🚫 VERY IMPORTANT NOTE: This repository is discontinued from 28/02/2022. GridapODEs has been merged into Gridap. Its development continues here 🚫
This package provides time integration tools for Gridap. As an example, the following code solves the heat equation.
using Gridap
using ForwardDiff
using GridapODEs.ODETools
using GridapODEs.TransientFETools
θ = 0.5
u(x,t) = (1.0-x[1])*x[1]*(1.0-x[2])*x[2]*t
u(t) = x -> u(x,t)
f(t) = x -> ∂t(u)(x,t)-Δ(u(t))(x) # or ∂t(u)(t)(x)-Δ(u(t))(x)
domain = (0,1,0,1)
partition = (4,4)
model = CartesianDiscreteModel(domain,partition)
order = 2
reffe = ReferenceFE(lagrangian,Float64,order)
V0 = FESpace(
model,
reffe,
conformity=:H1,
dirichlet_tags="boundary"
)
U = TransientTrialFESpace(V0,u)
Ω = Triangulation(model)
degree = 2*order
dΩ = Measure(Ω,degree)
a(u,v) = ∫( ∇(v)⋅∇(u) )dΩ
b(v,t) = ∫( v*f(t) )dΩ
m(u,v) = ∫( v*u )dΩ
res(t,u,v) = a(u,v) + m(∂t(u),v) - b(v,t)
jac(t,u,du,v) = a(du,v)
jac_t(t,u,dut,v) = m(dut,v)
op = TransientFEOperator(res,jac,jac_t,U,V0)
t0 = 0.0
tF = 1.0
dt = 0.1
U0 = U(0.0)
uh0 = interpolate_everywhere(u(0.0),U0)
ls = LUSolver()
ode_solver = ThetaMethod(ls,dt,θ)
sol_t = solve(ode_solver,op,uh0,t0,tF)
for (uh_tn, tn) in sol_t
# Here we have the solution uh_tn at tn
endIn order to give credit to the Gridap and GridapODEs contributors, we simply ask you to cite the Gridap main project as indicated here and the sub-packages you use as indicated in the corresponding repositories. Please, use the reference below in any publication in which you have made use of GridapODEs:
@misc{Badia_GridapODEs_2021,
author = {Badia, Santiago and Colomes, Oriol and Verdugo, Francesc},
doi = {10.5281/zenodo.5518455},
month = {9},
title = {{GridapODEs}},
url = {https://github.com/gridap/GridapODEs.jl},
year = {2021}
}