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Spectral Elements (7)
Coupling between FE and SE
• We use an integral form of
continuity condition at the
non-conforming FE/SE
interface (mortar method):
∫
'
( uF −uS) ⋅ NFdγ
= 0
γ
F=
1, ,
N F
γ
'
F
FE/SE interface
u
velocity
N FE surface shape function N FE nodes on γ
• These conditions are of the usual form Cv = b and are solved
via the method of Lagrange multipliers.
• More accurate than with local conditions (node-by-node basis).
F
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Spectral Elements (8)
Absorbing boundary conditions (ABCs)
• We use first-order Stacey ABCs:
n normal to boundary
∂ 1 ∂ β −α
∂
( u⋅ n) =− ⋅ ( u⋅ n) + ⋅ ( u⋅τ
)
∂n
α ∂t
α ∂τ
τ tangent to boundary
∂ 1 ∂ β −α
∂ α longitudinal wave speed
( u⋅ τ) =− ⋅ ( u⋅ τ) + ⋅ ( u⋅n)
∂n
β ∂t
β ∂τ
β transversal wave speed
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