BTW,

Here I used GmshIO to read the .msh file of version 2.2.
By default gmsh count $PhysicalNames from 1. This is also inherited by 
GmshIO::read_mesh(..).

I guess inside ParsedFunction it is assumed the user given boundary_id_type 
should start from zero, right?
If so, there may be incompatibility problem like what I showed in last email. 

I tried force the boundary_id 1 to zero, then the assetation failure never 
occur, meanwhile the code give the wrong final result since with improper 
boundary conditions.

Zhenyu
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