Solving laplace equation

[RogeliodelasCas]

To all,

I cannot find a quicksheet in mathcad help with an example to solve Laplace equation.

What i need is to obtain the solution of potential equation (laplace equation) in two and three dimensions.

The source of the potential could be a cylinder (electrode underground), where the radius is << than the length of it, it could be a geometry figure as a brick (an electrode that is used to protect underwater side of ships), but where the high of the brick is << than its length and width.

Thank you in advance,

Rogelio

[Fred_Kohlhepp]

Attached is a quicksheet for the heat equation. Might give you a place to start.

[RogeliodelasCas]

Thank you Fred,

Please, read my replay to Vladimir, the same will apply for the example that you sent me.

Regards,

Rogelio

[VladimirN]

Below is attached an example "Heat Flow on a Square Plate" for Mathcad 15.

[RogeliodelasCas]

Thank you Vladimir,

The problem with this example is that the source is dimensionless. How can I modify this example for the case that my source will have dimensions? What happen is that I have to obtain the potential in a plate that is under water that has several sources of current (anodes) attached to it, spread on the plate surface. So I need the potential profile not just far from the source (where dimensionless sources are ok for the modeling), but also close to the source, where the dimension of the source effects the potential profile.

Thank you in advance,

Rogelio

[Fred_Kohlhepp]

Rogelio de las Casas wrote:

Thank you Vladimir,

The problem with this example is that the source is dimensionless. How can I modify this example for the case that my source will have dimensions? What happen is that I have to obtain the potential in a plate that is under water that has several sources of current (anodes) attached to it, spread on the plate surface. So I need the potential profile not just far from the source (where dimensionless sources are ok for the modeling), but also close to the source, where the dimension of the source effects the potential profile.

Thank you in advance,

Rogelio

When I must force a problem with dimensions iinto a piece of Mathcad that does not accept dimensions (like ODE solvers) I rely on the "UnitsOf()" function.

Mathcad has a consistent set of internal units. If you divide your units by UnitsOf(your units) Mathcad will put the appropriately scaled number into the problem. You can use the same function to restore units to the results.

As to how you deal with the size and shape of your source: good luck!

[RogeliodelasCas]

Sorry, i did not explain correctly myself.

what i meant is that the examples that Vladimir and you provided do not have dimensions, there are mathematical points. I was not talking about units, i know that we cannot use units inside some mathcad functions and operators.

i need to resolve the equation where the source of charge has dimensions, it is not a mathematical point.

Rogelio

[Fred_Kohlhepp]

Does the attached file help/

[RogeliodelasCas]

No, it does not, it is the same one that Vladimir sent me before and it has the same approximation that the one you sent me privously. The source does not have dimensions.

Rogelio

[RichardJ]

This is not my field, but could you take the point source example, and integrate the solution over the dimensions of hte real source? A nested triple integral will be slow, but it might work?

[VladimirN]

Just note that earlier at a forum the theme "Solving Laplace's Equation" was already discussed: http://communities.ptc.com/thread/29521

Also, these materials may be helpful:

http://plasma.colorado.edu/mathcad/ (Chapter 1. "Electrostatics")

http://plasma.colorado.edu/mathcad/ES_Laplace.mcd ("Laplace Solver")

http://plasma.colorado.edu/mathcad/ES_Laplace_Dielectric.mcd ("Laplace's Equation with a Dielectric")

[RogeliodelasCas]

Vladimir,

thank you very much for this web site. i found very interesting things and i will play with them as soon as i have time.

regards,

Rogelio

[VladimirN]

You're welcome.

[AlanStevens]

If you scroll down the Quicksheet that Vladimir supplied you will see an example of the solution of Poisson's equation - this is really what you want, rather than Laplace's equation, as you have spatially extended sources.

In the example a uniform source is distributed over the whole region, but you should be able to see how to limit the region containing the source by specifying the values of i and j for which your source(s) is(are) non-zero.

Alan