Devito

Devito - Symbolic PDE Solver

Quick Reference

from devito import Grid, Function, TimeFunction, Eq, solve, Operator

# Create grid
grid = Grid(shape=(101, 101), extent=(1000., 1000.))

# Velocity model
v = Function(name='v', grid=grid, space_order=4)
v.data[:] = 1500.

# Wavefield
p = TimeFunction(name='p', grid=grid, time_order=2, space_order=4)

# Wave equation: d2p/dt2 = v^2 * laplacian(p)
stencil = Eq(p.forward, solve(p.dt2 - v**2 * p.laplace, p.forward))

# Compile and run
op = Operator([stencil])
op(time_M=100, dt=0.5)

Key Classes

| Class | Purpose | |-------|---------| | Grid | Computational domain definition | | Function | Spatial field on grid | | TimeFunction | Time-dependent field | | SparseTimeFunction | Point sources/receivers | | Operator | Compiled computation kernel |

Essential Operations

Grid and Fields

from devito import Grid, Function, TimeFunction

# 2D/3D Grid
grid = Grid(shape=(nx, nz), extent=(x_size, z_size))

# Velocity model (spatial field)
v = Function(name='v', grid=grid, space_order=4)
v.data[:] = 1500.

# Wavefield (time-dependent)
p = TimeFunction(name='p', grid=grid, time_order=2, space_order=4)

Source and Receivers

from examples.seismic import RickerSource, Receiver, TimeAxis

time_range = TimeAxis(start=0., stop=1000., step=dt)

# Source
src = RickerSource(name='src', grid=grid, f0=10., npoint=1, time_range=time_range)
src.coordinates.data[0, :] = [500., 20.]

# Receivers
rec = Receiver(name='rec', grid=grid, npoint=101, time_range=time_range)
rec.coordinates.data[:, 0] = np.linspace(0., 1000., 101)
rec.coordinates.data[:, 1] = 20.

Build and Run

# Wave equation
stencil = Eq(p.forward, solve(p.dt2 - v**2 * p.laplace, p.forward))
src_term = src.inject(field=p.forward, expr=src * dt**2 * v**2)
rec_term = rec.interpolate(expr=p)

# Compile and execute
op = Operator([stencil] + src_term + rec_term)
op(time_M=nt-1, dt=dt)

# Results
shot_record = rec.data        # (nt, nrec)
snapshot = p.data[0]          # Current wavefield

Symbolic Derivatives

| Syntax | Description | |--------|-------------| | p.dt, p.dt2 | First/second time derivative | | p.dx, p.dy, p.dz | Spatial derivatives | | p.laplace | Laplacian (auto-adapts to dims) | | p.forward | p at t+dt (time stepping) | | p.backward | p at t-dt (adjoint) |

Stability and Accuracy

CFL Condition: dt < dx / (v_max * sqrt(ndim))

| Dims | Max dt | |------|--------| | 2D | dx / (vmax 1.414) | | 3D | dx / (vmax 1.732) |

| Space Order | Stencil Points | Error | |-------------|----------------|-------| | 2 | 3 | O(h^2) | | 4 | 5 | O(h^4) | | 8 | 9 | O(h^8) |

Higher order = more accurate but slower. Use 4-8 for production.

When to Use vs Alternatives

| Scenario | Recommendation | |----------|---------------| | Seismic wave propagation (acoustic/elastic) | Devito - symbolic PDE, auto-optimized code | | Full Waveform Inversion (FWI) or RTM | Devito - adjoint support, GPU-ready | | Legacy seismic processing pipelines | Madagascar - established, large script library | | Simple 1D/2D wave demos | Custom NumPy - no dependencies, easier to debug | | General-purpose PDE solving (non-wave) | FEniCS - FEM-based, broader PDE support | | Production seismic imaging at scale | Devito - generates optimized C code, MPI support |

Choose Devito when: You need high-performance finite-difference wave propagation with symbolic equation specification. It auto-generates optimized C/OpenMP/GPU code from Python-level math, making it ideal for FWI, RTM, and research prototyping.

Avoid Devito when: You need finite-element methods (use FEniCS), or simple pedagogical examples where NumPy suffices.

Common Workflows

Acoustic wave forward modelling with sources and receivers

• [ ] Define Grid with shape and physical extent matching the velocity model
• [ ] Create velocity Function and populate with model values
• [ ] Create TimeFunction for the wavefield (timeorder=2, spaceorder=4+)
• [ ] Verify CFL condition: dt < dx / (v_max * sqrt(ndim))
• [ ] Build wave equation stencil: Eq(p.forward, solve(p.dt2 - v**2 * p.laplace, p.forward))
• [ ] Create source (RickerSource) and receivers, set coordinates
• [ ] Add source injection and receiver interpolation terms
• [ ] Compile Operator with stencil + source + receiver terms
• [ ] Run operator: op(time_M=nt-1, dt=dt)
• [ ] Extract shot record from rec.data and plot

References

• [Operators and Stencils](references/operators.md) - Detailed operator construction
• [Performance Optimization](references/performance.md) - GPU execution and tuning

Scripts

• [scripts/acousticwave.py](scripts/acousticwave.py) - Basic acoustic wave modeling

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: SteadfastAsArt
• Source: SteadfastAsArt/geoscience-skills
• License: MIT

Install and usage instructions live in the source repository linked above.