1 files changed, 132 insertions, 0 deletions
diff --git a/src/bhbrill3d.m b/src/bhbrill3d.m
new file mode 100644
index 0000000..ef7bccc
--- /dev/null
+++ b/src/bhbrill3d.m
@@ -0,0 +1,132 @@
+$Path = Union[$Path,{"~/SetTensor"}];
+Needs["SetTensor`"];
+
+Dimension = 3;
+x[1] = eta; x[2] = q; x[3] = phi
+qf[eta_,q_,phi_] := amp (Exp[-(eta-eta0)^2/sigma^2]+Exp[-(eta+eta0)^2/sigma^2]) Sin[q]^n (1+c Cos[phi]^2)
+
+md = {
+{Exp[2 qf[eta,q,phi]],0,0},
+{0,Exp[2 qf[eta,q,phi]],0},
+{0,0,Sin[q]^2}} psisph[eta,q,phi]^4;
+InitializeMetric[md];
+
+Clear[exc];
+DefineTensor[exc];
+SetTensor[exc[la,lb],{{0,0,0},{0,0,0},{0,0,0}}];
+
+tmp = RicciR[la,lb] Metricg[ua,ub]+exc[la,lb] Metricg[ua,ub] exc[lc,ld] Metricg[uc,ud]-
+  exc[la,lb] exc[lc,ld] Metricg[ua,uc] Metricg[ub,ud];
+tmp = RicciToAffine[tmp];
+tmp = EvalMT[tmp];
+tmp = ExpandAll[-Exp[2 qf[eta,q,phi]] psisph[eta,q,phi]^5/8 tmp]
+sav=tmp
+tmp = SubFun[sav,psisph[eta,q,phi],2 Cosh[eta/2]+psisph[eta,q,phi]]
+
+(* Make the stencil... *)
+
+stencil = ExpandAll[tmp /. {
+ D[psisph[eta,q,phi],eta]->(psisph[i+1,j,k]-psisph[i-1,j,k])/(2 deta),
+ D[psisph[eta,q,phi],eta,eta]->(psisph[i+1,j,k]+psisph[i-1,j,k]-2 psisph[i,j,k])/(deta deta),
+ D[psisph[eta,q,phi],q]->(psisph[i,j+1,k]-psisph[i,j-1,k])/(2 dq),
+ D[psisph[eta,q,phi],q,q]->(psisph[i,j+1,k]+psisph[i,j-1,k]-2 psisph[i,j,k])/(dq dq),
+ D[psisph[eta,q,phi],phi]->(psisph[i,j,k+1]-psisph[i,j,k-1])/(2 dphi),
+ D[psisph[eta,q,phi],phi,phi]->(psisph[i,j,k+1]+psisph[i,j,k-1]-2 psisph[i,j,k])/(dphi dphi),
+ psisph[eta,q,phi]->psisph[i,j,k]
+ }];
+
+ac = Coefficient[stencil,psisph[i,j,k]]
+an = Coefficient[stencil,psisph[i+1,j,k]]
+as = Coefficient[stencil,psisph[i-1,j,k]]
+ae = Coefficient[stencil,psisph[i,j,k+1]]
+aw = Coefficient[stencil,psisph[i,j,k-1]]
+aq = Coefficient[stencil,psisph[i,j+1,k]]
+ab = Coefficient[stencil,psisph[i,j-1,k]]
+rhs = -SubFun[tmp,psisph[eta,q,phi],0]
+
+FortranOutputOfDepList = "(i,j,k)";
+$FortranReplace = Union[{
+      "UND"->"_",
+      "(eta,q,phi)"->"(i,j,k)"
+}];
+fd = FortranOpen["bhbrill3d.x"];
+FortranWrite[fd,An[i,j,k],an ];
+FortranWrite[fd,As[i,j,k],as ];
+FortranWrite[fd,Ae[i,j,k],ae ];
+FortranWrite[fd,Aw[i,j,k],aw ];
+FortranWrite[fd,Aq[i,j,k],aq ];
+FortranWrite[fd,Ab[i,j,k],ab ];
+FortranWrite[fd,Ac[i,j,k],ac ];
+FortranWrite[fd,Rhs[i,j,k],rhs ];
+FortranClose[fd];
+
+(* Next part, write out conformal g's and d's *)
+
+
+xv = Exp[eta] Sin[q] Cos[phi];
+yv = Exp[eta] Sin[q] Sin[phi];
+zv = Exp[eta] Cos[q];
+
+mc = Table[ D[ {xv,yv,zv}[[i]], {eta,q,phi}[[j]] ],{i,1,3},{j,1,3}];
+mci = Simplify[Inverse[mc]];
+
+Clear[mct];
+DefineTensor[mct,{{1,2},1}];
+Iter[mct[ua,lb],
+  mct[ua,lb]=mc[[ua,-lb]];
+];
+
+Clear[mcti];
+DefineTensor[mcti,{{1,2},1}];
+Iter[mcti[ua,lb],
+  mcti[ua,lb]=mci[[ua,-lb]];
+];
+
+gijtmp = Exp[2 eta]/psisph[eta,q,phi]^4 Metricg[lc,ld] mcti[uc,la] mcti[ud,lb]
+
+Clear[i2];
+DefineTensor[i2,{{2,1},1}];
+
+fd = FortranOpen["gij.x"];
+Iter[i2[ua,ub],
+  v1 = {x,y,z}[[ua]];
+  v2 = {x,y,z}[[ub]];
+  metv = ToExpression["g"<>ToString[v1]<>ToString[v2]<>"[i,j,k]"];
+  gg[v1,v2]=Simplify[EvalMT[gijtmp,{la->-ua,lb->-ub}]];
+  FortranWrite[fd,metv,gg[v1,v2]];
+  For[ii=1,ii<=3,ii++,
+    v3 = {x,y,z}[[ii]];
+    dmetv = ToExpression["d"<>ToString[v3]<>ToString[metv]];
+    res = OD[gg[v1,v2],lc] mcti[uc,ld]/2;
+    res = EvalMT[res,ld-> -ii];
+    res = Simplify[res];
+    FortranWrite[fd,dmetv,res];
+  ];
+];
+FortranClose[fd];
+
+$FortranReplace = {
+  "UND"->"_",
+  "(eta,q,phi)"->""
+};
+
+fd = FortranOpen["psi_1st_deriv.x"];
+For[ii=1,ii<=3,ii++,
+  v1 = {x,y,z}[[ii]];
+  psv =ToExpression["psi"<>ToString[v1]<>"[i,j,k]"];
+  rhs = CD[Exp[-eta/2] psi3d[eta,q,phi],lc] mcti[uc,la];
+  rhs = EvalMT[rhs,{la->-ii}]/(Exp[-eta/2] psi3d[eta,q,phi]);
+  FortranWrite[fd,psv,rhs];
+];
+FortranClose[fd];
+
+fd = FortranOpen["psi_2nd_deriv.x"];
+Iter[i2[ua,ub],
+  v1 = {x,y,z}[[ua]];
+  v2 = {x,y,z}[[ub]];
+  psv = ToExpression["psi"<>ToString[v1]<>ToString[v2]<>"[i,j,k]"];
+  rhs = OD[OD[Exp[-eta/2] psi3d[eta,q,phi],lc] mcti[uc,la],ld] mcti[ud,lb];
+  rhs = EvalMT[rhs,{la->-ua,lb->-ub}]/(Exp[-eta/2] psi3d[eta,q,phi]);
+  FortranWrite[fd,psv,rhs];
+];
+FortranClose[fd];