Aggregation equation

The aggregation equations writes:

$$\partial_t \rho + \partial_x(a[\rho] \rho) = 0,$$

where $a[\rho] = -W' * \rho$ for $W: \mathbb{R} \longrightarrow \mathbb{R}$ sufficiently smooth ($W(x) = |x|$ or $W(x) = x^2 / 2$ for instance).

The convolution is computed using fast Fourier transforms. The CPU version is using the FFTW library while the CUDA version uses cuFFT.

Additional information

• The code is available here.

• Related documents:

  • B. Fabrèges, F. Lagoutière, S. Tran Tien and N. Vauchelet, Relaxation Limit of the Aggregation Equation with Pointy Potential, Axioms, 2021.
  • B. Fabrèges, H. Hivert, K. Le Balc’h, S. Martel, F. Delarue, F. Lagoutière and N. Vauchelet, Numerical schemes for the aggregation equation with pointy potentials, ESAIM: Proceedings and Surveys, 2019.