Calculating General Tensor Product of Gradients

• To: mathgroup at smc.vnet.net
• Subject: [mg120139] Calculating General Tensor Product of Gradients
• From: Thomas <thomasmarkovich at gmail.com>
• Date: Sat, 9 Jul 2011 07:33:53 -0400 (EDT)

Hi All,

I would like to calculate the tensor product of two gradients for any coordinate system I can define, whether it be 3 dimensions or 30 but I would like to leave it as an operator so that I can apply this to a vector function and get the appropriate answer.

This is to say that I want to calculate \Nabla \otimes \Nabla which in 3-D cartesian coordinates gives

d_xx  d_xy d_xz

d_yx  d_yy d_yz

d_zx  d_zy d_zz

which can then act on a function in 3D. Well, I want to define any gradient I want (maybe prolated spheroidal coordinates, etc) and find what \Nabla \otimes \Nabla is equal to so that I can then perform further computations. Unfortunately, I have no clue how to do this and so if you guys had any suggestion as to how to do this, I would be very thankful.

Best Regards,

Thomas



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