devito

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Symbolic PDE solver with automatic code generation for finite-difference computations. Use when Claude needs to: (1) Perform seismic wave propagation modeling, (2) Implement acoustic or elastic wave equations, (3) Run forward modeling for shot gathers, (4) Set up Full Waveform Inversion (FWI) workflows, (5) Implement Reverse Time Migration (RTM), (6) Create absorbing boundary conditions, (7) Generate optimized stencil code for CPUs/GPUs, (8) Solve custom PDEs with finite differences.

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Sourcesteadfastasart/geoscience-skills

Added on2026-05-16

NPX Install

npx skill4agent add steadfastasart/geoscience-skills devito

SKILL.md Content

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Devito - Symbolic PDE Solver

Quick Reference

python

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

python

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

python

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

python

# 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 / (v_max * 1.414)
3D	dx / (v_max * 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 (time_order=2, space_order=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 - Detailed operator construction
Performance Optimization - GPU execution and tuning

Scripts

scripts/acoustic_wave.py - Basic acoustic wave modeling

devito

NPX Install

Tags

SKILL.md Content

Devito - Symbolic PDE Solver

Quick Reference

Key Classes

Essential Operations

Grid and Fields

Source and Receivers

Build and Run

Symbolic Derivatives

Stability and Accuracy

When to Use vs Alternatives

Common Workflows

Acoustic wave forward modelling with sources and receivers

References

Scripts