Optimal-Transportation Meshfree Approximation Schemes - Solid ...

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OTM ─ Max-ent interpolation • Max-ent interpolation is smooth, meshfree • Finite-element interpolation is recovered in the limit of β→∞ β • Rapid decay, short range • Monotonicity, maximum principle • Good mass lumping properties • Kronecker-delta property at the boundary: – Displacement boundary conditions – Compatibility p y with finite elements Michael Ortiz UCLA 02/22/10
material points i OTM ─ Spatial discretization nodal points: Michael Ortiz UCLA 02/22/10
Page 1 and 2: Optimal-Transportation Meshfree App
Page 3 and 4: Caltech PSAAP Center Objective: Pre
Page 5 and 6: Simulation requirements • Hyperve
Page 7 and 8: Optimal transportation theory Gaspa
Page 9 and 10: Mass flows ─ Optimal transportati
Page 11 and 12: Optimal-Transportation Meshfree (OT
Page 13 and 14: OTM ─ Spatial discretization Stee
Page 15 and 16: material points i OTM ─ Spatial d
Page 17: OTM ─ Max-ent interpolation Micha
Page 21 and 22: OTM ─ Spatial discretization Np =
Page 23 and 24: OTM ─ Flow chart (i) Explicit nod
Page 25 and 26: (Kg/m ) 3 ) density OTM ─ Riemann
Page 27 and 28: ocity L error norm 2 vel e OTM ─
Page 29 and 30: OTM ─ Taylor anvil test t=0 t 0 t
Page 31 and 32: OTM ─ Bouncing balloons FE membra
Page 33 and 34: OTM ─ Bouncing balloons FE membra
Page 35 and 36: OTM ─ Seizing contact body 1 body
Page 37 and 38: Variational Fracture & fragmentatio
Page 39 and 40: OTM - Fracture & fragmentation Crac
Page 41 and 42: Variational Fracture & fragmentatio
Page 43 and 44: QMU - Simulation codes - OTM Michae
Page 45 and 46: QMU - Simulation codes - OTM Michae
Page 47 and 48: OTM ─ Summary and outlook • Opt

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