In[]:=
Clear["Global`*"]
μ
0
=1.2610^-6;(*NA-2*)​​
ϵ
0
=8.8510^-12;(*Fm-1*)​​f=2.4510^9;(*Hz*)​​​​r=0.001;(*1mmfortesting,optimallyshouldbe15cm*)​​disk=Disk[{0,0},r];(*domainofsimulation*)​​​​eq=​​
∇
{x,y}

∇
{x,y}
e[t,x,y]+
μ
0
ϵ
0
D[e[t,x,y],{t,2}]==0​​​​(*boundaryconditions*)​​bc={DirichletCondition[e[t,x,y]==Sin[2Pift],x<=-0.3r]};​​(*initialconditions*)​​ic={DirichletCondition[e[t,x,y]==0,t==0]};
(*DoesnotreturndSol?*)​​dSol=DSolve[Flatten@{eq,bc,ic},e,{t,0,
-9
10
},{x,y}∈disk]
(*Complainsaboutinitialconditions,whenrunhangsforever*)​​ndSol=NDSolve[Flatten@{eq,bc,ic},e,{t,0,
-9
10
},{x,y}∈disk]
(*Samebehaviourasabove*)​​ndSolV=NDSolve[Flatten@{eq,bc,ic},e,{t,0,
-9
10
},{x,y}∈disk]