, and a host-coupling API.
Validation against the Spada et al. (2011) and Martinec et al. (2018) community benchmarks covers the radial solver, the disc-load response, and the sea-level equation. Rotation is checked against the Spada test 3/2. Cross-code validation of the 3D viscosity path is ongoing (see the validation ladder).