4.6 Article

On Snapshot-Based Model Reduction Under Compatibility Conditions for a Nonlinear Flow Problem on Networks

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

ON PORT-HAMILTONIAN APPROXIMATION OF A NONLINEAR FLOW PROBLEM ON NETWORKS

Bjoern Liljegren-Sailer et al.

Summary: This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The approach is guided by energy-based modeling concepts, such as the port-Hamiltonian formalism and the theory of Legendre transformation. The results show that under mild assumptions, local conservation of mass, an energy bound, and the inheritance of the port-Hamiltonian structure can be achieved. The method is not limited to conventional space discretization and can also handle complexity reduction of the nonlinearities by inexact integration.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

Article Mathematics, Interdisciplinary Applications

EFFICIENT NUMERICAL METHODS FOR GAS NETWORK MODELING AND SIMULATION

Yue Qiu et al.

NETWORKS AND HETEROGENEOUS MEDIA (2020)

Article Mathematics, Applied

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Babak Maboudi Afkham et al.

JOURNAL OF SCIENTIFIC COMPUTING (2019)

Article Engineering, Electrical & Electronic

Non-Negative Orthogonal Greedy Algorithms

Thanh Thi Nguyen et al.

IEEE TRANSACTIONS ON SIGNAL PROCESSING (2019)

Article Automation & Control Systems

Discrete-time port-Hamiltonian systems: A definition based on symplectic integration

Paul Kotyczka et al.

SYSTEMS & CONTROL LETTERS (2019)

Article Mathematics, Applied

Damped wave systems on networks: exponential stability and uniform approximations

H. Egger et al.

NUMERISCHE MATHEMATIK (2018)

Article Mathematics, Applied

Incremental proper orthogonal decomposition for PDE simulation data

Hiba Fareed et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2018)

Article Mathematics, Applied

ADAPTIVE REFINEMENT STRATEGIES FOR THE SIMULATION OF GAS FLOW IN NETWORKS USING A MODEL HIERARCHY

Pia Domschke et al.

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS (2018)

Article Mathematics, Applied

ON STRUCTURE-PRESERVING MODEL REDUCTION FOR DAMPED WAVE PROPAGATION IN TRANSPORT NETWORKS

H. Egger et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Mathematics, Applied

A ROBUST CONSERVATIVE MIXED FINITE ELEMENT METHOD FOR ISENTROPIC COMPRESSIBLE FLOW ON PIPE NETWORKS

H. Egger

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Mathematics, Applied

Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics

Jan Giesselmann et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2017)

Article Mathematics, Applied

STRUCTURE PRESERVING MODEL REDUCTION OF PARAMETRIC HAMILTONIAN SYSTEMS

Babak Maboudi Afkham et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2017)

Article Computer Science, Information Systems

GasLib-A Library of Gas Network Instances

Martin Schmidt et al.

Article Engineering, Multidisciplinary

Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

J. A. Hernandez et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2017)

Article Mathematics, Applied

SYMPLECTIC MODEL REDUCTION OF HAMILTONIAN SYSTEMS

Liqian Peng et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2016)

Article Mathematics, Applied

STRUCTURE-PRESERVING MODEL REDUCTION FOR NONLINEAR PORT-HAMILTONIAN SYSTEMS

S. Chaturantabut et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2016)

Article Mathematics, Applied

PRESERVING LAGRANGIAN STRUCTURE IN NONLINEAR MODEL REDUCTION WITH APPLICATION TO STRUCTURAL DYNAMICS

Kevin Carlberg et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2015)

Article Engineering, Multidisciplinary

Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency

Charbel Farhat et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2014)

Article Mathematics, Applied

CONVERGENT FINITE DIFFERENCES FOR 1D VISCOUS ISENTROPIC FLOW IN EULERIAN COORDINATES

Trygve K. Karper

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2014)

Article Computer Science, Interdisciplinary Applications

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Travis C. Fisher et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

Article Mathematics, Applied

The Quantum Hydrodynamics System in Two Space Dimensions

Paolo Antonelli et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2012)

Article Computer Science, Interdisciplinary Applications

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

E. Celledoni et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Mathematics, Applied

A STATE SPACE ERROR ESTIMATE FOR POD-DEIM NONLINEAR MODEL REDUCTION

Saifon Chaturantabut et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2012)

Article Engineering, Multidisciplinary

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

Kevin Carlberg et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2011)

Article Mathematics, Interdisciplinary Applications

GAS PIPELINE MODELS REVISITED: MODEL HIERARCHIES, NONISOTHERMAL MODELS, AND SIMULATIONS OF NETWORKS

Jens Brouwer et al.

MULTISCALE MODELING & SIMULATION (2011)

Article Mathematics

Topics in structure-preserving discretization

Snorre H. Christiansen et al.

ACTA NUMERICA (2011)

Article Automation & Control Systems

Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces

Thomas Wolf et al.

EUROPEAN JOURNAL OF CONTROL (2010)

Article Mathematics, Applied

NONLINEAR MODEL REDUCTION VIA DISCRETE EMPIRICAL INTERPOLATION

Saifon Chaturantabut et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2010)

Article Engineering, Multidisciplinary

Modeling and simulation of a gas distribution pipeline network

A. Herran-Gonzalez et al.

APPLIED MATHEMATICAL MODELLING (2009)

Article Computer Science, Software Engineering

Optimizing Cubature for Efficient Integration of Subspace Deformations

Steven S. An et al.

ACM TRANSACTIONS ON GRAPHICS (2008)

Article Mathematics, Applied

ON THE COMPUTATION OF NULL SPACES OF SPARSE RECTANGULAR MATRICES

Craig Gotsman et al.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS (2008)

Article Mathematics, Applied

Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics

K Kunisch et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2002)

Article Mathematics, Applied

Galerkin proper orthogonal decomposition methods for parabolic problems

K Kunisch et al.

NUMERISCHE MATHEMATIK (2001)