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heatAll.C
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heatAll.C
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#include "heat.H"
// Double class' statics
int Double::nadds = 0;
int Double::nmults = 0;
int Double::ndivs = 0;
std::size_t Double::nbytes = 0;
// Command-line argument variables
int noout = 0;
int savi = 0;
int outi = 100;
int save = 0;
char const *runame = "heat_results";
char const *alg = "ftcs";
char const *prec = "double";
char const *ic = "const(1)";
Double lenx = 1.0;
Double alpha = 0.2;
Double dt = 0.004;
Double dx = 0.1;
Double bc0 = 0;
Double bc1 = 1;
Double maxt = 2.0;
Double min_change = 1e-8*1e-8;
// Various arrays of numerical data
Double *curr = 0; // current solution
Double *last = 0; // last solution
Double *exact = 0; // exact solution (when available)
Double *change_history = 0; // solution l2norm change history
Double *error_history = 0; // solution error history (when available)
Double *cn_Amat = 0; // A matrix for Crank-Nicholson
// Number of points in space, x, and time, t.
int Nx = (int) (lenx/dx);
int Nt = (int) (maxt/dt);
// Utilities
Double
l2_norm(int n, Double const *a, Double const *b)
{
int i;
Double sum = 0;
for (i = 0; i < n; i++)
{
Double diff = a[i] - b[i];
sum += diff * diff;
}
return sum / n;
}
void
copy(int n, Double *dst, Double const *src)
{
int i;
for (i = 0; i < n; i++)
dst[i] = src[i];
}
void
write_array(int t, int n, Double dx, Double const *a)
{
int i;
char fname[128];
char vname[64];
FILE *outf;
if (noout) return;
if (t == TSTART)
{
snprintf(fname, sizeof(fname), "%s/%s_soln_00000.curve", runame, runame);
snprintf(vname, sizeof(vname), "Temperature");
}
else if (t == TFINAL)
{
snprintf(fname, sizeof(fname), "%s/%s_soln_final.curve", runame, runame);
snprintf(vname, sizeof(vname), "Temperature");
}
else if (t == RESIDUAL)
{
snprintf(fname, sizeof(fname), "%s/%s_change.curve", runame, runame);
snprintf(vname, sizeof(vname), "%s/%s_l2_change", runame, runame);
}
else if (t == ERROR)
{
snprintf(fname, sizeof(fname), "%s/%s_error.curve", runame, runame);
snprintf(vname, sizeof(vname), "%s/%s_l2", runame, runame);
}
else
{
if (a == exact)
{
snprintf(fname, sizeof(fname), "%s/%s_exact_%05d.curve", runame, runame, t);
snprintf(vname, sizeof(vname), "exact_temperature");
}
else
{
snprintf(fname, sizeof(fname), "%s/%s_soln_%05d.curve", runame, runame, t);
snprintf(vname, sizeof(vname), "Temperature");
}
}
outf = fopen(fname,"w");
fprintf(outf, "# %s\n", vname);
for (i = 0; i < n; i++)
fprintf(outf, "%8.4g %8.4g\n", i*((double)dx), (double) a[i]);
fclose(outf);
}
void
set_initial_condition(int n, Double *a, Double dx, char const *ic)
{
int i;
Double x;
if (!strncmp(ic, "const(", 6)) /* const(val) */
{
double cval = strtod(ic+6, 0);
for (i = 0; i < n; i++)
a[i] = cval;
}
else if (!strncmp(ic, "step(", 5)) /* step(left,xmid,right) */
{
char *p;
double left = strtod(ic+5, &p);
double xmid = strtod(p+1, &p);
double right = strtod(p+1, 0);
for (i = 0, x = 0; i < n; i++, x+=dx)
{
if (x < xmid) a[i] = left;
else a[i] = right;
}
}
else if (!strncmp(ic, "ramp(", 5)) /* ramp(left,right) */
{
char *p;
double left = strtod(ic+5, &p);
double right = strtod(p+1, 0);
double dv = (right-left)/(n-1);
for (i = 0, x = left; i < n; i++, x+=dv)
a[i] = x;
}
else if (!strncmp(ic, "rand(", 5)) /* rand(seed,base,amp) */
{
char *p, *ep;
int seed = (int) strtol(ic+5,&p,10);
double base = strtod(p+1, &p);
double amp = strtod(p+1, 0);
const double maxr = ((long long)1<<31)-1;
srandom(seed);
for (i = 0; i < n; i++)
a[i] = base + amp * (2*random()/maxr - 1);
}
else if (!strncmp(ic, "sin(Pi*x)", 9)) /* sin(PI*x) */
{
for (i = 0, x = 0; i < n; i++, x+=dx)
a[i] = sin(M_PI*x);
}
else if (!strncmp(ic, "spikes(", 7)) /* spikes(Const,Amp,Loc,Amp,Loc,...) */
{
char *next;
double cval = strtod(ic+7, &next);
char const *p = next;
for (i = 0, x = 0; i < n; i++)
a[i] = cval;
while (*p != ')')
{
char *ep_amp, *ep_idx;
double amp = strtod(p+1, &ep_amp);
int idx = (int) strtod(ep_amp+1, &ep_idx);
assert(idx<n);
a[idx] = amp;
p = ep_idx;
}
}
write_array(TSTART, Nx, dx, a);
}
static void
r83_np_fa(int n, Double *a)
{
int i;
for ( i = 1; i <= n-1; i++ )
{
assert ( a[1+(i-1)*3] != 0.0 );
// Store the multiplier in L.
a[2+(i-1)*3] = a[2+(i-1)*3] / a[1+(i-1)*3];
// Modify the diagonal entry in the next column.
a[1+i*3] = a[1+i*3] - a[2+(i-1)*3] * a[0+i*3];
}
assert( a[1+(n-1)*3] != 0.0 );
}
void
initialize_crankn(int n,
Double alpha, Double dx, Double dt,
Double **_cn_Amat)
{
int i;
Double const w = alpha * dt / dx / dx;
// Build a tri-diagonal matrix
Double *cn_Amat = new Double[3*n]();
cn_Amat[0+0*3] = 0.0;
cn_Amat[1+0*3] = 1.0;
cn_Amat[0+1*3] = 0.0;
for ( i = 1; i < n - 1; i++ )
{
cn_Amat[2+(i-1)*3] = - w;
cn_Amat[1+ i *3] = 1.0 + 2.0 * w;
cn_Amat[0+(i+1)*3] = - w;
}
cn_Amat[2+(n-2)*3] = 0.0;
cn_Amat[1+(n-1)*3] = 1.0;
cn_Amat[2+(n-1)*3] = 0.0;
// Factor the matrix.
r83_np_fa(n, cn_Amat);
// Return the generated matrix
*_cn_Amat = cn_Amat;
}
// Licensing: This code is distributed under the GNU LGPL license.
// Modified: 30 May 2009 Author: John Burkardt
// Modified by Mark C. Miller, miller86@llnl.gov, July 23, 2017
static void
r83_np_sl ( int n, Double const *a_lu, Double const *b, Double *x)
{
int i;
for ( i = 0; i < n; i++ )
x[i] = b[i];
// Solve L * Y = B.
for ( i = 1; i < n; i++ )
x[i] = x[i] - a_lu[2+(i-1)*3] * x[i-1];
// Solve U * X = Y.
for ( i = n; 1 <= i; i-- )
{
x[i-1] = x[i-1] / a_lu[1+(i-1)*3];
if ( 1 < i )
x[i-2] = x[i-2] - a_lu[0+(i-1)*3] * x[i-1];
}
}
bool
update_solution_crankn(int n,
Double *curr, Double const *last,
Double const *cn_Amat,
Double bc_0, Double bc_1)
{
// Do the solve
r83_np_sl (n, cn_Amat, last, curr);
curr[0] = bc_0;
curr[n-1] = bc_1;
return true;
}
static char clargs[2048];
#define HANDLE_ARG(VAR, TYPE, STYLE, HELP) \
{ \
char const *style = #STYLE; \
char const *q = style[1]=='s'?"\"":""; \
void *valp = (void*) &VAR; \
int const len = strlen(#VAR)+1; \
std::stringstream strmvar; \
for (i = 1; i < argc; i++) \
{\
int valid_style = style[1]=='d'||style[1]=='g'||style[1]=='s'; \
if (strncmp(argv[i], #VAR"=", len)) \
continue; \
assert(valid_style); \
if (strlen(argv[i]+len)) \
{\
if (style[1] == 'd') /* int */ \
*((int*) valp) = (int) strtol(argv[i]+len,0,10); \
else if (style[1] == 'g') /* double */ \
*((Double*) valp) = (double) strtod(argv[i]+len,0); \
else if (style[1] == 's') /* char* */ \
*((char**) valp) = (char*) strdup(argv[i]+len); \
}\
}\
strmvar << VAR; \
if (help) \
{\
char tmp[256]; \
int len = snprintf(tmp, sizeof(tmp), " %s=%s%s%s", \
#VAR, q, strmvar.str().c_str(), q);\
snprintf(tmp, sizeof(tmp), "%s (%s)", #HELP, #TYPE); \
fprintf(stderr, " %s=%s%s%s%*s\n", \
#VAR, q, strmvar.str().c_str(), q, 80-len, tmp);\
}\
else \
{ \
char tmp[64]; \
fprintf(stderr, " %s=%s%s%s\n", \
#VAR, q, strmvar.str().c_str(), q);\
snprintf(tmp, sizeof(tmp), " %s=%s%s%s\n", \
#VAR, q, strmvar.str().c_str(), q);\
strcat(clargs, tmp); \
} \
}
void
process_args(int argc, char **argv)
{
int i;
int help = 0;
// quick pass for 'help' anywhere on command line
clargs[0] ='\0';
for (i = 0; i < argc && !help; i++)
help = 0!=strcasestr(argv[i], "help");
if (help)
fprintf(stderr, "Usage: ./heat <arg>=<value> <arg>=<value>...\n");
HANDLE_ARG(runame, char*, %s, name to give run and results dir);
HANDLE_ARG(prec, char*, %s, precision half|float|double|quad);
HANDLE_ARG(alpha, double, %g, material thermal diffusivity (sq-meters/second));
HANDLE_ARG(lenx, double, %g, material length (meters));
HANDLE_ARG(dx, double, %g, x-incriment. Best if lenx/dx==int. (meters));
HANDLE_ARG(dt, double, %g, t-incriment (seconds));
HANDLE_ARG(maxt, double, %g, >0:max sim time (seconds) | <0:min l2 change in soln);
HANDLE_ARG(bc0, double, %g, boundary condition @ x=0: u(0,t) (Kelvin));
HANDLE_ARG(bc1, double, %g, boundary condition @ x=lenx: u(lenx,t) (Kelvin));
HANDLE_ARG(ic, char*, %s, initial condition @ t=0: u(x,0) (Kelvin));
HANDLE_ARG(alg, char*, %s, algorithm ftcs|upwind15|crankn);
HANDLE_ARG(savi, int, %d, save every i-th solution step);
HANDLE_ARG(save, int, %d, save error in every saved solution);
HANDLE_ARG(outi, int, %d, output progress every i-th solution step);
HANDLE_ARG(noout, int, %d, disable all file outputs);
if (help)
{
fprintf(stderr, "Examples...\n");
fprintf(stderr, " ./heat dx=0.01 dt=0.0002 alg=ftcs\n");
fprintf(stderr, " ./heat dx=0.1 bc0=273 bc1=273 ic=\"spikes(273,5,373)\"\n");
exit(1);
}
// Handle possible termination by change threshold criterion
if (maxt < 0)
{
min_change = -maxt * -maxt;
maxt = INT_MAX;
}
// Handle output results dir creation and save of command-line
if (access(runame, F_OK) == 0)
{
fprintf(stderr, "An entry \"%s\" already exists\n", runame);
exit(1);
}
// Make the output dir and save clargs there too
mkdir(runame, S_IRWXU|S_IRWXG|S_IROTH|S_IXOTH);
char fname[128];
sprintf(fname, "%s/clargs.out", runame);
FILE *outf = fopen(fname, "w");
fprintf(outf, "%s", clargs);
fclose(outf);
}
void
compute_exact_solution(int n, Double *a, Double dx, char const *ic,
Double alpha, Double t, Double bc0, Double bc1)
{
int i;
Double x;
// For any time t for Sin(Pi*x) initial condition
// and zero boundary condition
if (bc0 == 0 && bc1 == 0 && !strncmp(ic, "sin(Pi*x)", 9))
{
for (i = 0, x = 0; i < n; i++, x+=dx)
a[i] = sin(M_PI*x)*exp(-alpha*M_PI*M_PI*t);
}
// For any time t for constant initial condition
// and zero boundary condition
else if (bc0 == 0 && bc1 == 0 && !strncmp(ic, "const(", 6))
{
Double cval = strtod(ic+6, 0);
for (i = 0, x = 0; i < n; i++, x+=dx)
{
int n;
Double fsum = 0;
// Brute force sum first 1000 terms of Fourier series
for (n = 1; n < 1000; n++)
{
Double coeff = 2*cval*(1-pow(-1.0,(double)n))/(n*M_PI);
Double func = sin(n*M_PI*x)*exp(((double)-alpha)*n*n*M_PI*M_PI*((double)t));
fsum += coeff * func;
}
a[i] = fsum;
}
}
// For t>>0 (steady state) for any initial and boundary conditions
else
{
for (i = 0, x = 0; i < n; i++, x+=dx)
a[i] = bc0 + (bc1-bc0)*x;
}
}
bool // false if unstable, true otherwise
update_solution_ftcs(
int n, // number of samples
Double *uk1, // new array of u(x,k+1) to compute/return
Double const *uk0, // old/last array u(x,k) of samples computed
Double alpha, // thermal diffusivity
Double dx, Double dt, // spacing in space, x, and time, t.
Double bc0, Double bc1) // boundary conditions @ x=0 & x=Lx
{
Double r = alpha * dt / (dx * dx);
// sanity check for stability
if (r > 0.5) return false;
// FTCS update algorithm
for (int i = 1; i < n-1; i++)
uk1[i] = r*uk0[i+1] + (1-2*r)*uk0[i] + r*uk0[i-1];
// enforce boundary conditions
uk1[0 ] = bc0;
uk1[n-1] = bc1;
return true;
}
bool
update_solution_upwind15(int n, Double *curr, Double const *last,
Double alpha, Double dx, Double dt,
Double bc_0, Double bc_1)
{
Double const f2 = 1.0/24;
Double const f1 = 1.0/6;
Double const f0 = 1.0/4;
Double const k = alpha * alpha * dt / (dx * dx);
Double const k2 = k*k;
int i;
curr[0 ] = bc_0;
curr[1 ] = last[1 ] + k * (last[0 ] - 2 * last[1 ] + last[2 ]);
curr[n-2] = last[n-2] + k * (last[n-3] - 2 * last[n-2] + last[n-1]);
curr[n-1] = bc_1;
for (i = 2; i < n-2; i++)
curr[i] = f2*(12*k2 -2*k )*last[i-2]
+f2*(12*k2 -2*k )*last[i+2]
-f1*(12*k2 -8*k )*last[i-1]
-f1*(12*k2 -8*k )*last[i+1]
+f0*(12*k2 -10*k +4)*last[i ];
return true;
}
static void
initialize(void)
{
Nx = (int) (lenx/dx)+1;
Nt = (int) (maxt/dt);
dx = lenx/(Nx-1);
curr = new Double[Nx]();
last = new Double[Nx]();
if (save)
{
exact = new Double[Nx]();
change_history = new Double[Nx]();
error_history = new Double[Nx]();
}
assert(strncmp(alg, "ftcs", 4)==0 ||
strncmp(alg, "upwind15", 8)==0 ||
strncmp(alg, "crankn", 6)==0);
#ifdef HAVE_FEENABLEEXCEPT
feenableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
#endif
if (!strncmp(alg, "crankn", 6))
initialize_crankn(Nx, alpha, dx, dt, &cn_Amat);
/* Initial condition */
set_initial_condition(Nx, last, dx, ic);
}
int finalize(int ti, Double maxt, Double change)
{
int retval = 0;
write_array(TFINAL, Nx, dx, curr);
if (save)
{
write_array(RESIDUAL, ti, dt, change_history);
write_array(ERROR, ti, dt, error_history);
}
if (outi)
{
printf("Iteration %04d: last change l2=%g\n", ti, (double) change);
printf("Counts: %s\n", Double::counts_string());
}
delete [] curr;
delete [] last;
if (exact) delete [] exact;
if (change_history) delete [] change_history;
if (error_history) delete [] error_history;
if (cn_Amat) delete [] cn_Amat;
if (strncmp(alg, "ftcs", 4)) free((void*)alg);
if (strncmp(prec, "double", 6)) free((void*)prec);
if (strncmp(ic, "const(1)", 8)) free((void*)ic);
return retval;
}
static bool
update_solution()
{
if (!strcmp(alg, "ftcs"))
return update_solution_ftcs(Nx, curr, last, alpha, dx, dt, bc0, bc1);
else if (!strcmp(alg, "upwind15"))
return update_solution_upwind15(Nx, curr, last, alpha, dx, dt, bc0, bc1);
else if (!strcmp(alg, "crankn"))
return update_solution_crankn(Nx, curr, last, cn_Amat, bc0, bc1);
return false;
}
static Double
update_output_files(int ti)
{
Double change;
if (ti>0 && save)
{
compute_exact_solution(Nx, exact, dx, ic, alpha, ti*dt, bc0, bc1);
if (savi && ti%savi==0)
write_array(ti, Nx, dx, exact);
}
if (ti>0 && savi && ti%savi==0)
write_array(ti, Nx, dx, curr);
change = l2_norm(Nx, curr, last);
if (save)
{
change_history[ti] = change;
error_history[ti] = l2_norm(Nx, curr, exact);
}
return change;
}
int main(int argc, char **argv)
{
int ti;
Double change;
// Read command-line args and set values
process_args(argc, argv);
// Allocate arrays and set initial conditions
initialize();
// Iterate to max iterations or solution change is below threshold
for (ti = 0; ti*dt < maxt; ti++)
{
// compute the next solution step
if (!update_solution())
{
fprintf(stderr, "Solution criteria violated. Make better choices\n");
exit(1);
}
// compute amount of change in solution
change = update_output_files(ti);
// Handle possible termination by change threshold
if (maxt == INT_MAX && change < min_change)
{
printf("Stopped after %06d iterations for threshold %g\n",
ti, (double) change);
break;
}
// Output progress
if (outi && ti%outi==0)
printf("Iteration %04d: last change l2=%g\n", ti, (double) change);
// Copy current solution to last
copy(Nx, last, curr);
}
// Delete storage and output final results
return finalize(ti, maxt, change);
}