Register to reply

PDE equation in spherical coordinates

by vibe3
Tags: coordinates, equation, spherical
Share this thread:
vibe3
#1
Jan31-12, 05:05 PM
P: 23
I am looking for ideas on how to solve this equation:
[tex]
\nabla \cdot \left( \vec{A} + F \hat{b} \right) = 0
[/tex]
where [itex]\vec{A}[/itex] and [itex]\hat{b}[/itex] are known vectors of [itex](r,\theta,\phi)[/itex] and [itex]F[/itex] is the unknown scalar function to be determined. Also, [itex]\nabla \cdot \hat{b} = 0[/itex]. So the equation can also be expressed as
[tex]
(\nabla F) \cdot \hat{b} + \nabla \cdot \vec{A} = 0
[/tex]

I am trying to solve this numerically, and so I have b and A on a 3D grid. But I would like to avoid using a 3D finite differencing scheme, if there is a way to simplify this to an algebraic equation.

I'm thinking it may be possible to expand these vectors in some sort of basis (like vector spherical harmonics?) along with some radial basis functions and then solve for the coefficients of [itex]F[/itex] in terms of the coefficients of [itex]\vec{A}[/itex] or something like that.

Does anyone have experience with this type of equation and would know an appropriate basis to use?
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history

Register to reply

Related Discussions
Laplace equation in spherical coordinates Calculus & Beyond Homework 0
Solution to diffusion equation in 1d spherical polar coordinates Advanced Physics Homework 3
Exact solution to advection equation in spherical coordinates Differential Equations 1
Triple Integral in Rectangular Coordinates Converting to Spherical Coordinates Calculus & Beyond Homework 2
Schrodinger equation in the spherical coordinates Quantum Physics 3