[Commits] [svn:einsteintoolkit] GRHydro_InitData/trunk/src/ (Rev. 190)

User: rhaas Date: 2013/01/11 09:04 AM

Modified: /trunk/src/ GRHydro_Bondi.c, GRHydro_BondiM.c

Log: GRHydro_InitData: implmented all of Bondi infall for KS coords only

From: Roland Haas roland.haas@physics.gatech.edu

File Changes:

Directory: /trunk/src/ ======================

File [modified]: GRHydro_Bondi.c Delta lines: +27 -19 =================================================================== --- trunk/src/GRHydro_Bondi.c 2013-01-11 15:04:01 UTC (rev 189) +++ trunk/src/GRHydro_Bondi.c 2013-01-11 15:04:03 UTC (rev 190) @@ -37,6 +37,7 @@ #include <math.h> #include <stdio.h> #include <stdlib.h> +#include <assert.h>

// set to 1 to tracing output #define LTRACE 1 @@ -129,7 +130,7 @@

for( i = 0 ; i < NDIM ; i++ ) { for( j = 0 ; j < NDIM ; j++ ) { - dxc_dxs[0][i] = 0. ; + dxc_dxs[j][i] = 0. ; } }

@@ -339,7 +340,6 @@ ****************************************************************************/ static void setutcon(CCTK_REAL *vcon, CCTK_REAL gcov[][NDIM]) { - int i,j; CCTK_REAL d,b,c;

d=gcov[TT][TT]; @@ -367,7 +367,7 @@ ****************************************************************************/ static void bl_gcov_func( CCTK_REAL *x, CCTK_REAL gcov[NDIM][NDIM]) { - int i,j,k ; + int i,j ; CCTK_REAL sth,cth,s2,r2,DD,mu ; CCTK_REAL r,th;

@@ -422,7 +422,6 @@ static void set_bondi_parameters( CCTK_REAL M_in, CCTK_REAL Mdot_in, CCTK_REAL rs_in, CCTK_REAL gam ) {

- CCTK_REAL my_pi, checkp; CCTK_REAL gtemp;

/* Set the solution-determining parameters: */ @@ -499,19 +498,18 @@ CCTK_REAL [][NEWT_DIM_B], CCTK_REAL *, CCTK_REAL *, int) ) { - CCTK_REAL f, df, dx[NEWT_DIM_B], x_old[NEWT_DIM_B], resid[NEWT_DIM_B], + CCTK_REAL f, df, dx[NEWT_DIM_B], resid[NEWT_DIM_B], jac[NEWT_DIM_B][NEWT_DIM_B]; - CCTK_REAL errx, x_orig[NEWT_DIM_B]; - int n_iter, id, jd, i_extra, doing_extra; + CCTK_REAL errx; + int n_iter, id, i_extra, doing_extra;

- int keep_iterating, i_increase; + int keep_iterating;

// Initialize various parameters and variables: errx = 1. ; df = f = 1.; i_extra = doing_extra = 0; - for( id = 0; id < n ; id++) x_old[id] = x_orig[id] = x[id] ;

n_iter = 0;

@@ -522,11 +520,7 @@

(*funcd) (x, dx, resid, jac, &f, &df, n); /* returns with new dx, f, df */

- /* Save old values before calculating the new: */ errx = 0.; - for( id = 0; id < n ; id++) { - x_old[id] = x[id] ; - }

/* don't use line search : */ for( id = 0; id < n ; id++) { @@ -662,19 +656,21 @@

if( *rho < 0. ) { if( r > 0.9*rs && r < 1.1*rs ) { - rho_guess = rhos; - *rho = rho_guess; + *rho = rhos; } else { // rhotmp = (sqrt(Qdot) - 1.) * (gamma_eos - 1.) / ( gamma_eos * K ); // rho_guess = pow( rhotmp , (1./(gamma_eos - 1.)) ); if(r < rs) { ur = pow(r,-0.5) ; } else { ur = 0.5*pow(r,-1.5) ; } - rho_guess = Mdot / (4.*M_PI * r * r * ur); - *rho = rho_guess; + *rho = Mdot / (4.*M_PI * r * r * ur); } - } + }

+ // safe guess value for multiple tries + rho_guess = *rho; + + // set global variables needed by residual function: r_sol = r ;

@@ -783,6 +779,10 @@ DLOOP2 { ucon[i] += dxc_dxs[i][j] * ucon_bl[j] ; } break;

+ default: + assert(0 && "Internal error"); + return; /* NOTREACHED */ + }

return; @@ -1007,6 +1007,8 @@ while( (j < (nbondi-1)) && (bad_bondi[j]) ) { j++; } if( (j==(nbondi-1)) && bad_bondi[j] ) { CCTK_WARN(CCTK_WARN_ABORT,"No available points with which to interpolate!\n"); + ileft = 0; /* NOTREACED */ + iright = 0; /* NOTREACHED */ } else { ileft = j ; @@ -1016,6 +1018,7 @@ while( (j < (nbondi-1)) && (bad_bondi[j]) ) { j++; } if( (j==(nbondi-1)) && bad_bondi[j] ) { CCTK_WARN(CCTK_WARN_ABORT,"Need another point to the right but cannot find one! \n"); + iright = 0; /* NOTREACHED */ } else { iright = j ; @@ -1036,6 +1039,7 @@ while( (j > 0) && (bad_bondi[j]) ) { j--; } if( (j==0) && bad_bondi[j] ) { CCTK_WARN(CCTK_WARN_ABORT,"Need another point to the left but cannot find one! \n"); + ileft = 0; /* NOTREACED */ } else { ileft = j; @@ -1059,7 +1063,7 @@

#if(LTRACE) for(i=0; i < nbondi; i++) { - CCTK_VWarn(CCTK_WARN_ALERT, __LINE__, __FILE__, CCTK_THORNSTRING,"radial-bondisoln %12d %26.16e %26.16e %26.16e %26.16e %12d \n",i,r_bondi[i],rho_bondi[i],u_bondi[i],v_bondi[i], bad_bondi[i]); + CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"radial-bondisoln %12d %26.16e %26.16e %26.16e %26.16e \n",i,r_bondi[i],rho_bondi[i],u_bondi[i],v_bondi[i]); } #endif

@@ -1089,6 +1093,10 @@ iso_cart_to_bl_spher_pos(xpos, x_spher); break;

+ default: + assert(0 && "Internal error"); + return; /* NOTREACHED */ + }

rspher = x_spher[RR];

File [modified]: GRHydro_BondiM.c Delta lines: +168 -39 =================================================================== --- trunk/src/GRHydro_BondiM.c 2013-01-11 15:04:01 UTC (rev 189) +++ trunk/src/GRHydro_BondiM.c 2013-01-11 15:04:03 UTC (rev 190) @@ -37,6 +37,7 @@ #include <math.h> #include <stdio.h> #include <stdlib.h> +#include <assert.h>

// set to 1 to tracing output #define LTRACE 1 @@ -81,7 +82,10 @@ #define EXTRA_NEWT_ITER_B (2 ) #define SMALL_BONDI (1.e-20)

+//some math helpers +#define SQR(x) ((x)*(x))

+ static CCTK_REAL Mdot, rs, vs_sq, vs, cs_sq, cs, rhos, hs, K, Qdot, gamma_eos, r_sol; static CCTK_REAL M, a, asq, Msq; static CCTK_REAL x_cen, y_cen, z_cen; @@ -121,7 +125,7 @@ for Kerr-Schild coordinates.

******************************************************************************/ -static void dxc_dxs_ks_calc(CCTK_REAL *x_cart, CCTK_REAL *x_spher, CCTK_REAL dxc_dxs[][NDIM] ) +static void dxc_dxs_ks_calc(CCTK_REAL *x_cart, CCTK_REAL *x_spher, CCTK_REAL dxc_dxs[NDIM][NDIM] ) { int i, j; CCTK_REAL r, th, ph; @@ -339,7 +343,6 @@ ****************************************************************************/ static void setutcon(CCTK_REAL *vcon, CCTK_REAL gcov[][NDIM]) { - int i,j; CCTK_REAL d,b,c;

d=gcov[TT][TT]; @@ -367,7 +370,7 @@ ****************************************************************************/ static void bl_gcov_func( CCTK_REAL *x, CCTK_REAL gcov[NDIM][NDIM]) { - int i,j,k ; + int i,j ; CCTK_REAL sth,cth,s2,r2,DD,mu ; CCTK_REAL r,th;

@@ -415,15 +418,15 @@ -- the Bondi solution here in is the isentropic, spherically symmetric, perfect fluid solution to Einstein's equations. That is, we only assume an r-dependence, there's a in-going radial velocity only, - and the EOS are : P = (G-1)*rho and P = K rho^G + and the EOS are : P = (G-1)*rho*eps and P = K rho^G where K = const. and G is the adiabatic constant "gam".

***************************************************************************/ static void set_bondi_parameters( CCTK_REAL M_in, CCTK_REAL Mdot_in, CCTK_REAL rs_in, CCTK_REAL gam ) {

- CCTK_REAL my_pi, checkp; CCTK_REAL gtemp; + static int first_call = 1;

/* Set the solution-determining parameters: */ M = M_in; @@ -454,20 +457,17 @@ Qdot = hs * hs * ( 1. - 3. * vs_sq ) ; gamma_eos = gam;

-#if( LTRACE ) - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"\n#######################################################\n"); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"Bondi Solution Parameters1: \n"); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"------------------------- \n\n"); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"M = %28.20e Mdot = %28.20e rs = %28.20e \n",M,Mdot,rs); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"vs = %28.20e cs = %28.20e rhos = %28.20e \n",vs,cs,rhos); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"hs = %28.20e K = %28.20e Qdot = %28.20e \n",hs,K,Qdot); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"gam= %28.20e r_sol= %28.20e \n",gamma_eos, r_sol); - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"rs = : %28.20e \n", rs) ; - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"urs = : %28.20e \n", vs) ; - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"rhos = : %28.20e \n", rhos) ; - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"K = : %28.20e \n", K) ; - CCTK_VWarn(CCTK_WARN_DEBUG, __LINE__, __FILE__, CCTK_THORNSTRING,"#######################################################\n\n"); -#endif + if( first_call ) { + CCTK_VInfo(CCTK_THORNSTRING,"#######################################################"); + CCTK_VInfo(CCTK_THORNSTRING,"Bondi Solution Parameters1: "); + CCTK_VInfo(CCTK_THORNSTRING,"-------------------------"); + CCTK_VInfo(CCTK_THORNSTRING,"M = %28.20e Mdot = %28.20e rs = %28.20e",M,Mdot,rs); + CCTK_VInfo(CCTK_THORNSTRING,"vs = %28.20e cs = %28.20e rhos = %28.20e",vs,cs,rhos); + CCTK_VInfo(CCTK_THORNSTRING,"hs = %28.20e K = %28.20e Qdot = %28.20e",hs,K,Qdot); + CCTK_VInfo(CCTK_THORNSTRING,"gam= %28.20e r_sol= %28.20e",gamma_eos, r_sol); + CCTK_VInfo(CCTK_THORNSTRING,"#######################################################"); + first_call = 0; + }

return;

@@ -499,19 +499,18 @@ CCTK_REAL [][NEWT_DIM_B], CCTK_REAL *, CCTK_REAL *, int) ) { - CCTK_REAL f, df, dx[NEWT_DIM_B], x_old[NEWT_DIM_B], resid[NEWT_DIM_B], + CCTK_REAL f, df, dx[NEWT_DIM_B], resid[NEWT_DIM_B], jac[NEWT_DIM_B][NEWT_DIM_B]; - CCTK_REAL errx, x_orig[NEWT_DIM_B]; - int n_iter, id, jd, i_extra, doing_extra; + CCTK_REAL errx; + int n_iter, id, i_extra, doing_extra;

- int keep_iterating, i_increase; + int keep_iterating;

// Initialize various parameters and variables: errx = 1. ; df = f = 1.; i_extra = doing_extra = 0; - for( id = 0; id < n ; id++) x_old[id] = x_orig[id] = x[id] ;

n_iter = 0;

@@ -522,11 +521,7 @@

(*funcd) (x, dx, resid, jac, &f, &df, n); /* returns with new dx, f, df */

- /* Save old values before calculating the new: */ errx = 0.; - for( id = 0; id < n ; id++) { - x_old[id] = x[id] ; - }

/* don't use line search : */ for( id = 0; id < n ; id++) { @@ -662,19 +657,21 @@

if( *rho < 0. ) { if( r > 0.9*rs && r < 1.1*rs ) { - rho_guess = rhos; - *rho = rho_guess; + *rho = rhos; } else { // rhotmp = (sqrt(Qdot) - 1.) * (gamma_eos - 1.) / ( gamma_eos * K ); // rho_guess = pow( rhotmp , (1./(gamma_eos - 1.)) ); if(r < rs) { ur = pow(r,-0.5) ; } else { ur = 0.5*pow(r,-1.5) ; } - rho_guess = Mdot / (4.*M_PI * r * r * ur); - *rho = rho_guess; + *rho = Mdot / (4.*M_PI * r * r * ur); } }

+ // safe guess value for multiple tries + rho_guess = *rho; + + // set global variables needed by residual function: r_sol = r ;

@@ -735,12 +732,115 @@

/***********************************************************************************/ /*********************************************************************************** + calc_b_bondi(): + --------- + -- calculates the contravariant magnetic vector Bcons from the amplitude of the + radial component of the contravariant magnetic field vector Boyer-Lindquist coordinates. + +***********************************************************************************/ +#if 0 +static void calc_b_bondi( CCTK_REAL B0, CCTK_REAL vtmp, CCTK_REAL x[NDIM], CCTK_REAL x_spher[NDIM], CCTK_REAL bcon[NDIM] ) +{ + int i,j; + CCTK_REAL bcon_bl[NDIM] = {0.}; // F^{ab} = (b^a u^b - b^b u^a) + CCTK_REAL bcon_ks[NDIM]; + CCTK_REAL gcov[NDIM][NDIM]; + CCTK_REAL r_iso; + CCTK_REAL dxc_dxs[NDIM][NDIM]; + CCTK_REAL f_bl = 1. - 2*M/x[RR]; + CCTK_REAL sqrt_detg_bl = SQR(x[RR])*sin(x[TH])/sqrt(f_bl); + CCTK_REAL lapse_bl = sqrt(f_bl); + + CCTK_REAL ucon_bl[NDIM] = {0.}; + CCTK_REAL w_lorentz_bl; // Lorentz factor in Boyer-Lindquist coords + + assert(a == 0.); + + ucon_bl[RR] = -vtmp; + + /* Find time component of 4-velocity: */ + bl_gcov_func( x_spher, gcov ); + setutcon( ucon_bl, gcov ); + w_lorentz_bl = lapse_bl*ucon_bl[TT]; + + /* Find time component of 4-velocity: */ + bcon_bl[RR] = B0*SQR(M)*w_lorentz_bl/sqrt_detg_bl; // -- " -- + bcon_bl[TT] = -gcov[RR][RR]/gcov[TT][TT] * bcon_bl[RR] * ucon_bl[RR]/ucon_bl[TT]; // Equ A16 of Villiers&Hawley (corrected) + + switch( coord_type ) { + + case COORD_BOYERLINDQUIST : + dxc_dxs_bl_calc(x, x_spher, dxc_dxs ); + DLOOP1 { bcon[i] = 0.; } + DLOOP2 { bcon[i] += dxc_dxs[i][j] * bcon_bl[j] ; } + break; + + + case COORD_KERRSCHILD : + bl_to_ks_con(x_spher,bcon_bl,bcon_ks); + dxc_dxs_ks_calc(x, x_spher, dxc_dxs ); + DLOOP1 { bcon[i] = 0.; } + DLOOP2 { bcon[i] += dxc_dxs[i][j] * bcon_ks[j] ; } + break; + + + case COORD_ISOTROPIC : + r_iso = x_spher[TT]; + bcon_bl[RR] /= 1. + 0.25 * (asq-Msq) / (r_iso*r_iso) ; /* BL to Isotropic coordinate transformation */ + /* I believe we can use BL's cartesian transformation, while using BL's radius : */ + dxc_dxs_iso_calc(x, x_spher, dxc_dxs ); + DLOOP1 { bcon[i] = 0.; } + DLOOP2 { bcon[i] += dxc_dxs[i][j] * bcon_bl[j] ; } + break; + + } + + return; +} +#endif +static void calc_b_bondi( CCTK_REAL B0, CCTK_REAL vtmp, CCTK_REAL x[NDIM], CCTK_REAL x_spher[NDIM], CCTK_REAL ucon[NDIM], CCTK_REAL bcon[NDIM]) +{ + int i,j; + CCTK_REAL bcon_spher[NDIM] = {0.}; // F^{ab} = (b^a u^b - b^b u^a) + CCTK_REAL ucon_spher[NDIM] = {0.}; + CCTK_REAL dxc_dxs[NDIM][NDIM]; + + assert(a == 0.); + assert(coord_type == COORD_KERRSCHILD); + + // Schwarzschild and spherical Kerr-Schild (Anil's Eddington coords) ^r components are identical + ucon_spher[RR] = -vtmp; + ucon_spher[TT] = (x_spher[RR] + (x_spher[RR]+2*M) * SQR(ucon_spher[RR])) / ( sqrt( (x_spher[RR]-2*M+x_spher[RR]*SQR(ucon_spher[RR]))*x_spher[RR] ) - 2*M*ucon_spher[RR] ); + + // Schwarzschild and Kerr-Schild ^t components differ since t_KS = t_SW + 2*M*ln(r/(2*M)-1) + // NB: we remove the sin(theta) factor from detg_BL since it factors out of the divergence operator + bcon_spher[RR] = B0*SQR(M)/SQR(x_spher[RR]) * // Equ A16 of Villiers&Hawley plus explict compuation of detg_BL and W_BL + sqrt(1-2*M/x_spher[RR] + SQR(ucon_spher[RR])); + bcon_spher[TT] = B0*SQR(M)/SQR(x_spher[RR]) * + (4*SQR(M) - SQR(ucon_spher[RR])*(SQR(x_spher[RR]+2*M*x_spher[RR]))) / + (2*M*sqrt(SQR(x_spher[RR])-2*M*x_spher[RR]+SQR(x_spher[RR]*ucon_spher[RR])) - + ucon_spher[RR]*SQR(x_spher[RR])); + + dxc_dxs_ks_calc(x, x_spher, dxc_dxs ); + + DLOOP1 { bcon[i] = 0.; } + DLOOP2 { bcon[i] += dxc_dxs[i][j] * bcon_spher[j] ; } + + DLOOP1 { ucon[i] = 0.; } + DLOOP2 { ucon[i] += dxc_dxs[i][j] * ucon_spher[j] ; } + + return; +} + +/***********************************************************************************/ +/*********************************************************************************** calc_vel_bondi(): --------- -- calculates the 4-velocity from the amplitude of the radial component of the 4-velocity in Boyer-Lindquist coordinates.

***********************************************************************************/ +#if 0 static void calc_vel_bondi( CCTK_REAL vtmp, CCTK_REAL x[NDIM], CCTK_REAL x_spher[NDIM], CCTK_REAL ucon[NDIM] ) { int i,j; @@ -783,10 +883,15 @@ DLOOP2 { ucon[i] += dxc_dxs[i][j] * ucon_bl[j] ; } break;

+ default: + assert(0 && "Internal error"); + return; /* NOTREACHED */ + }

return; } +#endif

/***********************************************************************************/ /*********************************************************************************** @@ -800,7 +905,7 @@ DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; CCTK_REAL det; - CCTK_REAL rhotmp, utmp, vtmp, rspher, xpos[NDIM], x_spher[NDIM], ucon[NDIM]; + CCTK_REAL rhotmp, utmp, vtmp, rspher, xpos[NDIM], x_spher[NDIM], ucon[NDIM], bcon[NDIM]; int retval; CCTK_REAL *r_bondi, *logr_bondi, *rho_bondi, *u_bondi, *v_bondi; CCTK_REAL dlogr,logrmin; @@ -818,6 +923,12 @@ # define sx(i_) scon[i_ + 0*size] # define sy(i_) scon[i_ + 1*size] # define sz(i_) scon[i_ + 2*size] +# define Bconsx(i_) Bcons[i_ + 0*size] +# define Bconsy(i_) Bcons[i_ + 1*size] +# define Bconsz(i_) Bcons[i_ + 2*size] +# define Bvecx(i_) Bvec[i_ + 0*size] +# define Bvecy(i_) Bvec[i_ + 1*size] +# define Bvecz(i_) Bvec[i_ + 2*size]

if( CCTK_EQUALS(bondi_coordinates,"Boyer-Lindquist") ) { coord_type = COORD_BOYERLINDQUIST ; @@ -986,7 +1097,6 @@ xpos[YY] = y[i] ; xpos[ZZ] = z[i] ;

- switch( coord_type ) {

case COORD_BOYERLINDQUIST : @@ -997,11 +1107,14 @@ ks_cart_to_ks_spher_pos( xpos, x_spher); break;

- case COORD_ISOTROPIC : iso_cart_to_bl_spher_pos(xpos, x_spher); break;

+ default: + assert(0 && "Internal error"); + return; /* NOTREACHED */ + }

rspher = x_spher[RR]; @@ -1032,7 +1145,7 @@

rho[i] = rhotmp; eps[i] = utmp/rhotmp; - calc_vel_bondi(vtmp, xpos, x_spher, ucon); + calc_b_bondi(bondi_bmag, vtmp, xpos, x_spher, ucon, bcon);

det = 1./alp[i]; /* temp var */

@@ -1040,15 +1153,25 @@ vely(i) = (ucon[YY]/ucon[TT] + betay[i]) * det; velz(i) = (ucon[ZZ]/ucon[TT] + betaz[i]) * det;

+ w_lorentz[i] = 1./sqrt(1-(gxx[i]*SQR(velx(i))+gyy[i]*SQR(vely(i))+gzz[i]*SQR(velz(i))+ + 2*(gxy[i]*velx(i)*vely(i)+gxz[i]*velx(i)*velz(i)+gyz[i]*vely(i)*velz(i))) );

+ Bvecx(i) = w_lorentz[i]*bcon[XX] - alp[i]*bcon[TT]*ucon[XX]; + Bvecy(i) = w_lorentz[i]*bcon[YY] - alp[i]*bcon[TT]*ucon[YY]; + Bvecz(i) = w_lorentz[i]*bcon[ZZ] - alp[i]*bcon[TT]*ucon[ZZ]; + SpatialDet(gxx[i],gxy[i],gxz[i],gyy[i],gyz[i],gzz[i],&det);

- Prim2ConGen(*GRHydro_eos_handle,gxx[i],gxy[i], + Prim2ConGenM(*GRHydro_eos_handle,gxx[i],gxy[i], gxz[i],gyy[i],gyz[i],gzz[i], det, &dens[i],&sx(i),&sy(i),&sz(i), - &tau[i],rho[i], + &tau[i], + &Bconsx(i),&Bconsy(i),&Bconsz(i), + rho[i], velx(i),vely(i),velz(i), - eps[i],&press[i],&w_lorentz[i]); + eps[i],&press[i], + Bvecx(i),Bvecy(i),Bvecz(i), + &w_lorentz[i]);

}

@@ -1061,6 +1184,12 @@ # undef sx # undef sy # undef sz +# undef Bconsx +# undef Bconsy +# undef Bconsz +# undef Bvecx +# undef Bvecy +# undef Bvecz

return;