initmesh: 'Hmax' parameter is not an upper bound on edge lengths

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Robin Merkle 2020-5-17

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https://ww2.mathworks.cn/matlabcentral/answers/526090-initmesh-hmax-parameter-is-not-an-upper-bound-on-edge-lengths

评论： Robin Merkle 2020-5-17

Hi all,

I am using initmesh() to generate a 2D-mesh in order to discretize a PDE-problem. The parameter 'Hmax' of this matlab function can be used to bound the edge lengths of the triangulation. Beeing precise, the documentation of initmesh() says:

"The Hmax property controls the size of the triangles on the mesh. initmesh creates a mesh where triangle edge lengths are approximately Hmax or less."

However, an easy example on the domain D=[0,1]^2 with Hmax=1 shows, that this is not the case: the generated mesh includes the triangle [0,0] - [1,0] - [0,1] with maximum edge length sqrt(2).

Code:

b1=0;b2=1; d0=decsg([3 4 b1 b2 b2 b1 b1 b1 b2 b2]');
[points,edges,triCL]=initmesh(d0,'Hmax',1,'MesherVersion','R2013a');
pdemesh(points,edges,triCL)

Indeed, after a few experiments it seems like the parameter 'Hmax' is a treshold on the max-min-edge length, i.e. it seems to be a bound on max(h_min(T)) over all triangles T in the triangulation, where h_min(T) denotes the minimal edge length of the triangle T.

Is there a reason for this? Do I misunderstand something?

Thank you in advance!

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darova 2020-5-17

在 MATLAB Online 中打开

Maybe Hmax controls smaller edges of the triangle

b1 = 0;
b2 = 1.01; 
d0 = decsg([3 4 b1 b2 b2 b1 b1 b1 b2 b2]');
[p,e,t] = initmesh(d0,'Hmax',1,'MesherVersion','R2013a');
pdemesh(p,e,t)

Robin Merkle 2020-5-17

Yes. That's what i meant by the max-min-edge length. But I don't understand why this is the case (since - at least to my knowledge - error bounds e.g. for PDE-solving methods are usually given in terms of the maximal edge length of all triangles). And, in addition, this is definitely not what is described in the matlab description of the function initmesh().

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