105 citations · 533 across the 41 of their papers we have counts for
11 papers · 1 filter
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
Xingjie Li, Fei Lu, Molei Tao +1
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, w…
Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials
Molei Tao, Shi Jin
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of th…
Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
Molei Tao
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the artic…
Explicit high-order symplectic integrators for charged particles in general electromagnetic fields
Molei Tao
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent…
Temporal homogenization of linear ODEs, with applications to parametric super-resonance and energy harvest
Molei Tao, Houman Owhadi
We consider the temporal homogenization of linear ODEs of the form , where is periodic and is small. Using a 2-scale expansion approach, we obtai…
Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs
Molei Tao, Houman Owhadi, Jerrold E. Marsden
We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owha…
Variational integrators for electric circuits
Sina Ober-Blöbaum, Molei Tao, Mulin Cheng +2
In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electrical circui…
Variational and linearly-implicit integrators, with applications
Molei Tao, Houman Owhadi
We show that symplectic and linearly-implicit integrators proposed by [Zhang and Skeel, 1997] are variational linearizations of Newmark methods. When used in conjunction with penal…
Structure preserving Stochastic Impulse Methods for stiff Langevin systems with a uniform global error of order 1 or 1/2 on position
Molei Tao, Houman Owhadi, Jerrold E. Marsden
Impulse methods are generalized to a family of integrators for Langevin systems with quadratic stiff potentials and arbitrary soft potentials. Uniform error bounds (independent fro…
From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials
Molei Tao, Houman Owhadi, Jerrold E. Marsden
We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for…
Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging
Molei Tao, Houman Owhadi, Jerrold E. Marsden
We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the…