Tarang.jl

A High-Performance Spectral PDE Solver for Julia

CPU | GPU | MPI Distributed | Symbolic Equations

Features

Spectral Methods

Fourier, Chebyshev, and Legendre bases
Spectral accuracy for smooth solutions
Automatic differentiation operators

GPU Acceleration

Native CUDA support with cuFFT
KernelAbstractions.jl backend
Automatic CPU/GPU dispatch

MPI Parallelization

PencilArrays pencil decomposition
Scalable to thousands of cores
Efficient distributed FFTs

Symbolic Equations

Natural mathematical syntax for PDEs
Automatic operator construction
Flexible boundary conditions

Quick Start

Installation

using Pkg

# Basic installation
Pkg.add(url="https://github.com/subhk/Tarang.jl")

# With GPU support
Pkg.add(["CUDA", "KernelAbstractions"])

# With MPI support
Pkg.add(["MPI", "PencilArrays", "PencilFFTs"])

1D Diffusion

using Tarang

domain = PeriodicDomain(64)                     # 64-point periodic [0, 2π]
T = ScalarField(domain, "T")                    # Temperature field

problem = IVP([T])
add_parameters!(problem, kappa=0.01)
add_equation!(problem, "∂t(T) - kappa*Δ(T) = 0")

solver = InitialValueSolver(problem, RK222(); dt=0.01)
run!(solver; stop_time=1.0)                     # That's it!

2D Rayleigh-Benard Convection

using Tarang

# Channel domain: periodic in x (Fourier), bounded in z (Chebyshev)
domain = ChannelDomain(256, 64; Lx=4.0, Lz=1.0)

u = VectorField(domain, "u")                   # Velocity
T = ScalarField(domain, "T")                   # Temperature
p = ScalarField(domain, "p")                   # Pressure

problem = IVP([u, p, T])
add_parameters!(problem, Pr=1.0, Ra=2e6)
add_equation!(problem, "∂t(u) - Pr*Δ(u) + ∇(p) - Ra*Pr*T*ez = -u⋅∇(u)")
add_equation!(problem, "div(u) = 0")
add_equation!(problem, "∂t(T) - Δ(T) = -u⋅∇(T)")
add_bc!(problem, "u(z=0) = 0")
add_bc!(problem, "u(z=1) = 0")
add_bc!(problem, "T(z=0) = 1")
add_bc!(problem, "T(z=1) = 0")

solver = InitialValueSolver(problem, RK222(); dt=1e-3)
diagnose(solver)                                # Print solver summary
run!(solver; stop_time=10.0, log_interval=100)  # Run with progress

Pro Tip

Use diagnose(solver) at any time to inspect field layout, compiled RHS status, dealiasing mode, and memory usage.

GPU Example

using Tarang, CUDA

# Just add device=GPU() — everything else stays the same
domain = PeriodicDomain(512, 512; device=GPU(), dtype=Float32)
field = ScalarField(domain, "u")
forward_transform!(field)   # Uses cuFFT automatically

Scientific Applications

Fluid Dynamics

Navier-Stokes, Rayleigh-Benard convection, channel flow, jets

Turbulence

LES models (Smagorinsky, AMD), stochastic forcing, GQL approximation

Magnetohydrodynamics

MHD with magnetic fields, dynamo problems, magnetic dissipation

Geophysical Flows

Rotating shallow water, stratified turbulence, surface dynamics

Problem Types

Type	Description	Example
IVP	Initial Value Problems	Time-dependent Navier-Stokes
BVP	Boundary Value Problems	Steady-state solutions
EVP	Eigenvalue Problems	Linear stability analysis
LBVP	Linear BVPs	Poisson equation
NLBVP	Nonlinear BVPs	Steady nonlinear systems

Spectral Bases

Basis	Domain	Usage
`RealFourier`	Periodic	Horizontal directions, real-valued fields
`ComplexFourier`	Periodic	Complex-valued fields
`ChebyshevT`	Bounded	Wall-bounded domains, boundary conditions
`Legendre`	Bounded	Alternative to Chebyshev

Documentation

Installation

Setup and configuration

Tutorials

Step-by-step guides

GPU Guide

CUDA acceleration

API Reference

Complete documentation

Installation Options

Setup	Command	Use Case
Basic	`Pkg.add(url="...")`	Single CPU, getting started
GPU	`+ CUDA, KernelAbstractions`	NVIDIA GPU acceleration
MPI	`+ MPI, PencilArrays, PencilFFTs`	Cluster computing
Full	All of the above	Maximum flexibility

Requirements

Julia 1.10 or later
For GPU: NVIDIA GPU with CUDA support
For MPI: OpenMPI or MPICH installed

Contributing

We welcome contributions! See our GitHub repository for:

Bug reports and feature requests
Documentation improvements
Pull requests

Citation

If you use Tarang.jl in your research, please cite:

@software{tarang_jl,
  author = {Kar, Subhajit},
  title  = {Tarang.jl: A Spectral PDE Solver for Julia},
  url    = {https://github.com/subhk/Tarang.jl},
  year   = {2024}
}

License

Tarang.jl is released under the MIT License.

Made for the scientific computing community