emanuele casarotti verce training, university of liverpool (uk), 1

Virtual(Earthquake(and(seismology(Research(Community(e8science(environment(in(Europe(Project(283543(–(FP78INFRASTRUCTURES8201182(–(www.verce.eu(–([email protected]

HEX Meshing 101Emanuele Casarotti

VERCE training, University of Liverpool (UK), 1-3 July 2015

Istituto Nazionale di Geofisica e Vulcanologia @INGVterremoti

VERCE training, University of Liverpool (UK), 1-3 July 2015Hex(Meshing(101

MESHINGPDEquations are discretized and solved inside subdomains (cells, elements)

Hexahedra Prism Tetrahedra Pyramid

Meshing depends on your problem and your numerical method

Mesh design affects directly size and performance of your simulation and indirectly the cost of your hardware.


MESH: an underestimated task

MESHGEOMETRY CREATION

DESIGN

SOLVER

PDE - SIMULATION WORKFLOW

MESHING


MESH: an underestimated task

MESHGEOMETRY CREATION

DESIGN

SOLVER

PDE - SIMULATION WORKFLOW

MESHING

HUMAN time

10%weeks

CPU time

0%15%

80%

90%5%

CPU time


MESHER (CUBIT, TRELIS, GMESH, GID, ABAQUS, ANSYS,HEXPRESS,MESHGEMS…)

CAD MESHACIS (CUBIT, Autocad)

STEP IGES (Rhinoceros)

Facets (GOCAD) STL

ExodusII

Graphical Interface

Command line

Abaqus (ASCII) IDEAS NASTRAN Petran LS-Dyna ExodusII (NETCDF)

MESHING WORKFLOW


Map

Sweep

Sub-map

Tetmesh

Triprimitive

THEX


Tri/Tet Methods

http://www.simulog.fr/mesh/gener2.htm

Octree Advancing Front Delaunay

http://www.ansys.com

courtesy of Steven Owen (SANDIA)


courtesy of Steven Owen (SANDIA)

Quad/Hex Methods

Structured • Requires geometry to conform to specific characteristics • Regular patterns of quads/hexes formed based on characteristics of geometry

Unstructured • No specific requirements for geometry • quads/hexes placed to conform to geometry. • No connectivity requirement (although optimization of connectivity is beneficial)

• Internal nodes always attached to same number of elements


Structured

3D Mapped Meshing

• 6 topological surfaces • opposite surfaces must have similar mapped meshes

Geometry Requirements

Sweepingcourtesy of Steven Owen (SANDIA)


Full complexity

Exponential ACCURACY of high-order methods

Suitable for implementation in parallel architectures

Mechanical proprieties can vary inside each element

Low Number of elements for wavelength

EFFICIENCY!!!! (Diagonal Mass Matrix - Explicit time scheme)

SPECTRAL ELEMENT METHOD (SPECFEM3D)


Full complexity

Exponential ACCURACY of high-order methods

Suitable for implementation in parallel architectures

Mechanical proprieties can vary inside each element

Low Number of elements for wavelength

EFFICIENCY!!!! (Diagonal Mass Matrix - Explicit time scheme)

HEX

SPECTRAL ELEMENT METHOD (SPECFEM3D)


MESH: features

Seismic velocity can vary inside the volume

UNSTRUCTURED - ANISOTROPIC - CONFORMAL (honoring the geology)

(usually the dimension of the elements increase with depth)


MESH: parallelism?

Little volume (10x10x10 km)

Huge volume (300x300x100 km)

Long period ~ 1 million ~ 1/5 millions

Short period ~ 5/10 milions ~ 0.5/10 billions (Earth ~ 20 Ghex)


meshing - control ∆t (S.California)


meshing - control resolution (Alaska)

LRZ,(Garching(10(March(2015Hex(Meshing(101

HEX MeshingHEX Meshing

LRZ,(Garching(10(March(2015Hex(Meshing(101

HEX MeshingHEX Meshing

courtesy of Walt Disney


MESHER: CUBIT/TRELIS

US national lab: cubit.sandia.gov

Academic: csimsoft.com

Trelis

2D/3D solid-modeler mesher:Geometry preparationAutomatic meshing

algorithmsQuality analysisHexahedra/Tetrahedra

The CUBIT Geometry and Mesh Generation Toolkit

http://cubit.sandia.gov

http://csimsoft.com


THE MESHING WORKFLOW

Import Solid

Model

1

Simplify

Geometry

2

Decompose

Geometry

3

Imprint &

Merge

4

Set Schemes

& Intervals

5

Mesh

6

Check

Quality

7

Apply

B.C.s

8

Export

Mesh

9



Import Solid

Model

1

Simplify

Geometry

2

Decompose

Geometry

3

Imprint &

Merge

4

Set Schemes

& Intervals

5

Mesh

6

Check

Quality

7

Apply

B.C.s

8

Export

Mesh

9

Order!!



Import Solid

Model

1

Simplify

Geometry

2

Decompose

Geometry

3

Imprint &

Merge

4

Set Schemes

& Intervals

5

Mesh

6

Check

Quality

7

Apply

B.C.s

8

Export

Mesh

9


I - Construction of the geometryII - Meshing the geometryIII - Boundary condition + Export the mesh


I - Construction of the geometryII - Meshing the geometryIII - Boundary condition + Export the mesh

0 - Define purpose and resolution of mesh


MESHING STRATEGIESa) brutal (by hand in cubit)


MESHING STRATEGIESa) brutal (by hand in cubit)b) “Not-honoring”


MESHING STRATEGIES

10.4.1983 ML 3.8

STH

NIS

DMPOC9

CAI

STH

NIS OC9

DMP

CAI

a) brutal (by hand in cubit)

c) GEOcubit (scripting)b) “Not-honoring”


Grenoble Valley, Marco Stupazzini et . al. 2007

MESHING STRATEGIES (a)


MESHING STRATEGIES (b)

Grenoble Valley, Marco Stupazzini et . al. 2007


goal: meshing automatically some reference geological cases

MESHING STRATEGIES (c)


10.4.1983 ML 3.8

STH

NIS

DMPOC9

CAI

STH

NIS OC9

DMP

CAI

Numb. Hex. : ~6.200.000 256 processors

~300 s wall clock

MESHING STRATEGIES (c)

Golfo di Napoli, E. Casarotti et . al. 2007


Semi-automatic (user defines interfaces, tomography, topography,To, ∆h)

Parallel (faster both for the creation of the NURBS geometry and for the mesh - huge mesh and volume)

“cake-layered” volume (main discontinuities honored + tomography)

Each chunk has the same number of elements

goal: meshing automatically some reference geological cases MESHING STRATEGIES (c)


https://github.com/geodynamics/specfem3d/tree/devel/CUBIT_GEOCUBITdeveloper*

mesh: layered geological volume (parallel)

mesh: spherical layered geological volume*

mesh: hex27*mesh: cpml*

mesh: export in SPECFEM3D_cartesian formatenvironment: python script, cubit GUI, interative, cluster queue

mesh: automatic assign of the boundary condition

mesh: vertical “sandwich” layered geological volume*

GEOCUBIT

https://github.com/geodynamics/specfem3d/tree/devel/CUBIT_GEOCUBIT


GEOCUBIT - simplify

GEOCUBIT.py --build_volume --mesh —cfg=examples/scal.cfg —id_proc=[ID]

GEOCUBIT.py --collect —meshfiles=mesh_vol_*.cub --export2SPECFEM3D

[cubit.options]cubit_info=offecho_info=offworking_dir=mesh_california/output_dir=mesh_california/output

[simulation.cpu_parameters]number_processor_xi =15number_processor_eta =15#[geometry.volumes]volume_type = layercake_volume_ascii_regulargrid_regularmaplatitude_min = 131000latitude_max = 738000longitude_min = 3480000longitude_max = 4058000nx = 6071ny = 5781unit = utm

[geometry.volumes.layercake]nz = 3bottomflat = Truedepth_bottom = -60000filename =moho_6071_5781surf.xyz,topo_6071_5781surf.xyz,geometry_format=ascii

[meshing]map_meshing_type=regularmapiv_interval=3,4size=7500or_mesh_scheme=mapntripl=2smoothing=Falsecoarsening_top_layer=Falserefinement_depth=2,2

6 MHex - Carl Tape

http://geocubit.py/

http://geocubit.py/


a(short(praXcal(on(CUBIT/TRELIS

VERY


a(short(praXcal(on(CUBIT/TRELIS

VERY • Creating the geometry

• Setting the interval sizes and meshing schemes

• Meshing the geometry

• Specifying the boundary conditions

• Exporting the mesh


TOOLBARS

COMMAND(PANEL

COMMAND(LINE

GRAPHIC(WINDOW

POWER(TOOLS((TREE)

PROPERTIES(PAGE


Tools>OpXons..>Layout>(Show(script(tab


MESHING(“HELLO(WORD”

brick x 10 volume all size .5 mesh volume all


VERTEX

SURFACE

CURVE NODE

FACE/QUAD


MESHING(“LAYERED”

brick x 10 webcut body all with plane zplane offset 0 volume 1 size .5 volume 2 size 1 mesh vol all


MESHING(“LAYERED”

brick x 10 webcut body all with plane zplane offset 0 volume 1 size .5 volume 2 size 1 imprint body all merge body all mesh volume all


MESHING(“FAULT”brick x 10 webcut body all with plane yplane offset 0 rotate 40 about x unite body 2 4 imprint vol all merge vol all mesh vol all


MESHING(“FAULT”brick x 10 webcut body all with plane yplane offset 0 rotate 40 about x imprint merge unite body 2 4 imprint vol all merge vol all surface 25 19 31 scheme pave surface 25 19 31 scheme pave mesh surface 25 19 31 volume all redistribute nodes off volume all scheme Sweep sweep_transform least_squares volume all autosmooth_target off mesh vol all

CHECK_QUALITY


MESHING(“REFINE”brick x 10 webcut body all with plane zplane offset 0 volume 1 size .5 volume 2 size 1 imprint body all merge body all mesh volume all refine hex in vol 1 numsplit 1 bias 1.0 depth 1 smooth


MESHING(“REFINE”brick x 10 webcut body all with plane zplane offset 0 volume 1 size .5 volume 2 size 1 imprint body all merge body all mesh volume all refine surface 1 numsplit 1 bias 1 depth 2 smooth


EXPORTING(set duplicate block elements off block 1 hex in vol 1 block 2 hex in vol 2 set large exodus file on export mesh "test.e" overwrite


FIRST: get the topography


{1} create vertex from topography


{2} create spline from vertex


{3} create surface net u-v curve


{4} delete vertex and curve


FIRST: get the topography


[cubit.options] cubit_info=onecho_info=onjou_info=offjer_info=offworking_dir=tmpoutput_dir=gubbiosave_geometry_cubit = Truesave_surface_cubit = Falseexport_exodus_mesh = Truemonitored_cpu=0localdir_is_globaldir = Falseparallel_import = False#scratchdir=None

[simulation.cpu_parameters] number_processor_xi =1number_processor_eta =1

GUBBIO.CFG


[geometry.volumes] volume_type = layercake_volume_ascii_regulargrid_regularmaplongitude_min = 266906longtude_max = 324906latitude_min = 4776003latitude_max = 4856003nx = 30ny = 41unit = utm

[geometry.volumes.layercake] nz = 2#included the bottombottomflat = Truedepth_bottom = -60000filename = gubbio.vtk.square.utm33_30x41.xyzgeometry_format=ascii

GUBBIO.CFG


GUBBIO.CFG

[meshing] map_meshing_type=regularmapiv_interval=24,size=5000or_mesh_scheme=mapntripl=1smoothing=Falsecoarsening_top_layer=Falserefinement_depth=3


from geocubitlib import volumes volumes.volumes(cfg)

cubit.cmd('cd "/Users/casarotti/Dropbox (ICS)/TRELIS/gubbio_mesh”') cfg=“gubbio.cfg” import sys sys.path.append(“yourdirectory”)

from geocubitlib import mesh_volume mesh_volume.mesh(cfg)

from geocubitlib import exportlib from geocubitlib import boundary_definition

boundary_definition.define_bc() exportlib.e2SEM(listblock=[4],listflag=[-1])


Velocity model


ITALY&(5.8&MHex)

C.&ITALY&(0.2&MHex)

N.&ITALY&(1.6&MHex)&

S.&ITALY&(1.8&MHex)

CHILE&(Maule)

FULL&ITALY&(Di&Stefano&2014)

3s 4s(

CENTRAL&ITALY&

(Chiarabba&2010)

3s

NORTH&ITALY&(Di&Stefano&2011)

4s

SOUTH&ITALY&

(Di&Stefano&2011)

3s

Maule&(Hicks,&2012)

3s

emanuele casarotti verce training, university of liverpool (uk), 1

Documents