Control of port-Hamiltonian differential-algebraic systems and applications

V Mehrmann, B Unger - Acta Numerica, 2023 - cambridge.org
We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in
numerical simulation and control. The structure is ideal for automated network-based …

Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method

E Celledoni, V Grimm, RI McLachlan… - Journal of …, 2012 - Elsevier
We give a systematic method for discretizing Hamiltonian partial differential equations
(PDEs) with constant symplectic structure, while preserving their energy exactly. The same …

A highly efficient and accurate new scalar auxiliary variable approach for gradient flows

F Huang, J Shen, Z Yang - SIAM Journal on Scientific Computing, 2020 - SIAM
We present several essential improvements to the powerful scalar auxiliary variable (SAV)
approach. Firstly, by using the introduced scalar variable to control both the nonlinear and …

[PDF][PDF] Hamiltonian boundary value methods (energy preserving discrete line integral methods)

L Brugnano, F Iavernaro, D Trigiante - J. Numer. Anal. Ind. Appl. Math, 2010 - Citeseer
Recently, a new family of integrators (Hamiltonian Boundary Value Methods) has been
introduced, which is able to precisely conserve the energy function of polynomial …

[图书][B] Discrete variational derivative method: a structure-preserving numerical method for partial differential equations

D Furihata, T Matsuo - 2010 - books.google.com
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …

[图书][B] A concise introduction to geometric numerical integration

S Blanes, F Casas - 2017 - books.google.com
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

[PDF][PDF] Energy-Preserving Variant of Collocation Methods12

E Hairer - JNAIAM, 2010 - jnaiam.org
We propose a modification of collocation methods extending the 'averaged vector field
method'to high order. These new integrators exactly preserve energy for Hamiltonian …

A unified discretization framework for differential equation approach with Lyapunov arguments for convex optimization

K Ushiyama, S Sato, T Matsuo - Advances in Neural …, 2023 - proceedings.neurips.cc
The differential equation (DE) approach for convex optimization, which relates optimization
methods to specific continuous DEs with rate-revealing Lyapunov functionals, has gained …

Line integral solution of differential problems

L Brugnano, F Iavernaro - axioms, 2018 - mdpi.com
In recent years, the numerical solution of differential problems, possessing constants of
motion, has been attacked by imposing the vanishing of a corresponding line integral. The …

Relaxation exponential Rosenbrock-type methods for oscillatory Hamiltonian systems

D Li, X Li - SIAM Journal on Scientific Computing, 2023 - SIAM
It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of
the problems and the requirement of highly stable and energy-preserving schemes. The …