Sheehan I notice that ApproxFun handles 1D and 2D domains. Do you plan to extend it to 3D or 4D as well? Would that be complicated? If so, is this about software engineering, or about the numerical analysis behind the package?
-erik On Wed, Sep 10, 2014 at 6:22 PM, Sheehan Olver <[email protected]> wrote: > > This is to announce a new version of ApproxFun > (https://github.com/dlfivefifty/ApproxFun.jl), a package for approximating > functions. The biggest new feature is support for PDE solving. The > following lines solve Helmholtz equation u_xx + u_yy + 100 u = 0 with the > solution held to be one on the boundary: > > d=Interval()⊗Interval() # the domain to solve is a rectangle > > u=[dirichlet(d),lap(d)+100I]\ones(4) # first 4 entries are boundary > conditions, further entries are assumed zero > contour(u) # contour plot of the solution, > requires GadFly > > PDE solving is based on a recent preprint with Alex Townsend > (http://arxiv.org/abs/1409.2789). Only splitting rank 2 PDEs are > implemented at the moment. Examples included are: > > "examples/RectPDE Examples.ipynb": Poisson equation, Wave equation, > linear KdV, semiclassical Schrodinger equation with a potential, and > convection/convection-diffusion equations. > "examples/Wave and Klein–Gordon equation on a square.ipynb": On-the-fly > 3D simulation of time-evolution PDEs on a square. Requires GLPlot.jl > (https://github.com/SimonDanisch/GLPlot.jl). > "examples/Manipulate Helmholtz.upynb": On-the-fly variation of Helmholtz > frequency. Requires Interact.jl (https://github.com/JuliaLang/Interact.jl) > > Another new feature is faster root finding, thanks to Alex. -- Erik Schnetter <[email protected]> http://www.perimeterinstitute.ca/personal/eschnetter/
