Vector Operators

The following operators perform various transformations on vector quantities.

Vectors in three-dimensional problems are assumed to have one component in each of the coordinate directions. 

Vectors in two-dimensional problems are assumed to have two components both of which lie in the plane of the problem.  In some cases a third component is inferred to be a scalar,  such as the result of a cross-product or a curl.

CROSS ( vector1, vector2 )        

Forms the cross product of two vectors and returns the resulting vector.  In 2D, CROSS returns a scalar value equal to the component of the vector cross product normal to the problem plane.        

DOT ( vector1, vector2 )        

Forms the dot product of two vectors and returns a scalar value equal to the magnitude of the vector dot product.

MAGNITUDE ( vector )        

Returns a scalar equal to the magnitude of a vector argument.

MAGNITUDE ( argx, argy  [, argz ] )        

Returns a scalar equal to the magnitude of a vector whose components are argx and argy (and possibly argz in 3D).

NORMAL ( vector )        

Returns a scalar equal to the component of a vector argument normal to a boundary.*        

NORMAL ( argx, argy [, argz] )        

Returns a scalar equal to the boundary-normal component of a vector whose components are argx and argy (and possibly argz in 3D).*        

TANGENTIAL(arg)        

Returns a scalar equal to the component of a vector argument tangential to a boundary.*

TANGENTIAL ( argx,  argy [, argz ] )        

Returns a scalar equal to the boundary-tangential component of a vector whose components are argx and argy (and possibly argz in 3D).*        

VECTOR ( argx, argy [, argz ] )        

Constructs a vector whose components are the scalar arguments.        

XCOMP ( vector )        

Returns a scalar whose value is the first component of the vector argument (regardless of the names of the coordinates).

YCOMP ( vector )        

Returns a scalar whose value is the second component of the vector argument (regardless of the names of the coordinates).

ZCOMP ( vector )        

Returns a scalar whose value is the third component of the vector argument, if it exists (regardless of the names of the coordinates).        

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* Note: NORMAL and TANGENTIAL operators may only be used in boundary condition definitions or in boundary plots or integrals.