Julia is an innovative new programming language that promises to revolutionize scientific computing. In a nutshell, it is
Julia's main innovation is a carefully-designed type system combined with just-in-time compilation. The combination allows high-level user code to be compiled to machine-code on-the-fly.
The benchmark algorithm here is a simple time-integration of the Kuramoto-Sivashniksy equation
on a 1d periodic domain , with space and time, and where subscripts indicate differentiation. The algorithm uses a Fourier decomposition in space and 2nd-order Crank-Nicolson, Adams-Bashforth semi-implicit finite-differencing in time, with collocation computation of the nonlinear term . I implemented the same algorithm in Python, Matlab, C++, and in two forms in Julia. The codes and a detailed description of the algorithm is given below.
The left plot shows execution time of 3200 time steps of the algorithm as a function of , the number of gridpoints in the Fourier decomposition. The dominant cost of the algorithm should be the FFTs, which should scale as . All the codes use the same FFTW libraries, so ideally, they should all collapse onto the same line as linear and fixed-size overheads costs decrease relative to that.
The right plot shows