Spectral solution of Poisson equation over infinite branched channel

In this paper, we present a direct spectral collocation method for solving Poisson equation in polar coordinates. This equation is expressed spectrally over the unit circle. The resulting equation in spectral form is solved to give a solution to Poisson equation with Dirichlet boundary conditions at collocation points. The unit circle domain is conformally transformed to Y-geometry, retaining the value of the solution to give the solution of the same problem over Y-shape channel. Poisson equation can be solved similarly over many other geometries. The method is easy to implement, fast and gives spectral accuracy.