The best linear solver for sparse bandedblockbandedmatricies

ChrisRackauckas · May 24, 2020, 5:40am

And it’s still a little early, but there’s DiffEqOperators.jl for helping with auto-discretizations, along with the other 5 libraries on this topic, like NeuralNetDiffEq.jl for other cases, etc.

FEniCS.jl gives you a discretization you give to DifferentialEquations:

github.com

SciML/FEniCS.jl/blob/master/examples/heat_equation.jl

"""
Solve the heat equation ∂ₜu = Δu on [0,1] using OrdinaryDiffEq for time stepping.
Boundary conditions are such that an analytic solution is given by:
    sin(2π*x) * exp(-(2*π)^2*t)

This example demonstrates how to solve time dependent PDE's combining `fenics` and `DiffEq`.

"""
module HeatEquationExample

using Test
using OrdinaryDiffEq
using FEniCS

mesh = UnitIntervalMesh(50)
V = FunctionSpace(mesh, "P", 1)
u_str = "sin(2*pi*x[0]) * exp(-t*pow(2*pi, 2))"

tspan = (0.0, 0.1)
u = interpolate(Expression(u_str, degree = 2, pi = Float64(pi), t = tspan[1]), V)

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Etc.

So that’s finite difference, mesh-free neural net methods, and FEM. Then we point to ApproxFun for pseudospectral.

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The best linear solver for sparse bandedblockbandedmatricies

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