Solve a Wave Equation with Absorbing Boundary Conditions
Solve a 1D wave equation with absorbing boundary conditions.
Specify a wave equation with absorbing boundary conditions. Note that the Neumann value is for the first time derivative of 
.
In[1]:=
eqn = D[u[t, x], {t, 2}] ==
D[u[t, x], {x, 2}] +
NeumannValue[-Derivative[1, 0][u][t, x], x == 0 || x == 1];Specify initial conditions for the wave equation.
In[2]:=
u0[x_] := Evaluate[D[0.125 Erf[(x - 0.5)/0.125], x]];
ic = {u[0, x] == u0[x], Derivative[1, 0][u][0, x] == 0};Solve the equation using the finite element method.
In[3]:=
ufun = NDSolveValue[{eqn, ic}, u, {t, 0, 1}, {x, 0, 1},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"FiniteElement"}}];Visualize the wave equation with absorbing boundary conditions.
In[4]:=
list = Table[
Plot[ufun[t, x], {x, 0, 1}, PlotRange -> {-0.1, 1.3}], {t, 0, 1,
0.1}];
ListAnimate[list]
