Sundials for Julia

Introduction

Sundials.jl is a Julia package that interfaces to the Sundials library. Sundials (the C library and this package) provides the following:

• CVODE - for integration of ordinary differential equation systems (ODEs). CVODE treats stiff and nonstiff ODE systems of the form y' = f(t,y), y(t0) = y0
• CVODES - for integration and sensitivity analysis of ODEs. CVODES treats stiff and nonstiff ODE systems of the form y' = f(t,y,p), y(t0) = y0(p)
• IDA - for integration of differential-algebraic equation systems (DAEs). IDA treats DAE systems of the form F(t,y,y') = 0, y(t0) = y0, y'(t0) = y0'
• IDAS - for integration and sensitivity analysis of DAEs. IDAS treats DAE systems of the form F(t,y,y',p) = 0, y(t0) = y0(p), y'(t0) = y0'(p)
• KINSOL - for solution of nonlinear algebraic systems. KINSOL treats nonlinear systems of the form F(u) = 0

Julia is a fast, Matlab-like language that is well suited to modeling and simulations. It's particularly suited for use with Sundials because the functions representing the system will run at nearly the speed of C functions. Julia functions are compiled on the fly (JIT), so it is also possible to quickly recompile a system to model structural changes to the system.

I use Sundials in Sims, a Julia package to support equation-based modeling for simulations. Sims is like a lite version of Modelica. Sims can currently use Sundials or DASSL.

API

This package closely follows the Sundials C API. At a slightly higher level, many (but not all) Sundials.jl functions support passing Julia objects (like Arrays) instead of Sundials objects (like N_Vectors). See src/Sundials.jl for examples of how the higher-level interfacing works.

The Julia package Clang.jl was used to wrap Sundials. This directly uses Sundials' headers sort-of like SWIG. This is great work by Isaiah--it didn't take me much work to package a pretty complete interface to Sundials. For the wrapping code, see src/wrap_sundials.jl.

Because of Clang.jl, Sundials.jl provides good coverage of the Sundials library (the serial version).

Simplified Functions

Three functions kinsol, ode, and dae are provided as high-level, very simple functions. Here is an example for ode:

using Sundials

function f(t, y, ydot)
    ydot[1] = -0.04*y[1] + 1.0e4*y[2]*y[3]
    ydot[3] = 3.0e7*y[2]*y[2]
    ydot[2] = -ydot[1] - ydot[3]
end

t = [0.0, 4 * logspace(-1., 7., 9)]
res = Sundials.ode(f, [1.0, 0.0, 0.0], t)

Feedback on these simple functions is encouraged. Once Julia has keyword arguments for functions, it will be easier to add features to these basic functions.

Examples

See the examples directory.

Three-Body Problem is a notebook with a more thoroughly explained example.

Status

Please note that this is a developer preview. There could be bugs, and everything is subject to change. Of note are:

• You must have the Sundials installed.
• The API that matches the Sundials C API should be stable.
• The simplified API is not stable.
• There is no documentation for this package. Please see the general C documentation for Sundials. The API should be identical.
• Macros like DENSE_ELEM are not available.
• Nothing is (yet) exported from the module. You need to put Sundials. in front of everything.
• Parts of the Sundials API that access C structures are difficult. One can use the StrPack package to read or write to these structures, but nothing is built into this package. See this CVODE example.
• The parallel versions of Sundials have been wrapped, but I doubt that they are useable from Julia. Julia doesn't have an MPI interface that I am aware of.
• More work could be done to provide a better interface to N_Vectors.