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Hello Kaloyan Kirilov,

Thank you very much for providing those solutions. Unfortunately, I am still encountering the same error. I generated the mesh using gmsh, and for testing purposes, I simplified the mesh to the most basic case. Here is the content of the .geo file:

SetFactory("OpenCASCADE");
Circle(1) = {0, 0, 0, 4, 0, Pi/6};
Circle(2) = {0, 0, 0, 14, 0, Pi/6};
Line(3) = {2, 4};
Line(4) = {1, 3};
Curve Loop(1) = {3, -2, -4, 1};
Plane Surface(1) = {1};
Transfinite Curve {3, 4} = 3 Using Progression 1.1;
Transfinite Curve {1, 2} = 3 Using Progression 1;
Transfinite Surface {1};
Recombine Surface {1};//+
Physical Curve("p1", 5) = {3};
Physical Curve("p2", 6) = {4};
Physical Curve("up", 7) = {1};
Physical Curve("up2", 8) = {2};
Physical Surface("plane", 9) = {1};

In this file, I want "p1" and "p2" to represent the periodic boundaries for rotation.

Thank you once again for your guidance.

Best regards,

Yaguang.