[sasanghomi]

Dear friends

The following UDF is about the anisotropic conductivity matrix for a cylindrical shell.

ِDoes anybody understand different parts of this code?
I have some questions and I would be thankful if someone could help me.

1) What is the role of x Matrix? at first, the code is calculating x Matrix, but it is not understandable to me.

2) dmatrix is the tensor responsible for conductivity in cylindrical coordinate.
/* dmatrix is computed as xT*cond*x */
This line implies that matrix X transpose *vector cond*matrix X

This multiplication is not possible, I suppose. because;

matrix X[3*3]
matrix X transpose[3*3]
Vector cond [1*3]

Could anybody give me some hints? How dmatrix is calculated in the rest of the code?

/******************************************************************************
 UDF for defining the anisotropic conductivity matrix for a cylindrical shell
 ******************************************************************************/
 #include "udf.h"
 /* Computation of anisotropic conductivity matrix for
 * cylindrical orthotropic conductivity */
 /* axis definition for cylindrical conductivity */
 static const real origin[3] = {0.0, 0.0, 0.0};
 static const real axis[3] = {0.0, 0.0, 1.0};
 /* conductivities in radial, tangential and axial directions */
 static const real cond[3] = {1.0, 0.01, 0.01};
 DEFINE_ANISOTROPIC_CONDUCTIVITY(cyl_ortho_cond,c,t,dmatrix)
 {
 real x[3][3]; /* principal direction matrix for cell in cartesian coords. */
 real xcent[ND_ND];
 real R;
 C_CENTROID(xcent,c,t);
 NV_VV(x[0],=,xcent,-,origin);
 #if RP_3D
 NV_V(x[2],=,axis);
 #endif
 #if RP_3D
 R = NV_DOT(x[0],x[2]);
 NV_VS(x[0],-=,x[2],*,R);
 #endif
 R = NV_MAG(x[0]);
 if (R > 0.0)
 NV_S(x[0],/=,R);
 #if RP_3D
 N3V_CROSS(x[1],x[2],x[0]);
 #else
 x[1][0] = -x[0][1];
 x[1][1] = x[0][0];
#endif
 /* dmatrix is computed as xT*cond*x */
dmatrix[0][0] = cond[0]*x[0][0]*x[0][0]
 + cond[1]*x[1][0]*x[1][0]
 #if RP_3D
 + cond[2]*x[2][0]*x[2][0]
 #endif
 ;
 dmatrix[1][1] = cond[0]*x[0][1]*x[0][1]
 + cond[1]*x[1][1]*x[1][1]
 #if RP_3D
 + cond[2]*x[2][1]*x[2][1]
 #endif
 ;
 dmatrix[1][0] = cond[0]*x[0][1]*x[0][0]
 + cond[1]*x[1][1]*x[1][0]
 #if RP_3D
 + cond[2]*x[2][1]*x[2][0]
 #endif
 ;
 dmatrix[0][1] = dmatrix[1][0];
 #if RP_3D
 dmatrix[2][2] = cond[0]*x[0][2]*x[0][2]
 + cond[1]*x[1][2]*x[1][2]
 + cond[2]*x[2][2]*x[2][2]
 ;
 dmatrix[0][2] = cond[0]*x[0][0]*x[0][2]
 + cond[1]*x[1][0]*x[1][2]
 + cond[2]*x[2][0]*x[2][2]
 ;
 dmatrix[2][0] = dmatrix[0][2];
 dmatrix[1][2] = cond[0]*x[0][1]*x[0][2]
 + cond[1]*x[1][1]*x[1][2]
 + cond[2]*x[2][1]*x[2][2]
 ;
 dmatrix[2][1] = dmatrix[1][2];
 #endif
 }