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FK-3V-master.cu
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FK-3V-master.cu
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/*
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
Developed by: Hector Augusto Velasco-Perez
@ CHAOS Lab
@ Georgia Institute of Technology
August 07/10/2019
Special thanks to:
Dr. Flavio Fenton
Dr. Claire Yanyan Ji
Dr. Abouzar Kaboudian
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
*/
#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include "typedef3V-FK.h"
//#include "globalVariables.cuh"
#include "hostPrototypes.h"
#include "devicePrototypes.cuh"
#include "./common/CudaSafeCall.h"
// Weight constants
extern __constant__ REAL dt_d, rx_d, ry_d, rz_d;
extern __constant__ REAL rxyc_d, rxzc_d, ryzc_d, rxyzf_d;
extern __constant__ REAL rCxyz_d, rwe_d, rsn_d, rbt_d;
extern __constant__ REAL rxy_d, rbx_d, rby_d;
// Miscellaneous constants
extern __constant__ REAL expTau_vp_d, expTau_wp_d, expTau_wn_d;
extern __constant__ REAL invdx_d, invdy_d, invdz_d;
extern __device__ vec3dyn dev_data1[NN];
extern __device__ vec6dyn dev_data2[NN];
extern __device__ int dev_count;
/*========================================================================
* Main Entry of the Kernel
*========================================================================
*/
__global__ void FK_3V_kernel(stateVar g_out, stateVar g_in, conductionVar r,
REAL *J_d) {
/*------------------------------------------------------------------------
* Getting i and j global indices
*------------------------------------------------------------------------
*/
const int i = threadIdx.x;
const int j = blockIdx.x*blockDim.y + threadIdx.y;
const int k = blockIdx.y;
/*------------------------------------------------------------------------
* return if we are outside the domain
*------------------------------------------------------------------------
*/
if( i >= nx && j>=ny && k >= nz) {
return ;
}
/*------------------------------------------------------------------------
* Converting global index into matrix indices assuming
* the column major structure of the matlab matrices
*------------------------------------------------------------------------
*/
const int nxy = nx*ny;
const int i3d = k * nxy + j * nx + i;
/*------------------------------------------------------------------------
* Setting local variables
*------------------------------------------------------------------------
*/
#ifdef DOUBLE_PRECISION
REAL u = g_in.u[i3d] ;
REAL v = g_in.v[i3d] ;
REAL w = g_in.w[i3d] ;
/*------------------------------------------------------------------------
* Additional heaviside functions
*------------------------------------------------------------------------
*/
REAL p = ( u > theta_c ) ? 1.0:0.0 ;
REAL q = ( u > theta_v ) ? 1.0:0.0 ;
/*------------------------------------------------------------------------
* Calculating dependant tau's
*------------------------------------------------------------------------
*/
REAL tau_vnu = q*tau_v1n + (1.0-q)*tau_v2n;
g_out.v[i3d] =
( u > theta_c ) ? v*expTau_vp_d : 1.0-(1.0-v)*exp(-dt_d/tau_vnu);
g_out.w[i3d] =
( u > theta_c ) ? w*expTau_wp_d : 1.0-(1.0-w)*expTau_wn_d;
/*
REAL dv2dt = (1.0-p)*(1.0-v)/tau_vnu - p*v/tau_vp;
v += dv2dt*dt_d ;
g_out.v[i3d] = v ;
REAL dw2dt = (1.0-p)*(1.0-w)/tau_wn - p*w/tau_wp;
w += dw2dt*dt_d ;
g_out.w[i3d] = w ;
*/
/*------------------------------------------------------------------------
* I_sum
*------------------------------------------------------------------------
*/
//Fast inward (Sodium)
REAL J_fi = -p*v*(1.0-u)*(u-theta_c)/tau_d;
//Slow outward (Potassium)
REAL J_so = (1.0-p)*u/tau_o + p/tau_r;
//Slow inward (Calcium)
REAL J_si = -w*(1.0 + tanh(K*(u-u_csi)))/(2.0*tau_si);
REAL I_sum = J_fi + J_so + J_si ;
J_d[i3d] = I_sum;
/*------------------------------------------------------------------------
* Laplacian Calculation
*
* No flux boundary condition is applied on all boundaries through
* the Laplacian operator definition
*------------------------------------------------------------------------
*/
int S = ( j> 0 ) ? I3D(nx,nxy,i,j-1,k) : I3D(nx,nxy,i,j+1,k) ;
int N = ( j<(ny-1) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i,j-1,k) ;
int W = ( i> 0 ) ? I3D(nx,nxy,i-1,j,k) : I3D(nx,nxy,i+1,j,k) ;
int E = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i-1,j,k) ;
//////////////////////
int SWxy = (i>0 && j>0) ? I3D(nx,nxy,i-1,j-1,k) :
((i==0 && j>0) ? I3D(nx,nxy,i+1,j-1,k) :
((i>0 && j==0)? I3D(nx,nxy,i-1,j+1,k) : I3D(nx,nxy,i+1,j+1,k) ) ) ;
int SExy = (i<(nx-1) && j>0) ? I3D(nx,nxy,i+1,j-1,k) :
((i==(nx-1) && j>0) ? I3D(nx,nxy,i-1,j-1,k) :
((i<(nx-1) && j==0)? I3D(nx,nxy,i+1,j+1,k) : I3D(nx,nxy,i-1,j+1,k) ) ) ;
int NWxy = (i>0 && j<(ny-1)) ? I3D(nx,nxy,i-1,j+1,k) :
((i==0 && j<(ny-1)) ? I3D(nx,nxy,i+1,j+1,k) :
((i>0 && j==(ny-1))? I3D(nx,nxy,i-1,j-1,k) : I3D(nx,nxy,i+1,j-1,k) ) ) ;
int NExy = (i<(nx-1) && j<(ny-1)) ? I3D(nx,nxy,i+1,j+1,k) :
((i==(nx-1) && j<(ny-1)) ? I3D(nx,nxy,i-1,j+1,k) :
((i<(nx-1) && j==(ny-1))? I3D(nx,nxy,i+1,j-1,k) : I3D(nx,nxy,i-1,j-1,k) ) ) ;
#ifdef PERIODIC_Z // In the z direction
int B = ( k> 0 ) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j,nz-1) ;
int T = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,0) ;
int SWxz = (i>0 && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i==0 && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i>0 && k==0)? I3D(nx,nxy,i-1,j,nz-1) : I3D(nx,nxy,i+1,j,k+1) ) ) ;
int SExz = (i<(nx-1) && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i==(nx-1) && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i<(nx-1) && k==0)? I3D(nx,nxy,i+1,j,nz-1) : I3D(nx,nxy,i-1,j,k+1) ) ) ;
int NWxz = (i>0 && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i==0 && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i>0 && k==(nz-1))? I3D(nx,nxy,i-1,j,0) : I3D(nx,nxy,i+1,j,k-1) ) ) ;
int NExz = (i<(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i==(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i<(nx-1) && k==(nz-1))? I3D(nx,nxy,i+1,j,0) : I3D(nx,nxy,i-1,j,k-1) ) ) ;
//////////////////////////
int SWyz = (j>0 && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j==0 && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j>0 && k==0)? I3D(nx,nxy,i,j-1,nz-1) : I3D(nx,nxy,i,j+1,k+1) ) ) ;
int SEyz = (j<(ny-1) && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j==(ny-1) && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j<(ny-1) && k==0)? I3D(nx,nxy,i,j+1,nz-1) : I3D(nx,nxy,i,j-1,k+1) ) ) ;
int NWyz = (j>0 && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j==0 && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j>0 && k==(nz-1))? I3D(nx,nxy,i,j-1,0) : I3D(nx,nxy,i,j+1,k-1) ) ) ;
int NEyz = (j<(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j==(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j<(ny-1) && k==(nz-1))? I3D(nx,nxy,i,j+1,0) : I3D(nx,nxy,i,j-1,k-1) ) ) ;
#else
int B = ( k> 0 ) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j,k+1) ;
int T = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,k-1) ;
int SWxz = (i>0 && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i==0 && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i>0 && k==0)? I3D(nx,nxy,i-1,j,k+1) : I3D(nx,nxy,i+1,j,k+1) ) ) ;
int SExz = (i<(nx-1) && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i==(nx-1) && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i<(nx-1) && k==0)? I3D(nx,nxy,i+1,j,k+1) : I3D(nx,nxy,i-1,j,k+1) ) ) ;
int NWxz = (i>0 && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i==0 && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i>0 && k==(nz-1))? I3D(nx,nxy,i-1,j,k-1) : I3D(nx,nxy,i+1,j,k-1) ) ) ;
int NExz = (i<(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i==(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i<(nx-1) && k==(nz-1))? I3D(nx,nxy,i+1,j,k-1) : I3D(nx,nxy,i-1,j,k-1) ) ) ;
//////////////////////////
int SWyz = (j>0 && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j==0 && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j>0 && k==0)? I3D(nx,nxy,i,j-1,k+1) : I3D(nx,nxy,i,j+1,k+1) ) ) ;
int SEyz = (j<(ny-1) && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j==(ny-1) && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j<(ny-1) && k==0)? I3D(nx,nxy,i,j+1,k+1) : I3D(nx,nxy,i,j-1,k+1) ) ) ;
int NWyz = (j>0 && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j==0 && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j>0 && k==(nz-1))? I3D(nx,nxy,i,j-1,k-1) : I3D(nx,nxy,i,j+1,k-1) ) ) ;
int NEyz = (j<(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j==(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j<(ny-1) && k==(nz-1))? I3D(nx,nxy,i,j+1,k-1) : I3D(nx,nxy,i,j-1,k-1) ) ) ;
#endif
#ifdef ANISOTROPIC_TISSUE
/*------------------------------------------------------------------------
* Anisotropic Laplacian
*------------------------------------------------------------------------
*/
REAL rx = r.x[k];
REAL ry = r.y[k];
REAL rz = r.z[k];
REAL rbx = r.bx[k];
REAL rby = r.by[k];
REAL du2dt = ( rCxyz_d * (rx + ry + rz)*u
+ rwe_d * (4.0*rx - ry - rz)*(g_in.u[W] + g_in.u[E])
+ rsn_d * (4.0*ry - rx - rz)*(g_in.u[N] + g_in.u[S])
+ rbt_d * (4.0*rz - ry - rx)*(g_in.u[T] + g_in.u[B])
+ rxyc_d * (rx + ry)*( g_in.u[SWxy] +
g_in.u[SExy] +
g_in.u[NWxy] +
g_in.u[NExy] )
+ rxzc_d * (rx + rz)*( g_in.u[SWxz] +
g_in.u[SExz] +
g_in.u[NWxz] +
g_in.u[NExz] )
+ ryzc_d * (ry + rz)*( g_in.u[SWyz] +
g_in.u[SEyz] +
g_in.u[NWyz] +
g_in.u[NEyz] ) ) ;
du2dt -= ( dt_d*( 0.5*I_sum
+ rxyzf_d * ( ( J_d[E] + J_d[W] )
+ ( J_d[N] + J_d[S] )
+ ( J_d[B] + J_d[T] ) ) ) / C_m ) ;
/*
REAL du2dt = (
+ ( g_in.u[W] - 2.f*u + g_in.u[E] )*rx
+ ( g_in.u[N] - 2.f*u + g_in.u[S] )*ry
+ ( g_in.u[T] - 2.f*u + g_in.u[B] )*rz );
du2dt -= dt_d*I_sum/C_m ;
*/
// Correction to NSWE boundary conditions
REAL b_S = (j > 0 )? 0.0:
((j==0 && (i==0 || i==(nx-1)))? 0.0:
rby*(g_in.u[I3D(nx,nxy,i+1,j,k)] - g_in.u[I3D(nx,nxy,i-1,j,k)])) ;
REAL b_N = (j < (ny-1))? 0.0:
((j==(ny-1) && (i==0 || i==(nx-1)))? 0.0:
-rby*(g_in.u[I3D(nx,nxy,i+1,j,k)] - g_in.u[I3D(nx,nxy,i-1,j,k)])) ;
REAL b_W = (i > 0 )? 0.0:
((i==0 && (j==0 || j==(ny-1)))? 0.0:
rbx*(g_in.u[I3D(nx,nxy,i,j+1,k)] - g_in.u[I3D(nx,nxy,i,j-1,k)])) ;
REAL b_E = (i < (nx-1))? 0.0:
((i==(nx-1) && (j==0 || j==(ny-1)))? 0.0:
-rbx*(g_in.u[I3D(nx,nxy,i,j+1,k)] - g_in.u[I3D(nx,nxy,i,j-1,k)])) ;
du2dt += (
( b_S + b_N )*ry
+ ( b_W + b_E )*rx );
// Correcion to SW SE NW NE boundary conditions
REAL b_SW = (i>0 && j>0)? 0.0 :
((i==0 && j>1)? rbx*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i,j-2,k)]) :
((i>1 && j==0)? rby*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i-2,j,k)]) : 0.0)) ;
REAL b_SE = (i<(nx-1) && j>0)? 0.0 :
((i==(nx-1) && j>1)? -rbx*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i,j-2,k)]) :
((i<(nx-2) && j==0)? rby*(g_in.u[I3D(nx,nxy,i+2,j,k)] - g_in.u[i3d]) : 0.0)) ;
REAL b_NW = (i>0 && j<(ny-1))? 0.0 :
((i==0 && j<(ny-2))? rbx*(g_in.u[I3D(nx,nxy,i,j+2,k)] - g_in.u[i3d]) :
((i>1 && j==(ny-1))? -rby*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i-2,j,k)]) : 0.0)) ;
REAL b_NE = (i<(nx-1) && j<(ny-1))? 0.0 :
((i==(nx-1) && j<(ny-2))? -rbx*(g_in.u[I3D(nx,nxy,i,j+2,k)] - g_in.u[i3d]) :
((i<(nx-2) && j==(ny-1))? -rby*(g_in.u[I3D(nx,nxy,i+2,j,k)] - g_in.u[i3d]) : 0.0)) ;
du2dt += ( r.xy[k]*( (g_in.u[SWxy] + b_SW) +
(g_in.u[NExy] + b_NE) -
(g_in.u[SExy] + b_SE) -
(g_in.u[NWxy] + b_NW) ) );
#else
/*------------------------------------------------------------------------
* Isotropic Laplacian
*------------------------------------------------------------------------
*/
REAL du2dt = ( rCxyz_d*u
+ rwe_d*(g_in.u[W] + g_in.u[E])
+ rsn_d*(g_in.u[N] + g_in.u[S])
+ rbt_d*(g_in.u[T] + g_in.u[B])
+ rxyc_d*( g_in.u[SWxy] +
g_in.u[SExy] +
g_in.u[NWxy] +
g_in.u[NExy] )
+ rxzc_d*( g_in.u[SWxz] +
g_in.u[SExz] +
g_in.u[NWxz] +
g_in.u[NExz] )
+ ryzc_d*( g_in.u[SWyz] +
g_in.u[SEyz] +
g_in.u[NWyz] +
g_in.u[NEyz] ) ) ;
du2dt -= ( dt_d*( 0.5*I_sum
+ rxyzf_d * ( ( J_d[E] + J_d[W] )
+ ( J_d[N] + J_d[S] )
+ ( J_d[B] + J_d[T] ) ) ) / C_m ) ;
/*
REAL du2dt = (
+ ( g_in.u[W] - 2.f*u + g_in.u[E] )*rx_d
+ ( g_in.u[N] - 2.f*u + g_in.u[S] )*ry_d
+ ( g_in.u[T] - 2.f*u + g_in.u[B] )*rz_d );
du2dt -= dt_d*I_sum/C_m ;
*/
#endif
/*------------------------------------------------------------------------
* Time integration
*------------------------------------------------------------------------
*/
u += du2dt ;
g_out.u[i3d] = u ;
/*------------------------------------------------------------------------
* Single precision
*------------------------------------------------------------------------
*/
#else
REAL u = g_in.u[i3d] ;
REAL v = g_in.v[i3d] ;
REAL w = g_in.w[i3d] ;
/*------------------------------------------------------------------------
* Additional heaviside functions
*------------------------------------------------------------------------
*/
REAL p = ( u > theta_c ) ? 1.0:0.0 ;
REAL q = ( u > theta_v ) ? 1.0:0.0 ;
/*------------------------------------------------------------------------
* Calculating dependant tau's
*------------------------------------------------------------------------
*/
REAL tau_vnu = q*tau_v1n + (1.f-q)*tau_v2n;
g_out.v[i3d] =
( u > theta_c ) ? v*expTau_vp_d : 1.0f-(1.0f-v)*expf(-dt_d/tau_vnu);
g_out.w[i3d] =
( u > theta_c ) ? w*expTau_wp_d : 1.0f-(1.0f-w)*expTau_wn_d;
/*
REAL dv2dt = (1.f-p)*(1.f-v)/tau_vnu - p*v/tau_vp;
v += dv2dt*dt_d ;
g_out.v[i3d] = v ;
REAL dw2dt = (1.f-p)*(1.f-w)/tau_wn - p*w/tau_wp;
w += dw2dt*dt_d ;
g_out.w[i3d] = w ;
*/
/*------------------------------------------------------------------------
* I_sum
*------------------------------------------------------------------------
*/
//Fast inward (Sodium)
REAL J_fi = -p*v*(1.f-u)*(u-theta_c)/tau_d;
//Slow outward (Potassium)
REAL J_so = (1.f-p)*u/tau_o + p/tau_r;
//Slow inward (Calcium)
REAL J_si = -w*(1.f + tanhf(K*(u-u_csi)))/(2.f*tau_si);
REAL I_sum = J_fi + J_so + J_si ;
J_d[i3d] = I_sum;
/*------------------------------------------------------------------------
* Laplacian Calculation
*
* No flux boundary condition is applied on all boundaries through
* the Laplacian operator definition
*------------------------------------------------------------------------
*/
int S = ( j> 0 ) ? I3D(nx,nxy,i,j-1,k) : I3D(nx,nxy,i,j+1,k) ;
int N = ( j<(ny-1) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i,j-1,k) ;
int W = ( i> 0 ) ? I3D(nx,nxy,i-1,j,k) : I3D(nx,nxy,i+1,j,k) ;
int E = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i-1,j,k) ;
int SWxy = (i>0 && j>0) ? I3D(nx,nxy,i-1,j-1,k) :
((i==0 && j>0) ? I3D(nx,nxy,i+1,j-1,k) :
((i>0 && j==0)? I3D(nx,nxy,i-1,j+1,k) : I3D(nx,nxy,i+1,j+1,k) ) ) ;
int SExy = (i<(nx-1) && j>0) ? I3D(nx,nxy,i+1,j-1,k) :
((i==(nx-1) && j>0) ? I3D(nx,nxy,i-1,j-1,k) :
((i<(nx-1) && j==0)? I3D(nx,nxy,i+1,j+1,k) : I3D(nx,nxy,i-1,j+1,k) ) ) ;
int NWxy = (i>0 && j<(ny-1)) ? I3D(nx,nxy,i-1,j+1,k) :
((i==0 && j<(ny-1)) ? I3D(nx,nxy,i+1,j+1,k) :
((i>0 && j==(ny-1))? I3D(nx,nxy,i-1,j-1,k) : I3D(nx,nxy,i+1,j-1,k) ) ) ;
int NExy = (i<(nx-1) && j<(ny-1)) ? I3D(nx,nxy,i+1,j+1,k) :
((i==(nx-1) && j<(ny-1)) ? I3D(nx,nxy,i-1,j+1,k) :
((i<(nx-1) && j==(ny-1))? I3D(nx,nxy,i+1,j-1,k) : I3D(nx,nxy,i-1,j-1,k) ) ) ;
#ifdef PERIODIC_Z // In the z direction
int B = ( k> 0 ) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j,nz-1) ;
int T = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,0) ;
int SWxz = (i>0 && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i==0 && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i>0 && k==0)? I3D(nx,nxy,i-1,j,nz-1) : I3D(nx,nxy,i+1,j,k+1) ) ) ;
int SExz = (i<(nx-1) && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i==(nx-1) && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i<(nx-1) && k==0)? I3D(nx,nxy,i+1,j,nz-1) : I3D(nx,nxy,i-1,j,k+1) ) ) ;
int NWxz = (i>0 && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i==0 && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i>0 && k==(nz-1))? I3D(nx,nxy,i-1,j,0) : I3D(nx,nxy,i+1,j,k-1) ) ) ;
int NExz = (i<(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i==(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i<(nx-1) && k==(nz-1))? I3D(nx,nxy,i+1,j,0) : I3D(nx,nxy,i-1,j,k-1) ) ) ;
//////////////////////////
int SWyz = (j>0 && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j==0 && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j>0 && k==0)? I3D(nx,nxy,i,j-1,nz-1) : I3D(nx,nxy,i,j+1,k+1) ) ) ;
int SEyz = (j<(ny-1) && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j==(ny-1) && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j<(ny-1) && k==0)? I3D(nx,nxy,i,j+1,nz-1) : I3D(nx,nxy,i,j-1,k+1) ) ) ;
int NWyz = (j>0 && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j==0 && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j>0 && k==(nz-1))? I3D(nx,nxy,i,j-1,0) : I3D(nx,nxy,i,j+1,k-1) ) ) ;
int NEyz = (j<(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j==(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j<(ny-1) && k==(nz-1))? I3D(nx,nxy,i,j+1,0) : I3D(nx,nxy,i,j-1,k-1) ) ) ;
#else
int B = ( k> 0 ) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j,k+1) ;
int T = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,k-1) ;
int SWxz = (i>0 && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i==0 && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i>0 && k==0)? I3D(nx,nxy,i-1,j,k+1) : I3D(nx,nxy,i+1,j,k+1) ) ) ;
int SExz = (i<(nx-1) && k>0) ? I3D(nx,nxy,i+1,j,k-1) :
((i==(nx-1) && k>0) ? I3D(nx,nxy,i-1,j,k-1) :
((i<(nx-1) && k==0)? I3D(nx,nxy,i+1,j,k+1) : I3D(nx,nxy,i-1,j,k+1) ) ) ;
int NWxz = (i>0 && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i==0 && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i>0 && k==(nz-1))? I3D(nx,nxy,i-1,j,k-1) : I3D(nx,nxy,i+1,j,k-1) ) ) ;
int NExz = (i<(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i+1,j,k+1) :
((i==(nx-1) && k<(nz-1)) ? I3D(nx,nxy,i-1,j,k+1) :
((i<(nx-1) && k==(nz-1))? I3D(nx,nxy,i+1,j,k-1) : I3D(nx,nxy,i-1,j,k-1) ) ) ;
//////////////////////////
int SWyz = (j>0 && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j==0 && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j>0 && k==0)? I3D(nx,nxy,i,j-1,k+1) : I3D(nx,nxy,i,j+1,k+1) ) ) ;
int SEyz = (j<(ny-1) && k>0) ? I3D(nx,nxy,i,j+1,k-1) :
((j==(ny-1) && k>0) ? I3D(nx,nxy,i,j-1,k-1) :
((j<(ny-1) && k==0)? I3D(nx,nxy,i,j+1,k+1) : I3D(nx,nxy,i,j-1,k+1) ) ) ;
int NWyz = (j>0 && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j==0 && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j>0 && k==(nz-1))? I3D(nx,nxy,i,j-1,k-1) : I3D(nx,nxy,i,j+1,k-1) ) ) ;
int NEyz = (j<(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j+1,k+1) :
((j==(ny-1) && k<(nz-1)) ? I3D(nx,nxy,i,j-1,k+1) :
((j<(ny-1) && k==(nz-1))? I3D(nx,nxy,i,j+1,k-1) : I3D(nx,nxy,i,j-1,k-1) ) ) ;
#endif
#ifdef ANISOTROPIC_TISSUE
/*------------------------------------------------------------------------
* Anisotropic Laplacian
*-------------------------------------------------------------------------
*/
REAL rx = r.x[k];
REAL ry = r.y[k];
REAL rz = r.z[k];
REAL rbx = r.bx[k];
REAL rby = r.by[k];
REAL du2dt = ( rCxyz_d * (rx + ry + rz)*u
+ rwe_d * (4.0*rx - ry - rz)*(g_in.u[W] + g_in.u[E])
+ rsn_d * (4.0*ry - rx - rz)*(g_in.u[N] + g_in.u[S])
+ rbt_d * (4.0*rz - ry - rx)*(g_in.u[T] + g_in.u[B])
+ rxyc_d * (rx + ry)*( g_in.u[SWxy] +
g_in.u[SExy] +
g_in.u[NWxy] +
g_in.u[NExy] )
+ rxzc_d * (rx + rz)*( g_in.u[SWxz] +
g_in.u[SExz] +
g_in.u[NWxz] +
g_in.u[NExz] )
+ ryzc_d * (ry + rz)*( g_in.u[SWyz] +
g_in.u[SEyz] +
g_in.u[NWyz] +
g_in.u[NEyz] ) ) ;
du2dt -= ( dt_d*( 0.5*I_sum
+ rxyzf_d * ( ( J_d[E] + J_d[W] )
+ ( J_d[N] + J_d[S] )
+ ( J_d[B] + J_d[T] ) ) ) / C_m ) ;
/*
REAL du2dt = (
+ ( g_in.u[W] - 2.f*u + g_in.u[E] )*rx
+ ( g_in.u[N] - 2.f*u + g_in.u[S] )*ry
+ ( g_in.u[T] - 2.f*u + g_in.u[B] )*rz );
du2dt -= dt_d*I_sum/C_m ;
*/
// Correction to NSWE boundary conditions
REAL b_S = (j > 0 ) ? 0.f :
((j==0 && (i==0 || i==(nx-1)))? 0.f:
rby*(g_in.u[I3D(nx,nxy,i+1,j,k)] - g_in.u[I3D(nx,nxy,i-1,j,k)]));
REAL b_N = (j < (ny-1)) ? 0.f :
((j==(ny-1) && (i==0 || i==(nx-1)))? 0.f:
-rby*(g_in.u[I3D(nx,nxy,i+1,j,k)] - g_in.u[I3D(nx,nxy,i-1,j,k)]));
REAL b_W = (i > 0 ) ? 0.f :
((i==0 && (j==0 || j==(ny-1)))? 0.f:
rbx*(g_in.u[I3D(nx,nxy,i,j+1,k)] - g_in.u[I3D(nx,nxy,i,j-1,k)]));
REAL b_E = (i < (nx-1)) ? 0.f :
((i==(nx-1) && (j==0 || j==(ny-1)))? 0.f:
-rbx*(g_in.u[I3D(nx,nxy,i,j+1,k)] - g_in.u[I3D(nx,nxy,i,j-1,k)]));
du2dt += (
( b_S + b_N )*ry
+ ( b_W + b_E )*rx );
// Correcion to SW SE NW NE boundary conditions
REAL b_SW = (i>0 && j>0) ? 0.0f :
((i==0 && j>1) ? rbx*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i,j-2,k)]) :
((i>1 && j==0) ? rby*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i-2,j,k)]) : 0.0f));
REAL b_SE = (i<(nx-1) && j>0) ? 0.0f :
((i==(nx-1) && j>1) ? - rbx*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i,j-2,k)]) :
((i<(nx-2) && j==0) ? rby*(g_in.u[I3D(nx,nxy,i+2,j,k)] - g_in.u[i3d]) : 0.0f));
REAL b_NW = (i>0 && j<(ny-1)) ? 0.0f :
((i==0 && j<(ny-2)) ? rbx*(g_in.u[I3D(nx,nxy,i,j+2,k)] - g_in.u[i3d]) :
((i>1 && j==(ny-1)) ? - rby*(g_in.u[i3d] - g_in.u[I3D(nx,nxy,i-2,j,k)]) : 0.0f));
REAL b_NE = (i<(nx-1) && j<(ny-1)) ? 0.0f :
((i==(nx-1) && j<(ny-2)) ? - rbx*(g_in.u[I3D(nx,nxy,i,j+2,k)] - g_in.u[i3d]) :
((i<(nx-2) && j==(ny-1)) ? - rby*(g_in.u[I3D(nx,nxy,i+2,j,k)] - g_in.u[i3d]) : 0.0f));
du2dt += ( r.xy[k]*( (g_in.u[SWxy] + b_SW) +
(g_in.u[NExy] + b_NE) -
(g_in.u[SExy] + b_SE) -
(g_in.u[NWxy] + b_NW) ) );
#else
/*------------------------------------------------------------------------
* Isotropic Laplacian
*------------------------------------------------------------------------
*/
REAL du2dt = ( rCxyz_d*u
+ rwe_d*(g_in.u[W] + g_in.u[E])
+ rsn_d*(g_in.u[N] + g_in.u[S])
+ rbt_d*(g_in.u[T] + g_in.u[B])
+ rxyc_d*( g_in.u[SWxy] +
g_in.u[SExy] +
g_in.u[NWxy] +
g_in.u[NExy] )
+ rxzc_d*( g_in.u[SWxz] +
g_in.u[SExz] +
g_in.u[NWxz] +
g_in.u[NExz] )
+ ryzc_d*( g_in.u[SWyz] +
g_in.u[SEyz] +
g_in.u[NWyz] +
g_in.u[NEyz] ) ) ;
du2dt -= ( dt_d*( 0.5f*I_sum
+ rxyzf_d * ( ( J_d[E] + J_d[W] )
+ ( J_d[N] + J_d[S] )
+ ( J_d[B] + J_d[T] ) ) ) / C_m ) ;
/*
REAL du2dt = (
+ ( g_in.u[W] - 2.f*u + g_in.u[E] )*rx_d
+ ( g_in.u[N] - 2.f*u + g_in.u[S] )*ry_d
+ ( g_in.u[T] - 2.f*u + g_in.u[B] )*rz_d );
du2dt -= dt_d*I_sum/C_m ;
*/
#endif
/*------------------------------------------------------------------------
* Time integration
*------------------------------------------------------------------------
*/
u += du2dt ;
g_out.u[i3d] = u ;
#endif
}
void FK_3V_wrapper(dim3 grid3D, dim3 block3D, stateVar gOut_d, stateVar gIn_d,
conductionVar r_d, REAL *J_current_d) {
/*
cudaEvent_t start,stop;
cudaEventCreate(&start);
cudaEventCreate(&stop);
float elapsedTime;
cudaEventRecord(start,0);
*/
FK_3V_kernel<<<grid3D, block3D>>>(gOut_d, gIn_d, r_d, J_current_d);
CudaCheckError();
/*
cudaEventRecord(stop,0);
cudaEventSynchronize(stop);
cudaEventElapsedTime(&elapsedTime,start,stop);
printf("3V kernel took: %f ms\n", elapsedTime);
//t += 2.0*dt;
*/
/*
SIM_2V_kernel<<<grid3D, block3D>>>(gIn_d, gOut_d, r_d, J_current_d);
CudaCheckError();
*/
//swapSoA(&gIn_d, &gOut_d);
}
// This function launches all functions that need to be prcessed at every frame
// No graphics functions are launched from here
void animation(dim3 grid3D, dim3 block3D,
stateVar g_h, stateVar gOut_d, stateVar gIn_d, REAL *J_current_d,
conductionVar r_d, paramVar param, REAL *pt_h, REAL *pt_d,
std::vector<electrodeVar> &electrode,
bool initConditionFlag) {
#pragma unroll
for (int i=0;i<(ITPERFRAME);i++) {
FK_3V_wrapper(grid3D,block3D,gOut_d,gIn_d,r_d,J_current_d);
swapSoA(&gIn_d, &gOut_d);
}
// Single point time tracking
singlePoint(gIn_d,pt_h,pt_d,param.singlePointPixel,electrode);
}
__global__ void singlePoint_kernel(stateVar g_in, REAL *pt_d,
int singlePointPixel) {
pt_d[0] = g_in.u[singlePointPixel];
pt_d[1] = g_in.v[singlePointPixel];
pt_d[2] = g_in.v[singlePointPixel];
}
void singlePoint(stateVar gIn_d, REAL *pt_h, REAL *pt_d,
int singlePointPixel, std::vector<electrodeVar> &electrode) {
singlePoint_kernel<<<1,1>>>(gIn_d, pt_d, singlePointPixel);
CudaCheckError();
CudaSafeCall(cudaMemcpy(pt_h, pt_d, 3*sizeof(REAL),cudaMemcpyDeviceToHost));
electrodeVar data = {
pt_h[0],
pt_h[1],
pt_h[2],
};
electrode.push_back(data);
}
__global__ void copyRender_kernel(int totpoints, stateVar g_in,
VolumeType *h_volume) {
int index = blockIdx.x * blockDim.x + threadIdx.x;
int stride = blockDim.x * gridDim.x;
for (int i = index; i < totpoints; i += stride) {
h_volume[i] = (unsigned char)255.f*(float)g_in.u[i]*0.9f;
}
}
// Convert numerical values of the PDE solution to colors (char)
//extern "C"
void copyRender(dim3 grid1D, dim3 block1D, int totpoints,
stateVar gIn_d, VolumeType *h_volume) {
/*
cudaEvent_t start,stop;
cudaEventCreate(&start);
cudaEventCreate(&stop);
float elapsedTime;
cudaEventRecord(start,0);
*/
copyRender_kernel<<<grid1D, block1D>>>(totpoints, gIn_d, h_volume);
CudaCheckError();
/*
cudaEventRecord(stop,0);
cudaEventSynchronize(stop);
cudaEventElapsedTime(&elapsedTime,start,stop);
printf("Time: %f ms\n", elapsedTime);
*/
}
__global__ void spiralTip_kernel(REAL *g_past, stateVar g_present,
VolumeType *h_vol) {
/*------------------------------------------------------------------------
* Getting i, and k global indices
*------------------------------------------------------------------------
*/
const int i = blockIdx.x*blockDim.x + threadIdx.x;
const int j = blockIdx.y;
const int k = threadIdx.y;
/*------------------------------------------------------------------------
* Return if we are outside the domain
*------------------------------------------------------------------------
*/
if( i >= nx && j>=ny && k >= nz) {
return ;
}
const int nxy = nx*ny;
int s0 = I3D(nx,nxy,i,j,k);
int sx = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i,j,k);
int sy = ( j<(ny-1) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i,j,k);
int sz = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,k);
int sxy = ( (j<(ny-1)) && (i<(nx-1) ) ) ? I3D(nx,nxy,i+1,j+1,k) : I3D(nx,nxy,i,j,k);
int sxz = ( (k<(nz-1)) && (i<(nx-1) ) ) ? I3D(nx,nxy,i+1,j,k+1) : I3D(nx,nxy,i,j,k);
int syz = ( (j<(ny-1)) && (k<(nz-1) ) ) ? I3D(nx,nxy,i,j+1,k+1) : I3D(nx,nxy,i,j,k);
#ifdef SPIRALTIP_INTERPOLATION
/*------------------------------------------------------------------------
* Calculate pixel position of filament
*------------------------------------------------------------------------
*/
REAL x1, x2, x3, x4, y1, y2, y3, y4;
REAL x3y1, x4y1, x3y2, x4y2, x1y3, x2y3, x1y4, x2y4, x2y1, x1y2, x4y3, x3y4;
REAL den1, den2, ctn1, ctn2, disc, xtip, ytip, px, py, sroot1, sroot2;
REAL gx, gy, gz, gx1, gx2, gx3, gx4, gy1, gy2, gy3, gy4, gz1, gz2, gz3, gz4;
/*------------------------------------------------------------------------
* Calculate pixel position of filament and plot
*------------------------------------------------------------------------
*/
int S = ( j>0 ) ? I3D(nx,nxy,i,j-1,k) : I3D(nx,nxy,i,j+1,k) ;
int Sx = ( (j>0) && (i<(nx-1)) ) ? I3D(nx,nxy,i+1,j-1,k) : I3D(nx,nxy,i-1,j+1,k) ;
int Sy = I3D(nx,nxy,i,j,k) ;
int Sxy = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i-1,j,k) ;
int Sz = ( j>0 ) ? I3D(nx,nxy,i,j-1,k+1) : I3D(nx,nxy,i,j+2,k+1) ;
int Sxz = ( j>0 ) ? I3D(nx,nxy,i+1,j-1,k+1) : I3D(nx,nxy,i,j+2,k+1) ;
int Syz = ( j>0 ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j+2,k+1) ;
int N = ( j<(ny-1) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i,j-1,k) ;
int Nx = ( (i<(nx-1)) && (j<(ny-1)) ) ? I3D(nx,nxy,i+1,j+1,k) : I3D(nx,nxy,i-1,j-1,k) ;
int Ny = ( j<(ny-2) ) ? I3D(nx,nxy,i,j+2,k) : (( j==(ny-2) ) ? I3D(nx,nxy,i,j,k) : I3D(nx,nxy,i,j-1,k)) ;
int Nxy = ( (i<(nx-1)) && (j<(ny-2)) ) ? I3D(nx,nxy,i+1,j+2,k) : ((j==(ny-2)) ? I3D(nx,nxy,i-1,j,k) : I3D(nx,nxy,i-1,j-1,k)) ;
int Nz = ( (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i,j+1,k+1) : I3D(nx,nxy,i,j-1,k-1) ;
int Nxz = ( (i<(nx-1)) && (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+1,j+1,k+1) : I3D(nx,nxy,i-1,j-1,k-1) ;
int Nyz = ( (j<(ny-2)) && (k<(nz-1)) ) ? I3D(nx,nxy,i,j+2,k+1) : ((k==(nz-2)) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j-1,k-1) );
int W = ( i>0 ) ? I3D(nx,nxy,i-1,j,k) : I3D(nx,nxy,i-1,j,k) ;
int Wx = I3D(nx,nxy,i,j,k) ;
int Wy = ( (i>0) && (j<(ny-1)) ) ? I3D(nx,nxy,i-1,j+1,k) : I3D(nx,nxy,i+1,j-1,k) ;
int Wxy = ( (j<(ny-1)) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i-1,j,k) ;
int Wz = ( (i>0) && (k<(nz-1)) ) ? I3D(nx,nxy,i-1,j,k+1) : I3D(nx,nxy,i+1,j,k-1) ;
int Wxz = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,k-1) ;
int Wyz = ( (i>0) && (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i-1,j+1,k+1) : I3D(nx,nxy,i+1,j-1,k-1) ;
int E = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i-1,j,k) ;
int Ex = ( i<(nx-2) ) ? I3D(nx,nxy,i+2,j,k) : ((i==(nx-2)) ? I3D(nx,nxy,i,j,k) : I3D(nx,nxy,i-1,j,k));
int Ey = ( (i<(nx-1)) && (j<(ny-1)) ) ? I3D(nx,nxy,i+1,j+1,k) : I3D(nx,nxy,i-1,j-1,k) ;
int Exy = ( (i<(nx-2)) && (j<(ny-1)) ) ? I3D(nx,nxy,i+2,j+1,k) : ( (i==(nx-2)) ? I3D(nx,nxy,i,j-1,k) : I3D(nx,nxy,i-1,j-1,k)) ;
int Ez = ( (i<(nx-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+1,j,k+1) : I3D(nx,nxy,i-1,j,k-1) ;
int Exz = ( (i<(nx-2)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+2,j,k+1) : ( (i==(nx-2)) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i-1,j,k-1) );
int Eyz = ( (i<(nx-1)) && (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+1,j+1,k+1) : I3D(nx,nxy,i-1,j-1,k-1) ;
int B = ( k>0 ) ? I3D(nx,nxy,i,j,k-1) : I3D(nx,nxy,i,j,k+1) ;
int Bx = ( (k>0) && (i<(nx-1)) ) ? I3D(nx,nxy,i+1,j,k-1) : I3D(nx,nxy,i-1,j,k+1) ;
int By = ( (k>0) && (j<(ny-1)) ) ? I3D(nx,nxy,i,j+1,k-1) : I3D(nx,nxy,i,j-1,k+1) ;
int Bxy = ( (i<(nx-1)) && (j<(ny-1)) && (k>0) ) ? I3D(nx,nxy,i+1,j+1,k-1) : I3D(nx,nxy,i-1,j-1,k+1) ;
int Bz = I3D(nx,nxy,i,j,k);
int Bxz = ( i<(nx-1) ) ? I3D(nx,nxy,i+1,j,k) : I3D(nx,nxy,i-1,j,k) ;
int Byz = ( j<(ny-1) ) ? I3D(nx,nxy,i,j+1,k) : I3D(nx,nxy,i,j-1,k) ;
int T = ( k<(nz-1) ) ? I3D(nx,nxy,i,j,k+1) : I3D(nx,nxy,i,j,k-1) ;
int Tx = ( (i<(nx-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+1,j,k+1) : I3D(nx,nxy,i-1,j,k-1) ;
int Ty = ( (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i,j+1,k+1) : I3D(nx,nxy,i,j-1,k-1) ;
int Txy = ( (i<(nx-1)) && (j<(ny-1)) && (k<(nz-1)) ) ? I3D(nx,nxy,i+1,j+1,k+1) : I3D(nx,nxy,i-1,j-1,k-1) ;
int Tz = ( k<(nz-2) ) ? I3D(nx,nxy,i,j,k+2) : ( (k==(nz-2)) ? I3D(nx,nxy,i,j,k) : I3D(nx,nxy,i,j,k-1));
int Txz = ( (i<(nx-1)) && k<(nz-2) ) ? I3D(nx,nxy,i+1,j,k+2) : ( (k==(nz-2)) ? I3D(nx,nxy,i-1,j,k) : I3D(nx,nxy,i-1,j,k-1));
int Tyz = ( (j<(ny-1)) && (k<(nz-2)) ) ? I3D(nx,nxy,i,j+1,k+2) : ( (k==(nz-2)) ? I3D(nx,nxy,i,j-1,k) : I3D(nx,nxy,i,j-1,k-1) );
/*------------------------------------------------------------------------
* XY plane
*------------------------------------------------------------------------
*/
x1 = g_present.u[s0];
x2 = g_present.u[sx];
x4 = g_present.u[sy];
x3 = g_present.u[sxy];
y1 = g_past[s0];
y2 = g_past[sx];
y4 = g_past[sy];
y3 = g_past[sxy];
x3y1 = x3*y1;
x4y1 = x4*y1;
x3y2 = x3*y2;
x4y2 = x4*y2;
x1y3 = x1*y3;
x2y3 = x2*y3;
x1y4 = x1*y4;
x2y4 = x2*y4;
x2y1 = x2*y1;
x1y2 = x1*y2;
x4y3 = x4*y3;
x3y4 = x3*y4;
den1 = 2.0*(x3y1 - x4y1 - x3y2 + x4y2 - x1y3 + x2y3 + x1y4 - x2y4);
den2 = 2.0*(x2y1 - x3y1 - x1y2 + x4y2 + x1y3 - x4y3 - x2y4 + x3y4);
ctn1 = x1 - x2 + x3 - x4 - y1 + y2 - y3 + y4;
ctn2 = x3y1 - 2.0*x4y1 + x4y2 - x1y3 + 2.0*x1y4 - x2y4;
disc = 4.0 * ( x3y1 - x3y2 - x4y1 + x4y2 - x1y3 + x1y4 + x2y3 - x2y4 )
* (x4y1 - x1y4 + Uth * (x1 - x4 - y1 + y4)) +
( -ctn2 + Uth * ctn1 ) * (-ctn2 + Uth * ctn1 );
px = -(Uth * ctn1 - ctn2)/den1;
py = (Uth * ctn1)/den2 -
(-2.0* x2y1 + x3y1 + 2.0 *x1y2 - x4y2 - x1y3 + x2y4)/den2;
sroot1 = sqrt(disc)/den1;
sroot2 = sqrt(disc)/den2;
/*------------------------------------------------------------------------
* XY plane
* Clockwise direction
*------------------------------------------------------------------------
*/
xtip = px + sroot1;
ytip = py + sroot2;
if ( ( ((xtip > 0.0) && (xtip < 1.0)) +
((ytip > 0.0) && (ytip < 1.0)) +
( disc > 0.0 ) ) > 2 ) {
/*
gx = (g_present.u[E] - g_present.u[W])*invdx_d;
gy = (g_present.u[N] - g_present.u[S])*invdy_d;
gz = (g_present.u[T] - g_present.u[B])*invdz_d;
*/
gx1 = (g_present.u[E] - g_present.u[W])*invdx_d;
gy1 = (g_present.u[N] - g_present.u[S])*invdy_d;
gz1 = (g_present.u[T] - g_present.u[B])*invdz_d;
gx2 = (g_present.u[Ex] - g_present.u[Wx])*invdx_d;
gy2 = (g_present.u[Nx] - g_present.u[Sx])*invdy_d;
gz2 = (g_present.u[Tx] - g_present.u[Bx])*invdz_d;
gx3 = (g_present.u[Ey] - g_present.u[Wy])*invdx_d;
gy3 = (g_present.u[Ny] - g_present.u[Sy])*invdy_d;
gz3 = (g_present.u[Ty] - g_present.u[By])*invdz_d;
gx4 = (g_present.u[Exy] - g_present.u[Wxy])*invdx_d;
gy4 = (g_present.u[Nxy] - g_present.u[Sxy])*invdy_d;
gz4 = (g_present.u[Txy] - g_present.u[Bxy])*invdz_d;
gx = (1.0 - xtip)*(1.0 - ytip)*gx1 +
xtip*(1.0 - ytip)*gx2 + ytip*(1.0 - xtip)*gx3 + xtip*ytip*gx4;
gy = (1.0 - xtip)*(1.0 - ytip)*gy1 +
xtip*(1.0 - ytip)*gy2 + ytip*(1.0 - xtip)*gy3 + xtip*ytip*gy4;
gz = (1.0 - xtip)*(1.0 - ytip)*gz1 +