106 citations · 677 across the 72 of their papers we have counts for
7 papers · 2 filters
An Empirical Chaos Expansion Method for Uncertainty Quantification
Melvin Leok, Gautam Wilkins
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computa…
Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated Optimization
Valentin Duruisseaux, Jeremy Schmitt, Melvin Leok
It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step siz…
High-Order Retractions on Matrix Manifolds using Projected Polynomials
Evan S. Gawlik, Melvin Leok
We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Gr…
Lie group variational integrators for rigid body problems using quaternions
Xuefeng Shen, Melvin Leok
Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the co…
Lagrangian and Hamiltonian Taylor Variational Integrators
Jeremy Schmitt, Tatiana Shingel, Melvin Leok
In this paper, we present a variational integrator that is based on an approximation of the Euler--Lagrange boundary-value problem via Taylor's method. This can viewed as a special…
Constructing equivalence-preserving Dirac variational integrators with forces
Helen Parks, Melvin Leok
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and…