https://github.com/geodynamics/citcoms
Tip revision: f8f8ac9d2debc000a1b14bbe2468aa3a3b16d3bd authored by Rajesh Kommu on 18 April 2014, 22:33:36 UTC
Minor cleanup related to caps_per_proc removal
Minor cleanup related to caps_per_proc removal
Tip revision: f8f8ac9
Stokes_flow_Incomp.c
/*
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
*
*<LicenseText>
*
* CitcomS by Louis Moresi, Shijie Zhong, Lijie Han, Eh Tan,
* Clint Conrad, Michael Gurnis, and Eun-seo Choi.
* Copyright (C) 1994-2005, California Institute of Technology.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*</LicenseText>
*
*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
*/
/* Functions which solve for the velocity and pressure fields using Uzawa-type iteration loop. */
#include <math.h>
#include <string.h>
#include <sys/types.h>
#include "element_definitions.h"
#include "global_defs.h"
#include <stdlib.h>
void myerror(struct All_variables *,char *);
static void solve_Ahat_p_fhat(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max);
static void solve_Ahat_p_fhat_CG(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max);
static void solve_Ahat_p_fhat_BiCG(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max);
static void solve_Ahat_p_fhat_iterCG(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max);
static void initial_vel_residual(struct All_variables *E,
double *V, double *P, double *F,
double imp);
/* Master loop for pressure and (hence) velocity field */
void solve_constrained_flow_iterative(E)
struct All_variables *E;
{
void v_from_vector();
void v_from_vector_pseudo_surf();
void p_to_nodes();
int cycles;
cycles=E->control.p_iterations;
/* Solve for velocity and pressure, correct for bc's */
solve_Ahat_p_fhat(E,E->U,E->P,E->F,E->control.accuracy,&cycles);
if(E->control.pseudo_free_surf)
v_from_vector_pseudo_surf(E);
else
v_from_vector(E);
p_to_nodes(E,E->P,E->NP,E->mesh.levmax);
}
/* ========================================================================= */
static double momentum_eqn_residual(struct All_variables *E,
double *V, double *P, double *F)
{
/* Compute the norm of (F - grad(P) - K*V)
* This norm is ~= E->monitor.momentum_residual */
void assemble_del2_u();
void assemble_grad_p();
void strip_bcs_from_residual();
double global_v_norm2();
int i, m;
double *r1, *r2;
double res;
const int lev = E->mesh.levmax;
const int neq = E->lmesh.neq;
r1 = malloc((neq+1)*sizeof(double));
r2 = malloc((neq+1)*sizeof(double));
/* r2 = F - grad(P) - K*V */
assemble_grad_p(E, P, E->u1, lev);
assemble_del2_u(E, V, r1, lev, 1);
for(i=0; i<neq; i++)
r2[i] = F[i] - E->u1[i] - r1[i];
strip_bcs_from_residual(E, r2, lev);
res = sqrt(global_v_norm2(E, r2));
free(r1);
free(r2);
return(res);
}
static void print_convergence_progress(struct All_variables *E,
int count, double time0,
double v_norm, double p_norm,
double dv, double dp,
double div)
{
double CPU_time0(), t;
t = CPU_time0() - time0;
fprintf(E->fp, "(%03d) %5.1f s v=%e p=%e "
"div/v=%.2e dv/v=%.2e dp/p=%.2e step %d\n",
count, t, v_norm, p_norm, div, dv, dp,
E->monitor.solution_cycles);
fprintf(stderr, "(%03d) %5.1f s v=%e p=%e "
"div/v=%.2e dv/v=%.2e dp/p=%.2e step %d\n",
count, t, v_norm, p_norm, div, dv, dp,
E->monitor.solution_cycles);
fflush(stderr);
}
static int keep_iterating(struct All_variables *E,
double acc, int converging)
{
const int required_converging_loops = 2;
if(E->control.check_continuity_convergence)
return (E->monitor.incompressibility > acc) ||
(converging < required_converging_loops);
else
return (E->monitor.incompressibility > acc) &&
(converging < required_converging_loops);
}
static void solve_Ahat_p_fhat(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max)
{
if(E->control.inv_gruneisen == 0)
solve_Ahat_p_fhat_CG(E, V, P, F, imp, steps_max);
else {
if(strcmp(E->control.uzawa, "cg") == 0)
solve_Ahat_p_fhat_iterCG(E, V, P, F, imp, steps_max);
else if(strcmp(E->control.uzawa, "bicg") == 0)
solve_Ahat_p_fhat_BiCG(E, V, P, F, imp, steps_max);
else
myerror(E, "Error: unknown Uzawa iteration\n");
}
}
/* Solve incompressible Stokes flow using
* conjugate gradient (CG) iterations
*/
static void solve_Ahat_p_fhat_CG(struct All_variables *E,
double *V, double *P, double *FF,
double imp, int *steps_max)
{
int m, j, count, valid, lev, npno, neq;
double *r1, *r2, *z1, *s1, *s2, *cu;
double *F;
double *shuffle;
double alpha, delta, r0dotz0, r1dotz1;
double v_res;
double inner_imp;
double global_pdot();
double global_v_norm2(), global_p_norm2(), global_div_norm2();
double time0, CPU_time0();
double v_norm, p_norm;
double dvelocity, dpressure;
int converging;
void assemble_c_u();
void assemble_div_u();
void assemble_del2_u();
void assemble_grad_p();
void strip_bcs_from_residual();
int solve_del2_u();
void parallel_process_termination();
void v_from_vector();
void v_from_vector_pseudo_surf();
void assign_v_to_vector();
inner_imp = imp * E->control.inner_accuracy_scale; /* allow for different innner loop accuracy */
npno = E->lmesh.npno;
neq = E->lmesh.neq;
lev = E->mesh.levmax;
F = (double *)malloc(neq*sizeof(double));
r1 = (double *)malloc((npno+1)*sizeof(double));
r2 = (double *)malloc((npno+1)*sizeof(double));
z1 = (double *)malloc((npno+1)*sizeof(double));
s1 = (double *)malloc((npno+1)*sizeof(double));
s2 = (double *)malloc((npno+1)*sizeof(double));
cu = (double *)malloc((npno+1)*sizeof(double));
time0 = CPU_time0();
count = 0;
v_res = E->monitor.fdotf;
/* copy the original force vector since we need to keep it intact
between iterations */
for(j=0;j<neq;j++)
F[j] = FF[j];
/* calculate the contribution of compressibility in the continuity eqn */
if(E->control.inv_gruneisen != 0) {
for(j=1;j<=npno;j++)
cu[j] = 0.0;
assemble_c_u(E, V, cu, lev);
}
/* calculate the initial velocity residual */
/* In the compressible case, the initial guess of P might be bad.
* Do not correct V with it. */
if(E->control.inv_gruneisen == 0)
initial_vel_residual(E, V, P, F, inner_imp*v_res);
/* initial residual r1 = div(V) */
assemble_div_u(E, V, r1, lev);
/* add the contribution of compressibility to the initial residual */
if(E->control.inv_gruneisen != 0)
for(j=1;j<=npno;j++)
r1[j] += cu[j];
E->monitor.vdotv = global_v_norm2(E, V);
E->monitor.incompressibility = sqrt(global_div_norm2(E, r1)
/ (1e-32 + E->monitor.vdotv));
v_norm = sqrt(E->monitor.vdotv);
p_norm = sqrt(E->monitor.pdotp);
dvelocity = 1.0;
dpressure = 1.0;
converging = 0;
if (E->control.print_convergence && E->parallel.me==0) {
print_convergence_progress(E, count, time0,
v_norm, p_norm,
dvelocity, dpressure,
E->monitor.incompressibility);
}
r0dotz0 = 0;
while( (count < *steps_max) && keep_iterating(E, imp, converging) ) {
/* require two consecutive converging iterations to quit the while-loop */
/* preconditioner BPI ~= inv(K), z1 = BPI*r1 */
for(j=1; j<=npno; j++)
z1[j] = E->BPI[lev][j] * r1[j];
/* r1dotz1 = <r1, z1> */
r1dotz1 = global_pdot(E, r1, z1, lev);
assert(r1dotz1 != 0.0 /* Division by zero in head of incompressibility iteration */);
/* update search direction */
if(count == 0)
for(j=1; j<=npno; j++)
s2[j] = z1[j];
else {
/* s2 = z1 + s1 * <r1,z1>/<r0,z0> */
delta = r1dotz1 / r0dotz0;
for(j=1; j<=npno; j++)
s2[j] = z1[j] + delta * s1[j];
}
/* solve K*u1 = grad(s2) for u1 */
assemble_grad_p(E, s2, F, lev);
valid = solve_del2_u(E, E->u1, F, inner_imp*v_res, lev);
if(!valid && (E->parallel.me==0)) {
fputs("Warning: solver not converging! 1\n", stderr);
fputs("Warning: solver not converging! 1\n", E->fp);
}
strip_bcs_from_residual(E, E->u1, lev);
/* F = div(u1) */
assemble_div_u(E, E->u1, F, lev);
/* alpha = <r1, z1> / <s2, F> */
alpha = r1dotz1 / global_pdot(E, s2, F, lev);
/* r2 = r1 - alpha * div(u1) */
for(j=1; j<=npno; j++)
r2[j] = r1[j] - alpha * F[j];
/* P = P + alpha * s2 */
for(j=1; j<=npno; j++)
P[j] += alpha * s2[j];
/* V = V - alpha * u1 */
for(j=0; j<neq; j++)
V[j] -= alpha * E->u1[j];
/* compute velocity and incompressibility residual */
E->monitor.vdotv = global_v_norm2(E, V);
E->monitor.pdotp = global_p_norm2(E, P);
v_norm = sqrt(E->monitor.vdotv);
p_norm = sqrt(E->monitor.pdotp);
dvelocity =
alpha * sqrt(global_v_norm2(E, E->u1) / (1e-32 + E->monitor.vdotv));
dpressure =
alpha * sqrt(global_p_norm2(E, s2) / (1e-32 + E->monitor.pdotp));
assemble_div_u(E, V, z1, lev);
if(E->control.inv_gruneisen != 0)
for(j=1;j<=npno;j++)
z1[j] += cu[j];
E->monitor.incompressibility = sqrt(global_div_norm2(E, z1)
/ (1e-32 + E->monitor.vdotv));
count++;
if (E->control.print_convergence && E->parallel.me==0) {
print_convergence_progress(E, count, time0,
v_norm, p_norm,
dvelocity, dpressure,
E->monitor.incompressibility);
}
if(!valid){
/* reset consecutive converging iterations */
converging = 0;
}else{
/* how many consecutive converging iterations? */
if(E->control.check_pressure_convergence) {
/* check dv and dp */
if(dvelocity < imp && dpressure < imp)
converging++;
else
converging = 0;
}else{
/* check dv only */
if(dvelocity < imp)
converging++;
else
converging = 0;
}
}
/* shift array pointers */
shuffle = s1;
s1 = s2;
s2 = shuffle;
shuffle = r1;
r1 = r2;
r2 = shuffle;
/* shift <r0, z0> = <r1, z1> */
r0dotz0 = r1dotz1;
if((E->sphere.caps == 12) && (E->control.inner_remove_rigid_rotation)){
/* allow for removal of net rotation at each iterative step
(expensive) */
if(E->control.pseudo_free_surf) /* move from U to V */
v_from_vector_pseudo_surf(E);
else
v_from_vector(E);
remove_rigid_rot(E); /* correct V */
assign_v_to_vector(E); /* assign V to U */
}
} /* end loop for conjugate gradient */
assemble_div_u(E, V, z1, lev);
if(E->control.inv_gruneisen != 0)
for(j=1;j<=npno;j++)
z1[j] += cu[j];
free((void *) F);
free((void *) r1);
free((void *) r2);
free((void *) z1);
free((void *) s1);
free((void *) s2);
free((void *) cu);
*steps_max=count;
}
/* Solve compressible Stokes flow using
* bi-conjugate gradient stablized (BiCG-stab) iterations
*/
static void solve_Ahat_p_fhat_BiCG(struct All_variables *E,
double *V, double *P, double *FF,
double imp, int *steps_max)
{
void assemble_div_rho_u();
void assemble_del2_u();
void assemble_grad_p();
void strip_bcs_from_residual();
int solve_del2_u();
void parallel_process_termination();
double global_pdot();
double global_v_norm2(), global_p_norm2(), global_div_norm2();
double CPU_time0();
int npno, neq;
int m, j, count, lev;
int valid;
double alpha, beta, omega,inner_imp;
double r0dotrt, r1dotrt;
double v_norm, p_norm;
double dvelocity, dpressure;
int converging;
double *F;
double *r1, *r2, *pt, *p1, *p2;
double *rt, *v0, *s0, *st, *t0;
double *u0;
double *shuffle;
double time0, v_res;
inner_imp = imp * E->control.inner_accuracy_scale; /* allow for different innner loop accuracy */
npno = E->lmesh.npno;
neq = E->lmesh.neq;
lev = E->mesh.levmax;
F = (double *)malloc(neq*sizeof(double));
r1 = (double *)malloc((npno+1)*sizeof(double));
r2 = (double *)malloc((npno+1)*sizeof(double));
pt = (double *)malloc((npno+1)*sizeof(double));
p1 = (double *)malloc((npno+1)*sizeof(double));
p2 = (double *)malloc((npno+1)*sizeof(double));
rt = (double *)malloc((npno+1)*sizeof(double));
v0 = (double *)malloc((npno+1)*sizeof(double));
s0 = (double *)malloc((npno+1)*sizeof(double));
st = (double *)malloc((npno+1)*sizeof(double));
t0 = (double *)malloc((npno+1)*sizeof(double));
u0 = (double *)malloc(neq*sizeof(double));
time0 = CPU_time0();
count = 0;
v_res = E->monitor.fdotf;
/* copy the original force vector since we need to keep it intact
between iterations */
for(j=0;j<neq;j++)
F[j] = FF[j];
/* calculate the initial velocity residual */
initial_vel_residual(E, V, P, F, inner_imp*v_res);
/* initial residual r1 = div(rho_ref*V) */
assemble_div_rho_u(E, V, r1, lev);
E->monitor.vdotv = global_v_norm2(E, V);
E->monitor.incompressibility = sqrt(global_div_norm2(E, r1)
/ (1e-32 + E->monitor.vdotv));
v_norm = sqrt(E->monitor.vdotv);
p_norm = sqrt(E->monitor.pdotp);
dvelocity = 1.0;
dpressure = 1.0;
converging = 0;
if (E->control.print_convergence && E->parallel.me==0) {
print_convergence_progress(E, count, time0,
v_norm, p_norm,
dvelocity, dpressure,
E->monitor.incompressibility);
}
/* initial conjugate residual rt = r1 */
for(j=1; j<=npno; j++)
rt[j] = r1[j];
valid = 1;
r0dotrt = alpha = omega = 0;
while( (count < *steps_max) && keep_iterating(E, imp, converging) ) {
/* require two consecutive converging iterations to quit the while-loop */
/* r1dotrt = <r1, rt> */
r1dotrt = global_pdot(E, r1, rt, lev);
if(r1dotrt == 0.0) {
/* XXX: can we resume the computation when BiCGstab failed? */
fprintf(E->fp, "BiCGstab method failed!!\n");
fprintf(stderr, "BiCGstab method failed!!\n");
parallel_process_termination();
}
/* update search direction */
if(count == 0)
for(j=1; j<=npno; j++)
p2[j] = r1[j];
else {
/* p2 = r1 + <r1,rt>/<r0,rt> * alpha/omega * (p1 - omega*v0) */
beta = (r1dotrt / r0dotrt) * (alpha / omega);
for(j=1; j<=npno; j++)
p2[j] = r1[j] + beta*(p1[j] - omega*v0[j]);
}
/* preconditioner BPI ~= inv(K), pt = BPI*p2 */
for(j=1; j<=npno; j++)
pt[j] = E->BPI[lev][j] * p2[j];
/* solve K*u0 = grad(pt) for u1 */
assemble_grad_p(E, pt, F, lev);
valid = solve_del2_u(E, u0, F, inner_imp*v_res, lev);
if(!valid && (E->parallel.me==0)) {
fputs("Warning: solver not converging! 1\n", stderr);
fputs("Warning: solver not converging! 1\n", E->fp);
}
strip_bcs_from_residual(E, u0, lev);
/* v0 = div(rho_ref*u0) */
assemble_div_rho_u(E, u0, v0, lev);
/* alpha = r1dotrt / <rt, v0> */
alpha = r1dotrt / global_pdot(E, rt, v0, lev);
/* s0 = r1 - alpha * v0 */
for(j=1; j<=npno; j++)
s0[j] = r1[j] - alpha * v0[j];
/* preconditioner BPI ~= inv(K), st = BPI*s0 */
for(j=1; j<=npno; j++)
st[j] = E->BPI[lev][j] * s0[j];
/* solve K*u1 = grad(st) for u1 */
assemble_grad_p(E, st, F, lev);
valid = solve_del2_u(E, E->u1, F, inner_imp*v_res, lev);
if(!valid && (E->parallel.me==0)) {
fputs("Warning: solver not converging! 2\n", stderr);
fputs("Warning: solver not converging! 2\n", E->fp);
}
strip_bcs_from_residual(E, E->u1, lev);
/* t0 = div(rho_ref * u1) */
assemble_div_rho_u(E, E->u1, t0, lev);
/* omega = <t0, s0> / <t0, t0> */
omega = global_pdot(E, t0, s0, lev) / global_pdot(E, t0, t0, lev);
/* r2 = s0 - omega * t0 */
for(j=1; j<=npno; j++)
r2[j] = s0[j] - omega * t0[j];
/* P = P + alpha * pt + omega * st */
for(j=1; j<=npno; j++)
s0[j] = alpha * pt[j] + omega * st[j];
for(j=1; j<=npno; j++)
P[j] += s0[j];
/* V = V - alpha * u0 - omega * u1 */
for(j=0; j<neq; j++)
F[j] = alpha * u0[j] + omega * E->u1[j];
for(j=0; j<neq; j++)
V[j] -= F[j];
/* compute velocity and incompressibility residual */
E->monitor.vdotv = global_v_norm2(E, V);
E->monitor.pdotp = global_p_norm2(E, P);
v_norm = sqrt(E->monitor.vdotv);
p_norm = sqrt(E->monitor.pdotp);
dvelocity = sqrt(global_v_norm2(E, F) / (1e-32 + E->monitor.vdotv));
dpressure = sqrt(global_p_norm2(E, s0) / (1e-32 + E->monitor.pdotp));
assemble_div_rho_u(E, V, t0, lev);
E->monitor.incompressibility = sqrt(global_div_norm2(E, t0)
/ (1e-32 + E->monitor.vdotv));
count++;
if(E->control.print_convergence && E->parallel.me==0) {
print_convergence_progress(E, count, time0,
v_norm, p_norm,
dvelocity, dpressure,
E->monitor.incompressibility);
}
if(!valid){
/* reset consecutive converging iterations */
converging = 0;
}else{
/* how many consecutive converging iterations? */
if(E->control.check_pressure_convergence) {
/* check dv and dp */
if(dvelocity < imp && dpressure < imp)
converging++;
else
converging = 0;
}else{
/* check dv only */
if(dvelocity < imp)
converging++;
else
converging = 0;
}
}
/* shift array pointers */
shuffle = p1;
p1 = p2;
p2 = shuffle;
shuffle = r1;
r1 = r2;
r2 = shuffle;
/* shift <r0, rt> = <r1, rt> */
r0dotrt = r1dotrt;
} /* end loop for conjugate gradient */
free((void *) F);
free((void *) r1);
free((void *) r2);
free((void *) pt);
free((void *) p1);
free((void *) p2);
free((void *) rt);
free((void *) v0);
free((void *) s0);
free((void *) st);
free((void *) t0);
free((void *) u0);
*steps_max=count;
}
/* Solve compressible Stokes flow using
* conjugate gradient (CG) iterations with an outer iteration
*/
static void solve_Ahat_p_fhat_iterCG(struct All_variables *E,
double *V, double *P, double *F,
double imp, int *steps_max)
{
int m, i;
int cycles, num_of_loop;
double relative_err_v, relative_err_p;
double *old_v, *old_p,*diff_v,*diff_p;
double div_res;
const int npno = E->lmesh.npno;
const int neq = E->lmesh.neq;
const int lev = E->mesh.levmax;
double global_v_norm2(),global_p_norm2();
double global_div_norm2();
void assemble_div_rho_u();
old_v = (double *)malloc(neq*sizeof(double));
diff_v = (double *)malloc(neq*sizeof(double));
old_p = (double *)malloc((npno+1)*sizeof(double));
diff_p = (double *)malloc((npno+1)*sizeof(double));
cycles = E->control.p_iterations;
initial_vel_residual(E, V, P, F,
imp * E->control.inner_accuracy_scale * E->monitor.fdotf);
div_res = 1.0;
relative_err_v = 1.0;
relative_err_p = 1.0;
num_of_loop = 0;
while((relative_err_v >= imp || relative_err_p >= imp) &&
(div_res > imp) &&
(num_of_loop <= E->control.compress_iter_maxstep)) {
for(i=0;i<neq;i++)
old_v[i] = V[i];
for(i=1;i<=npno;i++)
old_p[i] = P[i];
solve_Ahat_p_fhat_CG(E, V, P, F, imp, &cycles);
/* compute norm of div(rho*V) */
assemble_div_rho_u(E, V, E->u1, lev);
div_res = sqrt(global_div_norm2(E, E->u1) / (1e-32 + E->monitor.vdotv));
for(i=0;i<neq;i++)
diff_v[i] = V[i] - old_v[i];
relative_err_v = sqrt( global_v_norm2(E,diff_v) /
(1.0e-32 + E->monitor.vdotv) );
for(i=1;i<=npno;i++)
diff_p[i] = P[i] - old_p[i];
relative_err_p = sqrt( global_p_norm2(E,diff_p) /
(1.0e-32 + E->monitor.pdotp) );
if(E->parallel.me == 0) {
fprintf(stderr, "itercg -- div(rho*v)/v=%.2e dv/v=%.2e and dp/p=%.2e loop %d\n\n", div_res, relative_err_v, relative_err_p, num_of_loop);
fprintf(E->fp, "itercg -- div(rho*v)/v=%.2e dv/v=%.2e and dp/p=%.2e loop %d\n\n", div_res, relative_err_v, relative_err_p, num_of_loop);
}
num_of_loop++;
} /* end of while */
free((void *) old_v);
free((void *) old_p);
free((void *) diff_v);
free((void *) diff_p);
}
static void initial_vel_residual(struct All_variables *E,
double *V, double *P, double *F,
double acc)
{
void assemble_del2_u();
void assemble_grad_p();
void strip_bcs_from_residual();
int solve_del2_u();
int neq = E->lmesh.neq;
int lev = E->mesh.levmax;
int i, m, valid;
/* F = F - grad(P) - K*V */
assemble_grad_p(E, P, E->u1, lev);
for(i=0; i<neq; i++)
F[i] = F[i] - E->u1[i];
assemble_del2_u(E, V, E->u1, lev, 1);
for(i=0; i<neq; i++)
F[i] = F[i] - E->u1[i];
strip_bcs_from_residual(E, F, lev);
/* solve K*u1 = F for u1 */
valid = solve_del2_u(E, E->u1, F, acc, lev);
if(!valid && (E->parallel.me==0)) {
fputs("Warning: solver not converging! 0\n", stderr);
fputs("Warning: solver not converging! 0\n", E->fp);
}
strip_bcs_from_residual(E, E->u1, lev);
/* V = V + u1 */
for(i=0; i<neq; i++)
V[i] += E->u1[i];
}