overlapping multidomain chebyshev method: verification
DESCRIPTION
Overlapping Multidomain Chebyshev Method: Verification. Profile. S eismic wave P ropagation and I maging in C omplex media: a E uropean network. PETER DANECEK Early Stage Researcher Host Institution: INGV Bologna, Italy Place of Origin: Zlin, Czech Republic - PowerPoint PPT PresentationTRANSCRIPT
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Overlapping Multidomain Chebyshev Method:
Verification
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Seismic wave Propagation and Imaging
in Complex media: a European network
PETER DANECEK Early Stage Researcher
Host Institution: INGV Bologna, ItalyPlace of Origin: Zlin, Czech Republic Appointment Time: Juni 2006
Project: Multidomain Chebyshev Method for Wave Propagation on Continental and Global Scales with Application.
Task Groups: TG Numerical Methods, TG Global Scale
Cooperation: OGS Trieste, Munich University
PETER DANECEK Early Stage Researcher
Host Institution: INGV Bologna, ItalyPlace of Origin: Zlin, Czech Republic Appointment Time: Juni 2006
Project: Multidomain Chebyshev Method for Wave Propagation on Continental and Global Scales with Application.
Task Groups: TG Numerical Methods, TG Global Scale
Cooperation: OGS Trieste, Munich University
Profile
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Overview
• Motivation and design goals
• Numerical method: OMDC• Geometry• Results• Future work
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Design goals
• Parallel 3D method with good scalability
• Efficient, structured method=> implicit topology
• Continental & Global Scale Seismology => spherical geometry
• Justification: - current Earth models are smooth- grid generation AND inversion
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Numerical method (1)
N = 6
Overlapping Multidomain Chebyshev Method
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Numerical method (2)
€
D11 D12 D13 D14 D15 D16 D17 L 0
D21 D22 D23 D24 D25 D26 D27
D31 D32 D33 D34 D35 D36 D37
M M M M M M M N M
D51 D52 D53 D54 D55 D56 D57
D61 D62 D63 D64 D65 D66 D67
D21 D22 D23 D24 D25 D26 D27
D31 D32 D33 D34 D35 D36 D37
M N D41 D42 D43 D44 D45 D46 D47
D51 D52 D53 D54 D55 D56 D57
D61 D62 D63 D64 D65 D66 D67
0 L D71 D72 D73 D74 D75 D76 D77
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟
N = 6
OMDC
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Numerical method How does it relate to other methods?
OMDC?
?
? ?
?
?
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Numerical method How does it relate to other methods?
OMDC
low order FD
higher orderFD
SEM
FEMwith high order
ordinary polynomials
low orderFEM
Increasing order
Strong formulation
Weak formulationglobal
local
Fourier method
equal-spaced
Chebyshevmethod
special co-location
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Spherical geometry (1)
• Uniform mapping by continuous functions for the whole computational domain
• Elastic equations solve directly in spherical coordinate system
• Orthogonality between coordinate lines
• Few pre-calculated/stored parameter
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Spherical geometry (2)
• Sphere decomposed into six equally shaped chunks
• Each chunk has a uniform mapping by continuous functions
• Coordinates lines along the surface are no longer orthogonal
• Derivatives are coupled• Elastic equations solve
directly in the resulting coordinate systems
• Still moderate number of pre-calculated/stored parameter
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Results (1)
• 8 processors• N = 8• 32x32x40 elements• 226x226x282 points• Unity sphere with r= 0.8..1.0, == -5..+5 degree
• Grid spacing: 0.17..1.08 *10-
3
• Vs = 0.1, Vp = 0.2• ca. 10 ppw, c < 0.1, leap-frog
• Source: point force in radial direction
• Absorbing boundaries
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Results (1)
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Results (2)
• 64 processors• N = 8• 32x32x40 elements• 226x226x282 points• Unity sphere with r= 0.8..1.0, == -5..+5 degree
• Grid spacing: 0.17..1.08 *10-3
• Vs = 0.1, Vp = 0.2• ca. 10 ppw, c < 0.1, leap-frog
• Source: Explosion (stress)• Absorbing boundaries
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Results (2)
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Results
model 1
model 2
www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland
Future work
• Time histories• Comparison against known solution• Boundary conditions• Complex models• Code extensions and improvements• Test the limits• Comparison with other methods• Applications• More work on Cubed Sphere geometry