70 citations · 380 across the 25 of their papers we have counts for
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math.NA2010★ 3 cited
Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case
Matthew Dobson, Claude Le Bris, Frederic Legoll
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach c…
math.NA2010★ 7 cited
The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain
Matthew Dobson, Christoph Ortner, Alexander V. Shapeev
We show under general conditions that the linearized force-based quasicontinuum (QCF) operator has a positive spectrum, which is identical to the spectrum of the quasinonlocal quas…