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Topic: surface area of pdedemo3
Replies: 5   Last Post: Jul 2, 2013 4:16 PM

 Messages: [ Previous | Next ]
 Alan Weiss Posts: 1,430 Registered: 11/27/08
Re: surface area of pdedemo3
Posted: Jun 25, 2013 1:19 PM

On 6/25/2013 11:33 AM, Steven Finch wrote:
> Here is more detail. If I append the existing Matlab PDE demo with
> the commands:
>
> pi*mean(sqrt(1+ux.^2+uy.^2))
>
> a coarse estimate 3.8042 of the surface area is obtained. What steps
> can be taken to refine this numerical result? Explicit code would be
> helpful to me. Thank you!
>
>
>
> "Steven Finch" wrote in message
> <kqa2u4\$2on\$1@newscl01ah.mathworks.com>...

>> What is the surface area of the saddle surface in
>> http://www.mathworks.com/help/pde/examples/minimal-surface-problem-on-the-unit-disk.html
>>
>> ?

After refining the result as follows, I got an estimate of the area of
3.8251. All I did was apply another round of refinemesh, and I set the
rtol to 1e-4 instead of 1e-3 (I don't know if refining rtolis is
important or not). To calculate the area, I added up the areas of the
triangles on the surface.

I imagine that it is easier and less error-prone to use Bill Greene's
suggestion rather than my special-purpose triangle summation function.

Alan Weiss
MATLAB mathematical toolbox documentation

Alan Weiss
MATLAB mathematical toolbox documentation

Date Subject Author
6/24/13 Steven Finch
6/25/13 Alan Weiss
6/25/13 Steven Finch
6/25/13 Bill Greene
6/25/13 Alan Weiss
7/2/13 Steven Finch