A catalog of subroutines and functions used in GR_IRDR_ver4peos.f -- subroutine grav4(sou,pot,scmp,sicomp,pnagth,iesy,ilini,imini,iord) Poisson solver: the volume integral term subroutine grav4sfout(sousf,pot,scmp,sicomp,iesy,iaho,ilini,imini) Poisson solver: the surface integral term subroutine hegr4(sou,pot,scmp,sicomp,pnagth,iesy,ilini,imini,iord) Helmholtz solver: the volume integral term subroutine hegr4sfout(omega,sou,dsou,spot,scmp,sicomp,pnagth, Helmholtz solver: the surface integral term subroutine hrhafn(omega) Compute radial green's functino for the Helmholtz solver. subroutine sphbess(x,l,sj,sy) Spheircal bessel function for the radial green's function of the Helmholtz solver. -- subroutine halfsou(sou) Not used subroutine halfsousym(sou,ixysym,iyzsym,izxsym) Interpolate a source term on the grid points to the mid-points in r-cooridnate. subroutine halfsou2(sou,isy) Not used -- Coordinate patch kit (grid, sin, cos, Plm radial green's etc) subroutine nonvfl(iddd) For the fluid coordinate. subroutine nonvgr For the gravitational field coordinate. subroutine nonvint(rs) Not important -- Interpolation subroutine subroutine fl2grspl(flv,grv,rs,hhrg,rrrg,isw) From the fluid coordinate grid to the field coordinate grid. subroutine gr2flspl(grvo,flv,rs,isw,isweq) From the field coordinate grid to the fluid coordinate grid. subroutine vfl2vgrcap(gradf,gradg,rs,hhrg,rrrg,isw) Interporate the gradient of a fuction from the fluid coordinate grid to the field coordinate grid. subroutine vgr2vflcap(rs) Interporate from the field coordinate grid to the fluid coordinate grid. -- Input Output subroutine subroutine subio(istat,iseq,char) Input Output subroutine subroutine subiors(istat,iseq,char) Not important; with a different format, -- Calculations relating to source terms subroutine excurve(chgra) Calculations of the extrinsic curvature. subroutine liegmab Calculations of the Lie_phi gamma (for non-conformally flat metric) subroutine psisource(sou,chgra) Calculations of the source term of Hamiltonian constraint. Either one of two should be chosen. subroutine alpssource(sou,chgra) subroutine alps2source(sou,chgra) Calculations of the source term of for alpha*psi or alpha*psi^2 subroutine shiftsource(souvec,sou,chgra) Calculations of the source term of the Momentum constraint. subroutine hijsource(souten,chgra,chope,iter) Calculations of the source term of the h_ij (for non-conformally flat metric) subroutine surfsouscalar(fnc,ssou,dssou) Calculations of the source of the surface term subroutine surfhijsource(ssouten,dssouten,iter,chgra,chope) Calculations of the source of the surface term for hij -- Set variables subroutine ap2alps Compute alpha*psi from alpha and psi subroutine alps2ap Compute alpha from alpha*psi and psi subroutine bvu2d Lower the index of the shift: beta^a -> beta_a subroutine bvd2u Raise the index of the shift: beta_a -> beta^a subroutine bv2ov Compute the rotating shift from the shift: omega^a = beta^a + \Omega \phi^a subroutine invhij Raise the indexes of non-conformal flat part of the metric h_{ij} -> h^{ij} subroutine symmetry I don't remember. Probably impose symmetry to all functions subroutine cleargeometry Zero clear for the geometric variables relating to the conformal metric (Used for non-conformal flat metric) subroutine hijdet1(iter) Not used subroutine adjusthij(iter) Impose the determinant of the conformal metric to be 1. subroutine gauge(iter) Impose the Dirac gauge condition. subroutine adjustasymptopia(isaj) Adjust the value of the alpha and psi in the asymptotics. subroutine cristoffel Compute Cristoffel symbol of the conformal metric (for non-conformally flat metric) subroutine riccitensor Compute Ricci tensor of the conformal metric (for non-conformally flat metric) subroutine laphab(delhab,irg,itg,ipg) Not used -- Derivative relating subroutines subroutine dadbscalargsym(fnc,dabfnc,irg,itg,ipg,i,j,k) Compute the flat second derivatives of a function f, D_a D_b f subroutine dadbscalargsym_2(fnc,dabfnc,irg,itg,ipg, Not used subroutine dadbscalarg(fnc,dabfnc,irg,itg,ipg, Notused subroutine grderiv1r(fnc,deriv,irg,itg,ipg,ixysym,iyzsym,izxsym) Compute the (flat) r-derivative of a function f, D_r f subroutine grderiv1phi(fnc,deriv,irg,itg,ipg,ixysym,iyzsym,izxsym) Compute the (flat) phi-derivative of a function f, D_phi f subroutine grderiv2phi(fnc,deriv,irg,itg,ipg,ixysym,iyzsym,izxsym) Compute the (flat) 2nd phi-derivative of a function f, D^2_phi f subroutine grgrad4(fnc,grad,ixysym,iyzsym,izxsym) Compute the gradient of a function at ALL GR grid points. 4th order FD formula subroutine grgrad(fnc,dfdx,dfdy,dfdz,irg,itg,ipg,ixysym,iyzsym,izxsym) Compute the gradient of a function at ONE GR grid point. 4th order FD formula subroutine grgrad1g(fnc,grad1,irg,itg,ipg,ixysym,iyzsym,izxsym) Compute the gradient of a function at ONE GR grid point. 4th order FD formula (different format for the output) subroutine grgrad_2(fnc,dfdx,dfdy,dfdz,irg,itg,ipg, Not used. Compute the gradient of a function at ONE GR grid point. 2nd order FD subroutine grgrad1g_2(fnc,grad1,irg,itg,ipg,ixysym,iyzsym,izxsym) Not used. Compute the gradient of a function at ONE GR grid point. 2nd order FD (different format for the output) -- Update variables (with softning): subroutine grimpro(back,rnew,fffac,epsmax,irerr,iterr,iperr) Update metric variables subroutine flimpro(back,rnew,fffac,epsmax,irerr,iterr,iperr,isw) Update fluid variables subroutine rsimpro(back,rnew,fffac,epsmax,iterr,iperr) Update NS surface variables subroutine paimpro(ome,ber,radi,convf,iter,fmax0,isw) Update parameters for the irrotational BNS. subroutine paimproco(ome,ber,radi,convf,iter,fmax0,isw) Update parameters for the corotational BNS. -- Linear equation solver subroutine minv(aa,bb,nn,nnz) -- Compute mass, angular momentum and other quantities. subroutine physq(istat,iseq,chgra) -- Iteration to seek for a particular value of the rest mass. subroutine mascon(imascond,emxemd,ahores,emdc,restmass,emddiff, -- Compute the first integral of the equations of motion. subroutine fluid(iter,itmx,convf,cfvep,fmax0,ahores,emxemd,char) Compute the emden (or h-1) function and the velocity potential for the irrotational BNS. subroutine fluidco(iter,itmx,convf,cfvep,fmax0,ahores,emxemd,char) Compute the emden (or h-1) function and the velocity potential for the corotational BNS. subroutine gravep(sou,pot,wgrtp,scmp) Posson solver on the fluid coordinate. subroutine gravpot(sou,ddvpot,wgrtp,scmp,rs) Returns r derivative of the potential on the fluid cooridnate. subroutine sf2fc(sfv,fcv,rs) Interpolation from the surface fitted coordinate to the spherical coordinate for the fluid. subroutine fc2sf(fcv,sfv,rs) Interpolation from the spherical coordinate for the fluid to the surface fitted coordinate. -- Derivatives for the fluid variables: subroutine flgrad(fnc,grad,rs,isw,iswx) Compute the gradient of the fluid variable. 2nd order. subroutine flgrad4(fnc,grad,rs,isw,iswx) Compute the gradient of the fluid variable. 4th order. subroutine flgrad1f(fnc,ir,it,ip,grad1) Compute the gradient of the fluid variable. 4th order. Different format for the output. subroutine dadbscalarf(fnc,dabfnc,ir,it,ip) Compute the second derivatives of functions D_a D_b f subroutine flfcgrad4(fnc,grad,isw) Not used subroutine fouri(fp,dfp,scfn,scdf,isw) Not used -- subroutine maxden(emd,emdmx,ddmax) Search the location of the maximum density. subroutine lagint(x,n,y,v,f) Laglange interpolation with 4th order. subroutine subioca output values interpolated to the cartesian grid. -- Functions: Laglange formulas function d2fncdx2(xg,fnc,rv) 2nd derivatives function fn_lagint(x,y,v) 4th order Laglange interpolation function dfncdx(xg,fnc,rv) 1st derivative with 4th order. function dfncdx1st(xg,fnc,rv) 1st derivative with 1st order formula function dfncdx2nd(xg,fnc,rv) 1st derivative with 2nd order formula function dfncdx3rd(xg,fnc,rv) 1st derivative with 3rd order formula function d2fdx2_3rd(xg,fnc,rv) 2nd derivative with 3rd order formula