overlapping multidomain chebyshev method: verification

www.spice-rtn.orgSPICE Research and Training Workshop III, July 22-28, Kinsale, Ireland

Overlapping Multidomain Chebyshev Method:

Verification


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


Overview

• Motivation and design goals

• Numerical method: OMDC• Geometry• Results• Future work


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


Numerical method (1)

N = 6

Overlapping Multidomain Chebyshev Method


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


Numerical method How does it relate to other methods?

OMDC?

?

? ?

?

?


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


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


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


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


Results (1)


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


Results (2)


Results

model 1

model 2


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

overlapping multidomain chebyshev method: verification

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