Using the heat equation and Neumann Values in mathematica I've been trying to visualise heat diversions in 2D. The code used is here :
Needs["NDSolveFEM"]
Clear["Global`*"]
(Define the spatial domain as a square[0,1] x[0,1]) domain = Rectangle[{0, 0}, {1, 1}];
(Create a mesh for the 2D spatial domain) mesh = ToElementMesh[domain, "MaxCellMeasure" -> 0.01];
(Define your temperature distribution at t=0 as an interpolation
function)
fI = Interpolation[
Flatten[Table[{{x, y}, 20}, {x, 0, 1, 0.1}, {y, 0, 1, 0.1}], 1]];
(Define the heat conduction equation in 2D) eqn = D[T[t, x, y], t] - Laplacian[T[t, x, y], {x, y}] == 0;
(Set initial condition) IC = T[0, x, y] == 20;
(Set up Neumann boundary conditions to simulate insulation in 2D
using NeumannValue)
BC = {NeumannValue[0, True]};
NDSolve[{eqn == BC, IC}, T, {t, 0, 20}, {x, y} [Element] mesh]
But I keep getting the same error : error message obtained while running the program on the latest version of Mathematica
I've tried to remove the {} around the NeumannValue as I assume it's causing the error but I only obtain a singular matrix which can't solve the equation. Even Chat-GPT crashed while trying to explain the error. All help is appreciated !