576 citations · 1.9k across the 50 of their papers we have counts for
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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…
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…
Variational Integrators for Maxwell's Equations with Sources
Ari Stern, Yiying Tong, Mathieu Desbrun +1
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by…
Hamilton-Pontryagin Integrators on Lie Groups: Introduction and Structure-Preserving Properties
Nawaf Bou-Rabee, Jerrold E. Marsden
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principl…
Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
Ari Stern, Yiying Tong, Mathieu Desbrun +1
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete dif…
Symmetry reduction of discrete Lagrangian mechanics on Lie groups
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
For a discrete mechanical system on a Lie group determined by a (reduced) Lagrangian we define a Poisson structure via the pull-back of the Lie-Poisson structure on the…
Discrete Euler-Poincaré and Lie-Poisson Equations
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
In this paper, discrete analogues of Euler-Poincaré and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups with Lagrangians $L:TG \to {\mat…