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Thread Subject:
3D Helmholtz Equation

Subject: 3D Helmholtz Equation

From: Sutharsanan Veeriah

Date: 17 Apr, 2003 02:25:22

Message: 1 of 4

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.
Thank you.

Subject: 3D Helmholtz Equation

From: Timo Nieminen

Date: 17 Apr, 2003 17:12:54

Message: 2 of 4

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.

Finite-difference frequency-domain. 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.

Finite-difference time-domain. 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/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

Subject: 3D Helmholtz Equation

From: Sutharsanan Veeriah

Date: 17 Apr, 2003 22:34:41

Message: 3 of 4

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.
>
> Finite-difference frequency-domain. 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.
>
> Finite-difference time-domain. 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/>
> Shrine to Spirits:
 <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.

Subject: 3D Helmholtz Equation

From: Timo Nieminen

Date: 25 Apr, 2003 08:17:21

Message: 4 of 4

On Thu, 17 Apr 2003, Sutharsanan Veeriah wrote:

> 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.

Anyway, feel free to give more details. Can't make any really useful
suggestions without more information.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

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