1:34 PM
I'm going to put here in the chat room a block of code of 40 lines. I have done some tests in the sandbox chat room, so It should work. It's rather tiedous and slow. Hope it will not disturb anyone. This block of code will probably be use for further discussions. Thanks.
sh=2/10;sh2=2/100;sw=3/10;
coordinatesList={{0,0},{1,0},{1,sh},{1,1},{0,1},{0,sh+sh2},{sw,sh+sh2},{sw,sh},{0,sh}};
bmesh=ToBoundaryMesh["Coordinates"-> coordinatesList,"BoundaryElements"->{LineElement[{{1,2},{2,3},{3,4},{4,5},{5,6},{6,7},{7,8},{8,9},{9,1},{3,8}}]}];
bmeshRotated=ToBoundaryMesh["Coordinates"->((RotationMatrix[45 Degree] . #)& /@ coordinatesList),"BoundaryElements"->{LineElement[{{1,2},{2,3},{3,4},{4,5},{5,6},{6,7},{7,8},{8,9},{9,1},{3,8}}]}];
Row[{bmesh["Wireframe"],bmeshRotated["Wireframe"]}]
{mesh,meshRotated}=ToElementMesh /@ {bmesh,bmeshRotated};
{gr01,gr02}=Through[{mesh,meshRotated} @ "Wireframe"]
\[Epsilon]r=If[y<=sh,{{11.7,0.},{0.,11.7}},{{1.,0},{0.,1.}}];
\[Epsilon]rModified=If[(-x+y)/Sqrt[2]<=sh,{{11.7,0.},{0.,11.7}},{{1.,0},{0.,1.}}];
{ContourPlot[Norm[\[Epsilon]r],{x,-0.1,1.1},{y,-0.1,1.1},PlotLegends->Automatic,Epilog->First[gr01]],ContourPlot[Norm[\[Epsilon]rModified],{x,-1,1},{y,0.,2.},PlotLegends->Automatic,Epilog->First[gr02]]} //Row
op=Inactive[Div][-\[Epsilon]r.Inactive[Grad][u[x,y],{x,y}],{x,y}]-\[Rho]c/\[Epsilon]0;
opModified=Inactive[Div][-\[Epsilon]rModified.Inactive[Grad][u[x,y],{x,y}],{x,y}]-\[Rho]c/\[Epsilon]0;
\[CapitalGamma]D={DirichletCondition[u[x,y]==0,x==1||y==1||y==0],DirichletCondition[u[x,y]==10^3,0<=x<=sw&&sh<=y<=sh+sh2]};
\[CapitalGamma]DModified={DirichletCondition[u[x,y]==0,y==-x+Sqrt[2]||y==x+Sqrt[2]||y==x],DirichletCondition[u[x,y]==10^3,0<=(x+y)/Sqrt[2]<=sw&&sh<=(y-x)/Sqrt[2]<=sh+sh2]};
ufun=NDSolveValue[{op==0,\[CapitalGamma]D},u,{x,y}\[Element]mesh];
ufunModifed=NDSolveValue[{opModified==0,\[CapitalGamma]DModified},u,{x,y}\[Element]meshRotated];
{Show[ContourPlot[ufun[x,y],{x,y}\[Element]mesh, ColorFunction->"Temperature"],bmesh["Wireframe"]],Show[ContourPlot[ufunModifed[x,y],{x,y}\[Element]meshRotated, ColorFunction->"Temperature"],bmeshRotated["Wireframe"]]} //Row // Style[#,ImageSizeMultipliers->{1, 1}]&
I have finish to write my block of code. Sorry for the interruption.
Here is the result of the code above :
