Strange behaviour of pde-toolbox in labeling or a bug?

Your geometry is unusual in that none of the rectangles intersect each other. The algorithm in function decsg is designed to generally compute the intersections among the input entities and produce a completely new set of regions that are only related to the input entities. Generally, the number of output entities does not match the number of input entities and, as you have discovered, decsg assigns region numbers to these output entities in a way that is not easy to predict.

Bill

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Mohammad Monfared 2013-10-18

Thanks for your response Bill,

As a matter of fact the domain of my problem consists of many rectangular sub-domains which their side borders coincide with the neighboring sub-domains. Constructing 'c' and 'a' matrices, I need to know each sub-domain number to assign the correct values. For example for sub-domain 'R6' I have a sub-domain-number related function, 'F6' to assign.

So how can I access to the predefined(unchanged) sub-domain names(/numbers)? (as I know a common way is to use the 4th row of matrix 't' from 'initmesh' outputs, right?)

Mohammad Monfared 2013-10-18

the problem domain and their changed sub-domain labels:

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Answer 2

Bill Greene 2013-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/90647-strange-behaviour-of-pde-toolbox-in-labeling-or-a-bug#answer_100206

Hi,

The way I have dealt with the problem of defining coefficient matrices when I have had geometries similar to yours is to simply ignore the sub-domain numbers. I write a function to define the coefficient as shown in this doc page:

http://www.mathworks.com/help/pde/ug/scalar-coefficients-in-function-form.html

This page also shows how you can compute the centroid of each triangle inside this function. Then you simply assign coefficient values based on this location. In your case you can use the x-coordinate to determine which rectangle the element is in.

Hope that helps.

Bill

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Bill Greene 2013-10-20

Without knowing the physics of your problem, I can't really say much definitive. It is not uncommon to have a single scalar equation for u and a "c" coefficient that has different terms in the x and y directions to reflect different properties in those directions. But, for a single PDE, the "a" coefficient is also a scalar. If you have more than one value for "a", I would guess you are missing an equation. That would mean u is a vector with two components.

Bill

Mohammad Monfared 2013-10-21

编辑：Mohammad Monfared 2013-10-21

This is the equation of my interest actually:

the water flow equation in a porous media. Domain is in x-z plane.

How can I model it by Pde toolbox?

thanks,

Mohammad

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