Timo Nieminen wrote:
>
>
> On Thu, 17 Apr 2003, Sutharsanan Veeriah wrote:
>
>> How can I solve the 3D Helmholtz equation using the Matlab
software
>> besides the finite elemental method. If there are any
solutions, can
>> someone suggest where can I get the codes as reference.
>
> Finitedifference frequencydomain. Make a 3D grid. Write discrete
> approximations for the differential operators using these grid
points.
> This gives you a large number of linear equations. Your boundary
> conditions will give you more equations. Solve your linear system.
>
> Finitedifference timedomain. Make 3D grid, set up initial
conditions,
> find time derivatives from spatial derivatives, step forward in
time.
> Probably some boundary condition drives the system at every point
in time.
>
> Expansion in wavefunctions. Write a general solution for the
Helmholtz eqn
> in the coordinate system of your choice. Approximate this by a
finite
> subset of this solution. Expansion coeeficients are the unknowns
you need
> to find. Choose a sufficiently large set of points where boundary
> conditions are specified, write equations for fields at these
points. This
> gives you a linear system. Solve it. Works best if the linear
system is
> overdetermined.
>
> Approximate the 3D Helmholtz equation. For example, paraxial
> approximation.
>
> Lots of methods. Which methods are usable depends on the specific
problem.
>
> 
> Timo Nieminen  Home page:
<http://www.physics.uq.edu.au/people/nieminen/>
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<http://www.users.bigpond.com/timo_nieminen/spirits.html>
>
Thanks Timo for the wonderful explanation. I have read about the
boundary conditions that play a very important role in solving an
equation such as this. Anyway, I am having problems solving the
boundary condition for this equation.
