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Rewrite cost function for adaptive step

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This commit is contained in:
Ian Jauslin
2024-11-18 17:09:17 -05:00
parent 9fa10c8db4
commit d81ad18618
6 changed files with 211 additions and 264 deletions
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307
src/navier-stokes.c
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@@ -36,7 +36,7 @@ int uk(
double adaptive_tolerance,
double adaptive_factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
_Complex double* u0,
_Complex double* g,
bool irreversible,
@@ -90,7 +90,7 @@ int uk(
time=starting_time;
while(final_time<0 || time<final_time){
// step
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
time+=step;
step=next_step;
@@ -136,7 +136,7 @@ int enstrophy(
double adaptive_tolerance,
double adaptive_factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
_Complex double* u0,
_Complex double* g,
bool irreversible,
@@ -193,7 +193,7 @@ int enstrophy(
// iterate
time=starting_time;
while(final_time<0 || time<final_time){
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
time+=step;
@@ -281,7 +281,7 @@ int quiet(
double adaptive_tolerance,
double adaptive_factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
double starting_time,
_Complex double* u0,
_Complex double* g,
@@ -317,7 +317,7 @@ int quiet(
// iterate
time=starting_time;
while(final_time<0 || time<final_time){
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
time+=step;
step=next_step;
@@ -483,7 +483,7 @@ int ns_step(
double adaptive_tolerance,
double adaptive_factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
double L,
_Complex double* g,
double time,
@@ -508,15 +508,15 @@ int ns_step(
} else if (algorithm==ALGORITHM_RK4) {
ns_step_rk4(u, K1, K2, N1, N2, nu, *delta, L, g, fft1, fft2, ifft, *tmp1, *tmp2, tmp3, irreversible, keep_en_cst, target_en);
} else if (algorithm==ALGORITHM_RKF45) {
ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, *tmp1, *tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en, true);
ns_step_rkf45(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, *tmp1, *tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en, true);
} else if (algorithm==ALGORITHM_RKDP54) {
// only compute k1 on the first step
// first-same-as-last with 2-nd argument
ns_step_rkdp54(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en, time==starting_time);
ns_step_rkdp54(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en, time==starting_time);
} else if (algorithm==ALGORITHM_RKBS32) {
// only compute k1 on the first step
// first-same-as-last with 4-th argument
ns_step_rkbs32(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, tmp1, tmp3, tmp4, tmp2, tmp5, irreversible, keep_en_cst, target_en, time==starting_time);
ns_step_rkbs32(u, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, K1, K2, N1, N2, nu, delta, next_delta, L, g, fft1, fft2, ifft, tmp1, tmp3, tmp4, tmp2, tmp5, irreversible, keep_en_cst, target_en, time==starting_time);
} else {
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers.edu\n",algorithm);
}
@@ -674,7 +674,7 @@ int ns_step_rkf45(
double tolerance,
double factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
int K1,
int K2,
int N1,
@@ -701,7 +701,7 @@ int ns_step_rkf45(
bool compute_k1
){
int kx,ky;
double err,relative;
double cost;
// k1: u(t)
if(compute_k1){
@@ -748,72 +748,29 @@ int ns_step_rkf45(
}
ns_rhs(k6, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// compute error
err=0;
if(adaptive_norm==NORM_L1){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]));
// next step
tmp[klookup_sym(kx,ky,K2)]=(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]);
}
// next step
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
// u
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
// U: save to k6, which is no longer needed
k6[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)*(16./135*k1[klookup_sym(kx,ky,K2)]+6656./12825*k3[klookup_sym(kx,ky,K2)]+28561./56430*k4[klookup_sym(kx,ky,K2)]-9./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]);
}
}
else if(adaptive_norm==NORM_k3){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,1.5);
// next step
tmp[klookup_sym(kx,ky,K2)]=(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
}
}
}
else if(adaptive_norm==NORM_k32){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,0.75);
// next step
tmp[klookup_sym(kx,ky,K2)]=(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,0.75);
}
}
}
else if(adaptive_norm==NORM_ENSTROPHY){
double sumu, sumU;
sumu=0;
sumU=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=(kx*kx+ky*ky)*cabs2((*delta)*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]));
// next step
tmp[klookup_sym(kx,ky,K2)]=(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
sumU+=(kx*kx+ky*ky)*cabs2(u[klookup_sym(kx,ky,K2)]+(*delta)*(16./135*k1[klookup_sym(kx,ky,K2)]+6656./12825*k3[klookup_sym(kx,ky,K2)]+28561./56430*k4[klookup_sym(kx,ky,K2)]-9./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]));
sumu+=(kx*kx+ky*ky)*cabs2(u[klookup_sym(kx,ky,K2)]+tmp[klookup_sym(kx,ky,K2)]);
}
}
err=sqrt(err);
relative=(sqrt(sumu)+sqrt(sumU))/sumu;
}
else{
fprintf(stderr,"bug: unknown norm: %u, contact ian.jauslin@rutgers.edu\n", adaptive_norm);
exit(-1);
}
// cost function
cost=ns_adaptive_cost(tmp,k6,adaptive_cost,K1,K2,g,L);
// compare relative error with tolerance
if(err<relative*tolerance){
// add to output
if(cost<tolerance){
// copy to output
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
u[klookup_sym(kx,ky,K2)]+=tmp[klookup_sym(kx,ky,K2)];
u[klookup_sym(kx,ky,K2)]=tmp[klookup_sym(kx,ky,K2)];
}
}
// next delta to use in future steps (do not exceed max_delta)
*next_delta=fmin(max_delta, (*delta)*pow(relative*tolerance/err,0.2));
*next_delta=fmin(max_delta, (*delta)*pow(tolerance/cost,0.2));
// keep enstrophy constant
if(keep_en_cst){
@@ -827,9 +784,9 @@ int ns_step_rkf45(
}
// error too big: repeat with smaller step
else{
*delta=factor*(*delta)*pow(relative*tolerance/err,0.2);
*delta=factor*(*delta)*pow(tolerance/cost,0.2);
// do not recompute k1
ns_step_rkf45(u,tolerance,factor,max_delta,adaptive_norm,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible,keep_en_cst,target_en,false);
ns_step_rkf45(u,tolerance,factor,max_delta,adaptive_cost,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible,keep_en_cst,target_en,false);
}
return 0;
@@ -843,7 +800,7 @@ int ns_step_rkbs32(
double tolerance,
double factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
int K1,
int K2,
int N1,
@@ -869,7 +826,7 @@ int ns_step_rkbs32(
bool compute_k1
){
int kx,ky;
double err,relative;
double cost;
// k1: u(t)
// only compute it if it is the first step (otherwise, it has already been computed due to the First Same As Last property)
@@ -894,64 +851,27 @@ int ns_step_rkbs32(
ns_rhs(k3, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// k4 : u(t+delta)
// tmp cpmputed here is the next step
// tmp computed here is the next step
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
tmp[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)*(2./9*(*k1)[klookup_sym(kx,ky,K2)]+1./3*k2[klookup_sym(kx,ky,K2)]+4./9*k3[klookup_sym(kx,ky,K2)]);
}
}
ns_rhs(*k4, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
// compute error
err=0;
if(adaptive_norm==NORM_L1){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(5./72*(*k1)[klookup_sym(kx,ky,K2)]-1./12*k2[klookup_sym(kx,ky,K2)]-1./9*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]));
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)]);
}
}
}
else if(adaptive_norm==NORM_k3){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(5./72*(*k1)[klookup_sym(kx,ky,K2)]-1./12*k2[klookup_sym(kx,ky,K2)]-1./9*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,1.5);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
}
}
}
else if(adaptive_norm==NORM_k32){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(5./72*(*k1)[klookup_sym(kx,ky,K2)]-1./12*k2[klookup_sym(kx,ky,K2)]-1./9*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,0.75);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,0.75);
}
}
}
else if(adaptive_norm==NORM_ENSTROPHY){
double sumu, sumU;
sumu=0;
sumU=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=(kx*kx+ky*ky)*cabs2((*delta)*(5./72*(*k1)[klookup_sym(kx,ky,K2)]-1./12*k2[klookup_sym(kx,ky,K2)]-1./9*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]));
sumU+=(kx*kx+ky*ky)*cabs2(u[klookup_sym(kx,ky,K2)]+(*delta)*(7./24*(*k1)[klookup_sym(kx,ky,K2)]+1./4*k2[klookup_sym(kx,ky,K2)]+1./3*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]));
sumu+=(kx*kx+ky*ky)*cabs2(tmp[klookup_sym(kx,ky,K2)]);
}
}
err=sqrt(err);
relative=(sqrt(sumu)+sqrt(sumU))/sumu;
}
else{
fprintf(stderr,"bug: unknown norm: %u, contact ian.jauslin@rutgers,edu\n", adaptive_norm);
exit(-1);
}
// compare relative error with tolerance
if(err<relative*tolerance){
// next step
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
// U: store in k3, which is no longer needed
k3[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)*(7./24*(*k1)[klookup_sym(kx,ky,K2)]+1./4*k2[klookup_sym(kx,ky,K2)]+1./3*k3[klookup_sym(kx,ky,K2)]+1./8*(*k4)[klookup_sym(kx,ky,K2)]);
}
}
// compute cost
cost=ns_adaptive_cost(tmp, k3, adaptive_cost, K1, K2, g, L);
// compare cost with tolerance
if(cost<tolerance){
// add to output
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
@@ -959,7 +879,7 @@ int ns_step_rkbs32(
}
}
// next delta to use in future steps (do not exceed max_delta)
*next_delta=fmin(max_delta, (*delta)*pow(relative*tolerance/err,1./3));
*next_delta=fmin(max_delta, (*delta)*pow(tolerance/cost,1./3));
// k1 in the next step will be this k4 (first same as last)
tmp=*k1;
@@ -978,9 +898,9 @@ int ns_step_rkbs32(
}
// error too big: repeat with smaller step
else{
*delta=factor*(*delta)*pow(relative*tolerance/err,1./3);
*delta=factor*(*delta)*pow(tolerance/cost,1./3);
// this will reuse the same k1 without re-computing it
ns_step_rkbs32(u,tolerance,factor,max_delta,adaptive_norm,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,tmp,irreversible,keep_en_cst,target_en,false);
ns_step_rkbs32(u,tolerance,factor,max_delta,adaptive_cost,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,tmp,irreversible,keep_en_cst,target_en,false);
}
return 0;
@@ -993,7 +913,7 @@ int ns_step_rkdp54(
double tolerance,
double factor,
double max_delta,
unsigned int adaptive_norm,
unsigned int adaptive_cost,
int K1,
int K2,
int N1,
@@ -1021,7 +941,7 @@ int ns_step_rkdp54(
bool compute_k1
){
int kx,ky;
double err,relative;
double cost;
// k1: u(t)
// only compute it if it is the first step (otherwise, it has already been computed due to the First Same As Last property)
@@ -1078,57 +998,20 @@ int ns_step_rkdp54(
}
// store in k2, which is not needed anymore
ns_rhs(*k2, tmp, K1, K2, N1, N2, nu, L, g, fft1, fft2, ifft, irreversible);
//next step
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
// U: store in k6, which is not needed anymore
k6[klookup_sym(kx,ky,K2)]=u[klookup_sym(kx,ky,K2)]+(*delta)*(5179./57600*(*k1)[klookup_sym(kx,ky,K2)]+7571./16695*k3[klookup_sym(kx,ky,K2)]+393./640*k4[klookup_sym(kx,ky,K2)]-92097./339200*k5[klookup_sym(kx,ky,K2)]+187./2100*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]);
}
}
// compute error
err=0;
if(adaptive_norm==NORM_L1){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]));
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)]);
}
}
}
else if(adaptive_norm==NORM_k3){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,1.5);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
}
}
}
else if(adaptive_norm==NORM_k32){
relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=cabs((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]))/pow(kx*kx+ky*ky,0.75);
relative+=cabs(tmp[klookup_sym(kx,ky,K2)]-u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,0.75);
}
}
}
else if(adaptive_norm==NORM_ENSTROPHY){
double sumu, sumU;
sumu=0;
sumU=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
err+=(kx*kx+ky*ky)*cabs2((*delta)*(-71./57600*(*k1)[klookup_sym(kx,ky,K2)]+71./16695*k3[klookup_sym(kx,ky,K2)]-71./1920*k4[klookup_sym(kx,ky,K2)]+17253./339200*k5[klookup_sym(kx,ky,K2)]-22./525*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]));
sumU+=(kx*kx+ky*ky)*cabs2(u[klookup_sym(kx,ky,K2)]+(*delta)*(5179./57600*(*k1)[klookup_sym(kx,ky,K2)]+7571./16695*k3[klookup_sym(kx,ky,K2)]+393./640*k4[klookup_sym(kx,ky,K2)]-92097./339200*k5[klookup_sym(kx,ky,K2)]+187./2100*k6[klookup_sym(kx,ky,K2)]+1./40*(*k2)[klookup_sym(kx,ky,K2)]));
sumu+=(kx*kx+ky*ky)*cabs2(tmp[klookup_sym(kx,ky,K2)]);
}
}
err=sqrt(err);
relative=(sqrt(sumu)+sqrt(sumU))/sumu;
}
else{
fprintf(stderr,"bug: unknown norm: %u, contact ian.jauslin@rutgers,edu\n", adaptive_norm);
exit(-1);
}
// compute cost
cost=ns_adaptive_cost(tmp, k6, adaptive_cost, K1, K2, g, L);
// compare relative error with tolerance
if(err<relative*tolerance){
if(cost<tolerance){
// add to output
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
@@ -1136,9 +1019,9 @@ int ns_step_rkdp54(
}
}
// next delta to use in future steps (do not exceed max_delta)
*next_delta=fmin(max_delta, (*delta)*pow(relative*tolerance/err,1./5));
*next_delta=fmin(max_delta, (*delta)*pow(tolerance/cost,0.2));
// k1 in the next step will be this k4 (first same as last)
// k1 in the next step will be this k7 (first same as last)
tmp=*k1;
*k1=*k2;
*k2=tmp;
@@ -1155,9 +1038,71 @@ int ns_step_rkdp54(
}
// error too big: repeat with smaller step
else{
*delta=factor*(*delta)*pow(relative*tolerance/err,1./5);
*delta=factor*(*delta)*pow(tolerance/cost,0.2);
// this will reuse the same k1 without re-computing it
ns_step_rkdp54(u,tolerance,factor,max_delta,adaptive_norm,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible,keep_en_cst,target_en,false);
ns_step_rkdp54(u,tolerance,factor,max_delta,adaptive_cost,K1,K2,N1,N2,nu,delta,next_delta,L,g,fft1,fft2,ifft,k1,k2,k3,k4,k5,k6,tmp,irreversible,keep_en_cst,target_en,false);
}
return 0;
}
// compute error for adaptive step methods
double ns_adaptive_cost(
_Complex double* u,
_Complex double* U,
unsigned int adaptive_cost,
int K1,
int K2,
_Complex double* g,
double L
){
int kx,ky;
if(adaptive_cost==COST_L1){
double cost=0;
double relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
cost+=cabs(u[klookup_sym(kx,ky,K2)]-U[klookup_sym(kx,ky,K2)]);
relative+=cabs(u[klookup_sym(kx,ky,K2)]);
}
}
return cost/relative;
}
else if(adaptive_cost==COST_k3){
double cost=0;
double relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
cost+=cabs(u[klookup_sym(kx,ky,K2)]-U[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,3);
relative+=cabs(u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,3);
}
}
return cost/relative;
}
else if(adaptive_cost==COST_k32){
double cost=0;
double relative=0;
for(kx=0;kx<=K1;kx++){
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
cost+=cabs(u[klookup_sym(kx,ky,K2)]-U[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
relative+=cabs(u[klookup_sym(kx,ky,K2)])/pow(kx*kx+ky*ky,1.5);
}
}
return cost/relative;
}
else if(adaptive_cost==COST_ENSTROPHY){
double enu=compute_enstrophy(u,K1,K2,L);
return fabs(enu-compute_enstrophy(U,K1,K2,L))/enu;
}
else if(adaptive_cost==COST_ALPHA){
double alu=compute_alpha(u,K1,K2,g,L);
return fabs((alu-compute_alpha(U,K1,K2,g,L))/alu);
}
else{
fprintf(stderr,"bug: unknown norm: %u, contact ian.jauslin@rutgers.edu\n", adaptive_cost);
exit(-1);
}
return 0;