Dear GMSH,
Me and my colleagues have very high interest in using GMSH curvilinear
elements for our FEM code. Recently, I have implemented a .MSH reader
and a .VTK writer, and I have made a few observations:
I have attached to this e-mail a sphere32.geo file which discretizes a
sphere into 32 tetrahedrons. Also, I have attached a .vtk file where I
have applied a 5th order polynomial interpolation to the sphere (using
GMSH), and drawn the surfaces by connecting the provided interpolatory
points with triangles (no actual interpolation here). I have also
shrinked every of the 32 tetrahedrons for better visibility.
When I compare it to the surface visualisation that I get from GMSH UI,
I do not observe extra curvature of edges. In fact, it seems to me that
the GMSH UI visualisation of the sphere does not change much between
interpolatory order 2 and any higher orders. Is this the expected behaviour.
I have tried to export the mesh directly from GMSH to VTK. If I export
mesh of interpolatory order 3 or higher this way I observe some
unexpected spikes on the sphere in paraview.
Finally, the most important question for us. From the attached .vtk it
may be observed that some internal boundary surfaces of the tetrahedrons
are straight, and others are highly convex/concave. Is this the expected
behaviour, and if it is, then what is the motivation for making a curved
surface between two elements of the same material property.
Regards,
Aleksejs Fomins
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/** \file
* \brief Gmsh scriptum of a simple sphere.
*
* Copyright by Patrick Leidenberger and Benedikt Oswald, 2006-2006.
* All rights reserved.
*
* Objective: Gmsh scriptum of a simple sphere with radius=1m. You can get mesh with gmsh
* form that file with: gmsh -3 sphere.geo
*
* \author Patrick Leidenberger, Benedikt Oswald
* \date 2006 dec 15, created, Patrick Leidenberger
* \date 2006 dec 15, modified, Patrick Leidenberger
* \date 2009 aug 03, modified, Benedikt Oswald, adapted parameters
*
* \warning None.
* \attention
* \bug
* \todo
*/
Mesh.Algorithm = 2;
scaling = 1; // Scaling factor for all.
cl = scaling * 1; // Characteristic length for all.
// physical id's
abc1st = 101;
vacuum = 501;
// Center of sphere.
centerX = scaling * 0.0;
centerY = scaling * 0.0;
centerZ = scaling * 0.0;
// Radius of the sphere
radius = scaling * 1.0;
// Create points on the sphere surface.
ipt1 = newp; Point(ipt1) = {centerX, centerY, centerZ, cl};
ipt2 = newp; Point(ipt2) = {centerX - radius, centerY, centerZ, cl};
ipt3 = newp; Point(ipt3) = {centerX + radius, centerY, centerZ, cl};
ipt4 = newp; Point(ipt4) = {centerX, centerY - radius, centerZ, cl};
ipt5 = newp; Point(ipt5) = {centerX, centerY + radius, centerZ, cl};
ipt6 = newp; Point(ipt6) = {centerX, centerY, centerZ - radius, cl};
ipt7 = newp; Point(ipt7) = {centerX, centerY, centerZ + radius, cl};
// Create circle sections connecting two points on sphere surface.
icl1 = newreg; Circle(icl1) = {ipt2,ipt1,ipt4};
icl2 = newreg; Circle(icl2) = {ipt2,ipt1,ipt5};
icl3 = newreg; Circle(icl3) = {ipt2,ipt1,ipt6};
icl4 = newreg; Circle(icl4) = {ipt2,ipt1,ipt7};
icl5 = newreg; Circle(icl5) = {ipt3,ipt1,ipt4};
icl6 = newreg; Circle(icl6) = {ipt3,ipt1,ipt5};
icl7 = newreg; Circle(icl7) = {ipt3,ipt1,ipt6};
icl8 = newreg; Circle(icl8) = {ipt3,ipt1,ipt7};
icl9 = newreg; Circle(icl9) = {ipt4,ipt1,ipt6};
icl10 = newreg; Circle(icl10) = {ipt4,ipt1,ipt7};
icl11 = newreg; Circle(icl11) = {ipt5,ipt1,ipt6};
icl12 = newreg; Circle(icl12) = {ipt5,ipt1,ipt7};
// Make the surface mesh for 3 closed circle sections.
ill1 = newreg; Line Loop(ill1) = {icl1,-icl3,icl9} ; irs1= newreg; Ruled Surface(irs1) = {ill1};
ill2 = newreg; Line Loop(ill2) = {icl1,icl10,-icl4} ; irs2= newreg; Ruled Surface(irs2) = {ill2};
ill3 = newreg; Line Loop(ill3) = {icl2,-icl3,icl11} ; irs3= newreg; Ruled Surface(irs3) = {ill3};
ill4 = newreg; Line Loop(ill4) = {icl2,icl12,-icl4} ; irs4= newreg; Ruled Surface(irs4) = {ill4};
ill5 = newreg; Line Loop(ill5) = {icl5,icl9,-icl7} ; irs5= newreg; Ruled Surface(irs5) = {ill5};
ill6 = newreg; Line Loop(ill6) = {icl5,icl10,-icl8} ; irs6= newreg; Ruled Surface(irs6) = {ill6};
ill7 = newreg; Line Loop(ill7) = {icl6,icl11,-icl7} ; irs7= newreg; Ruled Surface(irs7) = {ill7};
ill8 = newreg; Line Loop(ill8) = {icl6,icl12,-icl8} ; irs8= newreg; Ruled Surface(irs8) = {ill8};
ilsl1 = newreg;
Surface Loop(ilsl1) = {irs1, irs2, irs3, irs4, irs5, irs6, irs7, irs8};
// Define physcial surface
Physical Surface (abc1st) = {irs1,irs2,irs3,irs4,irs5,irs6,irs7,irs8};
// Define volume of sphere.
ivl1 = newv; Volume(ivl1) = {ilsl1};
// Define physical volume
Physical Volume ( vacuum ) = {ivl1};
Coherence;
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# vtk DataFile Version 2.0
triangle_test_output, Created by CurvilinearGmshReaderTest
ASCII
DATASET UNSTRUCTURED_GRID
POINTS 1664 double
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CELL_TYPES 3200
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