Journal of Computational Physics, ISSN 0021-9991, 03/2017, Volume 332, pp. 83 - 98

Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and...

Spectral-collocation methods | Variational integrators | Lagrangian mechanics | Geometric numerical integration | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | SYMPLECTIC INTEGRATORS

Spectral-collocation methods | Variational integrators | Lagrangian mechanics | Geometric numerical integration | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | SYMPLECTIC INTEGRATORS

Journal Article

The Astrophysical Journal, ISSN 2041-8213, 08/2015, Volume 809, Issue 1, p. L9

2015 ApJ 809 L9 Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the...

PLANETS | GRAVITATIONAL RADIATION | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | ASTROPHYSICS | SATELLITES | ALGORITHMS | HARMONIC OSCILLATORS | VARIATIONAL METHODS

PLANETS | GRAVITATIONAL RADIATION | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | ASTROPHYSICS | SATELLITES | ALGORITHMS | HARMONIC OSCILLATORS | VARIATIONAL METHODS

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 05/2004, Volume 60, Issue 1, pp. 153 - 212

The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering...

discrete mechanics | subcycling | elastodynamics | multi‐time‐step | geometric integration | variational integrators | Subcycling | Variational integrators | Elastodynamics | Multi-time-step | Discrete mechanics | Geometric integration | NEWMARK ALGORITHM | MOLECULAR-DYNAMICS | STEPPING ALGORITHMS | multi-time-step | TRANSIENT ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NONLINEAR DYNAMICS | ENGINEERING, MULTIDISCIPLINARY | NUMERICAL INTEGRATORS | HAMILTONIAN-SYSTEMS | EXPLICIT FINITE-ELEMENTS | HELICOPTER ROTOR DYNAMICS | STRUCTURAL DYNAMICS | Finite element method | Accuracy | Algorithms | Mathematical analysis | Conservation | Integrators | Mathematical models | Convergence

discrete mechanics | subcycling | elastodynamics | multi‐time‐step | geometric integration | variational integrators | Subcycling | Variational integrators | Elastodynamics | Multi-time-step | Discrete mechanics | Geometric integration | NEWMARK ALGORITHM | MOLECULAR-DYNAMICS | STEPPING ALGORITHMS | multi-time-step | TRANSIENT ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NONLINEAR DYNAMICS | ENGINEERING, MULTIDISCIPLINARY | NUMERICAL INTEGRATORS | HAMILTONIAN-SYSTEMS | EXPLICIT FINITE-ELEMENTS | HELICOPTER ROTOR DYNAMICS | STRUCTURAL DYNAMICS | Finite element method | Accuracy | Algorithms | Mathematical analysis | Conservation | Integrators | Mathematical models | Convergence

Journal Article

Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 04/2019, Volume 145, Issue 720, pp. 1070 - 1088

We develop a variational integrator for the shallow‐water equations on a rotating sphere. The variational integrator is built around a discretization of the...

variational integrator on sphere | rotating shallow‐water equations | structure‐preserving discretization | DISCRETIZATION | ENERGY | POTENTIAL ENSTROPHY | NUMERICAL-INTEGRATION | rotating shallow-water equations | structure-preserving discretization | METEOROLOGY & ATMOSPHERIC SCIENCES | SCHEMES | Hydrodynamics | Equations | Framework

variational integrator on sphere | rotating shallow‐water equations | structure‐preserving discretization | DISCRETIZATION | ENERGY | POTENTIAL ENSTROPHY | NUMERICAL-INTEGRATION | rotating shallow-water equations | structure-preserving discretization | METEOROLOGY & ATMOSPHERIC SCIENCES | SCHEMES | Hydrodynamics | Equations | Framework

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 321, pp. 435 - 458

Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a...

Conservation laws | Geometric discretisation | Variational integrators | Noether theorem | Collisionless reconnection | Reduced magnetohydrodynamics | FACTORIZATION | PDES | RECONNECTION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATION | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATRIX POLYNOMIALS | FLUID | SYSTEMS | HAMILTONIAN-FORMULATION | Fluid dynamics | Magnetic fields | Analysis | Environmental law | Electric properties | Plasma Physics | Physics | MAGNETIC FIELDS | PLASMA | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ASTROPHYSICS | CONSERVATION LAWS | EQUATIONS | HAMILTONIANS | MAGNETOHYDRODYNAMICS | LAGRANGIAN FUNCTION | VARIATIONAL METHODS

Conservation laws | Geometric discretisation | Variational integrators | Noether theorem | Collisionless reconnection | Reduced magnetohydrodynamics | FACTORIZATION | PDES | RECONNECTION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATION | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATRIX POLYNOMIALS | FLUID | SYSTEMS | HAMILTONIAN-FORMULATION | Fluid dynamics | Magnetic fields | Analysis | Environmental law | Electric properties | Plasma Physics | Physics | MAGNETIC FIELDS | PLASMA | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ASTROPHYSICS | CONSERVATION LAWS | EQUATIONS | HAMILTONIANS | MAGNETOHYDRODYNAMICS | LAGRANGIAN FUNCTION | VARIATIONAL METHODS

Journal Article

IEEE Transactions on Industrial Electronics, ISSN 0278-0046, 09/2015, Volume 62, Issue 9, pp. 5393 - 5401

This paper deals with the discrete-time modeling of induction motors (IMs) by means of a variational integrator. A Lagrangian is first formulated for the IM,...

Algorithm design and analysis | Discrete-time systems | Induction motors | Rotors | Stators | Vectors | Mathematical model | Equations | SPEED | PREDICTIVE TORQUE CONTROL | INSTRUMENTS & INSTRUMENTATION | mathematical model | induction motors (IMs) | DRIVE | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Induction electric motors | Usage | Mathematical models | Models | Properties | Variational principles | Economic models | Approximation | Mathematical analysis | Integrators | Transaction processing | Sampling | Steady state

Algorithm design and analysis | Discrete-time systems | Induction motors | Rotors | Stators | Vectors | Mathematical model | Equations | SPEED | PREDICTIVE TORQUE CONTROL | INSTRUMENTS & INSTRUMENTATION | mathematical model | induction motors (IMs) | DRIVE | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Induction electric motors | Usage | Mathematical models | Models | Properties | Variational principles | Economic models | Approximation | Mathematical analysis | Integrators | Transaction processing | Sampling | Steady state

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 04/2018, Volume 114, Issue 3, pp. 215 - 231

Summary With the postulation of the principle of virtual action, we propose, in this paper, a variational framework for describing the dynamics of finite...

time integration | multibody dynamics | nonsmooth mechanics | variational integrators | time finite element method (TFEM) | FRICTION | STEPPING SCHEMES | MULTIBODY SYSTEMS | GENERALIZED-ALPHA SCHEME | UNILATERAL CONSTRAINTS | NONSMOOTH DYNAMICS | NUMERICAL SCHEME | RIGID-BODY DYNAMICS | MECHANICS | IMPACT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Energy conservation | Finite element method | Integrators | Percussion | Inclusions | Mechanical systems | Shape functions

time integration | multibody dynamics | nonsmooth mechanics | variational integrators | time finite element method (TFEM) | FRICTION | STEPPING SCHEMES | MULTIBODY SYSTEMS | GENERALIZED-ALPHA SCHEME | UNILATERAL CONSTRAINTS | NONSMOOTH DYNAMICS | NUMERICAL SCHEME | RIGID-BODY DYNAMICS | MECHANICS | IMPACT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Energy conservation | Finite element method | Integrators | Percussion | Inclusions | Mechanical systems | Shape functions

Journal Article

ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 11/2012, Volume 39, Issue 1, pp. 1 - 28

This article introduces the software package TIDES and revisits the use of the Taylor series method for the numerical integration of ODEs. The package TIDES...

variational equations | automatic differentiation | high precision | numerical integration of ODEs | Taylor series method | Taylor series method, automatic differentiation, high precision, variational equations, numerical integration of ODEs | MATHEMATICS, APPLIED | IVP | PERFORMANCE | ODES | ALGEBRAIC EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | DAES | NUMERICAL-INTEGRATION | Usage | Research | Mathematical software | Series, Taylor's | Differential equations

variational equations | automatic differentiation | high precision | numerical integration of ODEs | Taylor series method | Taylor series method, automatic differentiation, high precision, variational equations, numerical integration of ODEs | MATHEMATICS, APPLIED | IVP | PERFORMANCE | ODES | ALGEBRAIC EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | DAES | NUMERICAL-INTEGRATION | Usage | Research | Mathematical software | Series, Taylor's | Differential equations

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 10/2011, Volume 31, Issue 4, pp. 1497 - 1532

We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system,...

geometric mechanics | Hamiltonian mechanics | symplectic integrators | geometric numerical integration | variational integrators | MATHEMATICS, APPLIED | MECHANICS | PDES | SYSTEMS | GEOMETRY | SCHEMES | Hamilton-Jacobi equation | Mathematical analysis | Integrators | Mathematical models | Runge-Kutta method | Transformations | Variational principles | Galerkin methods

geometric mechanics | Hamiltonian mechanics | symplectic integrators | geometric numerical integration | variational integrators | MATHEMATICS, APPLIED | MECHANICS | PDES | SYSTEMS | GEOMETRY | SCHEMES | Hamilton-Jacobi equation | Mathematical analysis | Integrators | Mathematical models | Runge-Kutta method | Transformations | Variational principles | Galerkin methods

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 09/2013, Volume 71, pp. 14 - 23

We extend the notion of variational integrator for classical Euler–Lagrange equations to the fractional ones. As in the classical case, we prove that the...

Variational integrator | Noetherʼs theorem | Fractional calculus | Euler–Lagrange equations | Euler-Lagrange equations | Noether's theorem | SCHEME | MATHEMATICS, APPLIED | MECHANICS | NOETHERS THEOREM | FORMULATION

Variational integrator | Noetherʼs theorem | Fractional calculus | Euler–Lagrange equations | Euler-Lagrange equations | Noether's theorem | SCHEME | MATHEMATICS, APPLIED | MECHANICS | NOETHERS THEOREM | FORMULATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2013, Volume 242, pp. 498 - 530

In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of...

Variational integrators | Electric circuits | Multiscale integration | Structure-preserving integration | Degenerate systems | Noisy systems | HIGH OSCILLATION | ALGORITHM | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN MECHANICS | INTERCONNECTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPLICIT TOPOLOGICAL FORMULATION | DISCRETE MECHANICS | HAMILTONIAN-SYSTEMS | DIRAC STRUCTURES | DYNAMICS | Electric potential | Computer simulation | Dynamics | Voltage | Mathematical models | Integrators | Dynamical systems | ELECTRIC POTENTIAL | STOCHASTIC PROCESSES | EQUATIONS OF MOTION | RESISTORS | COMPARATIVE EVALUATIONS | SIMULATION | MATHEMATICAL METHODS AND COMPUTING | GAIN | LAGRANGIAN FUNCTION | VARIATIONAL METHODS | CONTROL

Variational integrators | Electric circuits | Multiscale integration | Structure-preserving integration | Degenerate systems | Noisy systems | HIGH OSCILLATION | ALGORITHM | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN MECHANICS | INTERCONNECTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPLICIT TOPOLOGICAL FORMULATION | DISCRETE MECHANICS | HAMILTONIAN-SYSTEMS | DIRAC STRUCTURES | DYNAMICS | Electric potential | Computer simulation | Dynamics | Voltage | Mathematical models | Integrators | Dynamical systems | ELECTRIC POTENTIAL | STOCHASTIC PROCESSES | EQUATIONS OF MOTION | RESISTORS | COMPARATIVE EVALUATIONS | SIMULATION | MATHEMATICAL METHODS AND COMPUTING | GAIN | LAGRANGIAN FUNCTION | VARIATIONAL METHODS | CONTROL

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2014, Volume 257, pp. 1040 - 1061

We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of...

Symplectic methods | Lie group integrators | Integral preserving methods | FREE RIGID-BODY | RUNGE-KUTTA METHODS | VARIATIONAL INTEGRATORS | CONSERVING ALGORITHMS | TIME INTEGRATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HOMOGENEOUS MANIFOLDS | HAMILTONIAN-SYSTEMS | NUMERICAL-INTEGRATION | GEOMETRIC INTEGRATION | MOSER-VESELOV ALGORITHM | Integrators | Computation | Bundles | Lie groups | Mathematics - Numerical Analysis

Symplectic methods | Lie group integrators | Integral preserving methods | FREE RIGID-BODY | RUNGE-KUTTA METHODS | VARIATIONAL INTEGRATORS | CONSERVING ALGORITHMS | TIME INTEGRATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HOMOGENEOUS MANIFOLDS | HAMILTONIAN-SYSTEMS | NUMERICAL-INTEGRATION | GEOMETRIC INTEGRATION | MOSER-VESELOV ALGORITHM | Integrators | Computation | Bundles | Lie groups | Mathematics - Numerical Analysis

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 12/2018, Volume 58, Issue 4, pp. 1009 - 1048

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising...

Computational Mathematics and Numerical Analysis | Stochastic differential equations | 65C30 | Geometric numerical integration methods | Numeric Computing | Mathematics, general | Mathematics | Variational integrators | Geometric mechanics | Stochastic Hamiltonian systems | MATHEMATICS, APPLIED | QUADRATIC-INVARIANTS | RUNGE-KUTTA METHODS | DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SYMPLECTIC SCHEMES | SYSTEMS | ORDER CONDITIONS | Differential equations

Computational Mathematics and Numerical Analysis | Stochastic differential equations | 65C30 | Geometric numerical integration methods | Numeric Computing | Mathematics, general | Mathematics | Variational integrators | Geometric mechanics | Stochastic Hamiltonian systems | MATHEMATICS, APPLIED | QUADRATIC-INVARIANTS | RUNGE-KUTTA METHODS | DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SYMPLECTIC SCHEMES | SYSTEMS | ORDER CONDITIONS | Differential equations

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 4/2009, Volume 29, Issue 2, pp. 421 - 443

This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein-Uhlenbeck theory of...

Ornstein-Uhlenbeck process | Variational integrators | Stochastic Hamiltonian systems | MATHEMATICS, APPLIED | MECHANICS | RIGID-BODY | MOTION | DIRAC STRUCTURES | EQUATIONS | stochastic Hamiltonian systems | SYSTEMS | variational integrators | Mathematics - Probability

Ornstein-Uhlenbeck process | Variational integrators | Stochastic Hamiltonian systems | MATHEMATICS, APPLIED | MECHANICS | RIGID-BODY | MOTION | DIRAC STRUCTURES | EQUATIONS | stochastic Hamiltonian systems | SYSTEMS | variational integrators | Mathematics - Probability

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 01/2018, Volume 38, Issue 1, pp. 377 - 398

Abstract Discrete Hamiltonian variational integrators are derived from type II and type III generating functions for symplectic maps, and in this article, we...

Hamiltonian mechanics | Symplectic integrators | Variational integrators | Geometric mechanics | Geometric numerical integration | MATHEMATICS, APPLIED | symplectic integrators | MECHANICS | geometric numerical integration | geometric mechanics | variational integrators

Hamiltonian mechanics | Symplectic integrators | Variational integrators | Geometric mechanics | Geometric numerical integration | MATHEMATICS, APPLIED | symplectic integrators | MECHANICS | geometric numerical integration | geometric mechanics | variational integrators

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2017, Volume 109, Issue 11, pp. 1549 - 1581

Summary This article presents a family of variational integrators from a continuous time point of view. A general procedure for deriving symplectic integration...

numerical integration methods | symplectic integrators | multibody dynamics | discontinuous Galerkin methods | variational integrators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENTS | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | Concretes | Numerical analysis | Pendulums | Runge-Kutta method | Integrators | Regularization | Cartesian coordinates

numerical integration methods | symplectic integrators | multibody dynamics | discontinuous Galerkin methods | variational integrators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENTS | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | Concretes | Numerical analysis | Pendulums | Runge-Kutta method | Integrators | Regularization | Cartesian coordinates

Journal Article

Nonlinearity, ISSN 0951-7715, 04/2015, Volume 28, Issue 4, pp. 871 - 900

In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et...

70-08 | 65P10 | affine constraints Mathematics Subject Classification: 70F25 | discrete variational calculus | 37M15 | geometric nonholonomic integrator | 37N05 | 37J60 | reduction by symmetries | nonholonomic mechanics | BALL | MATHEMATICS, APPLIED | MOLECULAR-DYNAMICS | RIGID-BODY | LAGRANGIAN SYSTEMS | PHYSICS, MATHEMATICAL | HAMILTONIZATION | MECHANICS | MOTION | MODELS | affine constraints | PLANE | HIERARCHY | Preservation | Dynamics | Mathematical analysis | Tables (data) | Nonlinearity | Integrators | Dynamical systems | Convergence

70-08 | 65P10 | affine constraints Mathematics Subject Classification: 70F25 | discrete variational calculus | 37M15 | geometric nonholonomic integrator | 37N05 | 37J60 | reduction by symmetries | nonholonomic mechanics | BALL | MATHEMATICS, APPLIED | MOLECULAR-DYNAMICS | RIGID-BODY | LAGRANGIAN SYSTEMS | PHYSICS, MATHEMATICAL | HAMILTONIZATION | MECHANICS | MOTION | MODELS | affine constraints | PLANE | HIERARCHY | Preservation | Dynamics | Mathematical analysis | Tables (data) | Nonlinearity | Integrators | Dynamical systems | Convergence

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 10/2017, Volume 27, Issue 5, pp. 1399 - 1434

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale...

65P10 | 37J05 | 70Q05 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 37N05 | 37J60 | Dirac structures | Hamiltonian DAEs | 70H05 | Mathematics | 70F25 | 70H45 | Geometric integration | 70G45 | Lagrange–Dirac systems | Interconnection | Analysis | 93B27 | Mathematical and Computational Engineering | Variational integrators | 93A30 | MATHEMATICS, APPLIED | PART I | PHYSICS, MATHEMATICAL | LIE-GROUPS | MECHANICS | MECHANICAL SYSTEMS | Lagrange-Dirac systems | GEOMETRY

65P10 | 37J05 | 70Q05 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 37N05 | 37J60 | Dirac structures | Hamiltonian DAEs | 70H05 | Mathematics | 70F25 | 70H45 | Geometric integration | 70G45 | Lagrange–Dirac systems | Interconnection | Analysis | 93B27 | Mathematical and Computational Engineering | Variational integrators | 93A30 | MATHEMATICS, APPLIED | PART I | PHYSICS, MATHEMATICAL | LIE-GROUPS | MECHANICS | MECHANICAL SYSTEMS | Lagrange-Dirac systems | GEOMETRY

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2015, Volume 310, pp. 37 - 71

Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete...

Conservation laws | Geometric discretisation | Variational integrators | Noether theorem | Lagrangian field theory | Linear and nonlinear PDEs | Linear and nonlinear pdes | MATHEMATICS, APPLIED | FACTORIZATION | PHYSICS, MULTIDISCIPLINARY | MULTISYMPLECTIC GEOMETRY | PHYSICS, MATHEMATICAL | PRINCIPLES | DISCRETIZATION | CONTINUUM-MECHANICS | MATRIX POLYNOMIALS | SYSTEMS | Differential equations | Fluid dynamics | Plasma physics

Conservation laws | Geometric discretisation | Variational integrators | Noether theorem | Lagrangian field theory | Linear and nonlinear PDEs | Linear and nonlinear pdes | MATHEMATICS, APPLIED | FACTORIZATION | PHYSICS, MULTIDISCIPLINARY | MULTISYMPLECTIC GEOMETRY | PHYSICS, MATHEMATICAL | PRINCIPLES | DISCRETIZATION | CONTINUUM-MECHANICS | MATRIX POLYNOMIALS | SYSTEMS | Differential equations | Fluid dynamics | Plasma physics

Journal Article