void implicit_1Dx(double *phi, double *xx,
double nu, double gamma, double h, double beta, double dt, int L,
int use_delj_trick) {
int ii;
double *dx = malloc((L-1) * sizeof(*dx));
double *dfactor = malloc(L * sizeof(*dfactor));
double *xInt = malloc((L-1) * sizeof(*xInt));
double Mfirst, Mlast;
double *MInt = malloc((L-1) * sizeof(*MInt));
double *V = malloc(L * sizeof(*V));
double *VInt = malloc((L-1) * sizeof(*VInt));
double *delj = malloc((L-1) * sizeof(*delj));
double *a = malloc(L * sizeof(*a));
double *b = malloc(L * sizeof(*b));
double *c = malloc(L * sizeof(*c));
double *r = malloc(L * sizeof(*r));
compute_dx(xx, L, dx);
compute_dfactor(dx, L, dfactor);
compute_xInt(xx, L, xInt);
Mfirst = Mfunc1D(xx[0], gamma, h);
Mlast = Mfunc1D(xx[L-1], gamma, h);
for(ii=0; ii < L; ii++)
V[ii] = Vfunc_beta(xx[ii], nu, beta);
for(ii=0; ii < L-1; ii++) {
MInt[ii] = Mfunc1D(xInt[ii], gamma, h);
VInt[ii] = Vfunc_beta(xInt[ii], nu, beta);
}
compute_delj(dx, MInt, VInt, L, delj, use_delj_trick);
compute_abc_nobc(dx, dfactor, delj, MInt, V, dt, L, a, b, c);
for(ii = 0; ii < L; ii++)
r[ii] = phi[ii]/dt;
/* Boundary conditions */
if(Mfirst <= 0)
b[0] += (0.5/nu - Mfirst)*2./dx[0];
if(Mlast >= 0)
b[L-1] += -(-0.5/nu - Mlast)*2./dx[L-2];
tridiag(a, b, c, r, phi, L);
free(dx);
free(dfactor);
free(xInt);
free(MInt);
free(V);
free(VInt);
free(delj);
free(a);
free(b);
free(c);
free(r);
}
void implicit_2Dy(double *phi, double *xx, double *yy,
double nu2, double m21, double gamma2, double h2,
double dt, int L, int M, int use_delj_trick){
int ii, jj;
double *dy = malloc((M-1) * sizeof(*dy));
double *dfactor = malloc(M * sizeof(*dfactor));
double *yInt = malloc((M-1) * sizeof(*yInt));
double Mfirst, Mlast;
double *MInt = malloc((M-1) * sizeof(*MInt));
double *V = malloc(M * sizeof(*V));
double *VInt = malloc((M-1) * sizeof(*VInt));
double *delj = malloc((M-1) * sizeof(*delj));
double *a = malloc(M * sizeof(*a));
double *b = malloc(M * sizeof(*b));
double *c = malloc(M * sizeof(*c));
double *r = malloc(M * sizeof(*r));
double x;
compute_dx(yy, M, dy);
compute_dfactor(dy, M, dfactor);
compute_xInt(yy, M, yInt);
for(jj=0; jj < M; jj++)
V[jj] = Vfunc(yy[jj], nu2);
for(jj=0; jj < M-1; jj++)
VInt[jj] = Vfunc(yInt[jj], nu2);
tridiag_malloc(M);
for(ii=0; ii < L; ii++){
x = xx[ii];
Mfirst = Mfunc2D(yy[0], x, m21, gamma2, h2);
Mlast = Mfunc2D(yy[M-1], x, m21, gamma2, h2);
for(jj=0; jj < M-1; jj++)
MInt[jj] = Mfunc2D(yInt[jj], x, m21, gamma2, h2);
compute_delj(dy, MInt, VInt, M, delj, use_delj_trick);
compute_abc_nobc(dy, dfactor, delj, MInt, V, dt, M, a, b, c);
for(jj = 0; jj < M; jj++)
r[jj] = phi[ii*M + jj]/dt;
if((ii==0) && (Mfirst <= 0))
b[0] += (0.5/nu2 - Mfirst)*2./dy[0];
if((ii==L-1) && (Mlast >= 0))
b[M-1] += -(-0.5/nu2 - Mlast)*2./dy[M-2];
tridiag_premalloc(a, b, c, r, &phi[ii*M], M);
}
tridiag_free();
free(dy);
free(dfactor);
free(yInt);
free(MInt);
free(V);
free(VInt);
free(delj);
free(a);
free(b);
free(c);
free(r);
}
void implicit_2Dx(double *phi, double *xx, double *yy,
double nu1, double m12, double gamma1, double h1,
double dt, int L, int M, int use_delj_trick){
int ii, jj;
double *dx = malloc((L-1) * sizeof(*dx));
double *dfactor = malloc(L * sizeof(*dfactor));
double *xInt = malloc((L-1) * sizeof(*xInt));
double Mfirst, Mlast;
double *MInt = malloc((L-1) * sizeof(*MInt));
double *V = malloc(L * sizeof(*V));
double *VInt = malloc((L-1) * sizeof(*VInt));
double *delj = malloc((L-1) * sizeof(*delj));
double *a = malloc(L * sizeof(*a));
double *b = malloc(L * sizeof(*b));
double *c = malloc(L * sizeof(*c));
double *r = malloc(L * sizeof(*r));
double *temp = malloc(L * sizeof(*temp));
double y;
compute_dx(xx, L, dx);
compute_dfactor(dx, L, dfactor);
compute_xInt(xx, L, xInt);
for(ii=0; ii < L; ii++)
V[ii] = Vfunc(xx[ii], nu1);
for(ii=0; ii < L-1; ii++)
VInt[ii] = Vfunc(xInt[ii], nu1);
tridiag_malloc(L);
for(jj=0; jj < M; jj++){
y = yy[jj];
Mfirst = Mfunc2D(xx[0], y, m12, gamma1, h1);
Mlast = Mfunc2D(xx[L-1], y, m12, gamma1, h1);
for(ii=0; ii < L-1; ii++)
MInt[ii] = Mfunc2D(xInt[ii], y, m12, gamma1, h1);
compute_delj(dx, MInt, VInt, L, delj, use_delj_trick);
compute_abc_nobc(dx, dfactor, delj, MInt, V, dt, L, a, b, c);
for(ii = 0; ii < L; ii++)
r[ii] = phi[ii*M + jj]/dt;
if((jj==0) && (Mfirst <= 0))
b[0] += (0.5/nu1 - Mfirst)*2./dx[0];
if((jj==M-1) && (Mlast >= 0))
b[L-1] += -(-0.5/nu1 - Mlast)*2./dx[L-2];
tridiag_premalloc(a, b, c, r, temp, L);
for(ii = 0; ii < L; ii++)
phi[ii*M + jj] = temp[ii];
}
tridiag_free();
free(dx);
free(dfactor);
free(xInt);
free(MInt);
free(V);
free(VInt);
free(delj);
free(a);
free(b);
free(c);
free(r);
free(temp);
}