2014, ISBN 9814579890, x, 293

Book

Annual Review of Fluid Mechanics, ISSN 0066-4189, 1/2014, Volume 46, Issue 1, pp. 493 - 517

The objective of this article is to review some developments in the use of adjoint equations in hydrodynamic stability theory. Adjoint-based sensitivity...

transient growth | receptivity | structural sensitivity | optimization | optimal perturbation | sensitivity | global mode | flow control | Optimal perturbation | Sensitivity | Global mode | Flow control | Structural sensitivity | Receptivity | Transient growth | Optimization | BOUNDARY-LAYER | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | MECHANICS | SYSTEMS | ALGEBRAIC GROWTH | SUCTION | Differential equations, Linear | Static stability (Fluid mechanics) | Usage | Models | Analysis | Boundary layer | Turbulence | Turbulent flow | Stability | Computational fluid dynamics | Mathematical analysis | Adjoints | Fluid flow | Cylinders

transient growth | receptivity | structural sensitivity | optimization | optimal perturbation | sensitivity | global mode | flow control | Optimal perturbation | Sensitivity | Global mode | Flow control | Structural sensitivity | Receptivity | Transient growth | Optimization | BOUNDARY-LAYER | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | MECHANICS | SYSTEMS | ALGEBRAIC GROWTH | SUCTION | Differential equations, Linear | Static stability (Fluid mechanics) | Usage | Models | Analysis | Boundary layer | Turbulence | Turbulent flow | Stability | Computational fluid dynamics | Mathematical analysis | Adjoints | Fluid flow | Cylinders

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2015, Volume 81, Issue 1, pp. 753 - 763

In this paper, we will show and integrate the ‘multiplier’ and ‘adjoint equations and Lagrangian’ approaches to the construction of conservation laws. The...

Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Multipliers | Adjoint equations | Mechanics | KdV type equations | Automotive Engineering | Mechanical Engineering | Jaulent–Miodek | MECHANICS | BACKLUND-TRANSFORMATIONS | Jaulent-Miodek | PARTIAL-DIFFERENTIAL EQUATIONS | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Environmental law | Mathematical analysis

Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Multipliers | Adjoint equations | Mechanics | KdV type equations | Automotive Engineering | Mechanical Engineering | Jaulent–Miodek | MECHANICS | BACKLUND-TRANSFORMATIONS | Jaulent-Miodek | PARTIAL-DIFFERENTIAL EQUATIONS | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Environmental law | Mathematical analysis

Journal Article

2003, American Mathematical Society translations, ISBN 0821835084, Volume ser. 2, v. 211., viii, 137

Book

1983, Operator theory, advances and applications, ISBN 3764315172, Volume 7, ix, 302

Book

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 09/2018, Volume 115, Issue 11, pp. 1371 - 1382

In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the...

time evolution equations | shape optimization problems | partial differential equations | adjoint variable method | DESIGN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TRACTION METHOD | Boundary value problems | Partial differential equations | Thermal resistance | Shape optimization | Evolution | Time integration | Design optimization

time evolution equations | shape optimization problems | partial differential equations | adjoint variable method | DESIGN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TRACTION METHOD | Boundary value problems | Partial differential equations | Thermal resistance | Shape optimization | Evolution | Time integration | Design optimization

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 59, Issue 5, pp. 1852 - 1864

This paper introduces three new operators and presents some of their properties. It defines a new class of variational problems (called Generalized Variational...

Fractional differential equation | Generalized variational calculus | Adjoint equation | Lagrangian | Variational calculus | Action principle | Hamiltonian | Fractional derivative | Field equation | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORMULATION

Fractional differential equation | Generalized variational calculus | Adjoint equation | Lagrangian | Variational calculus | Action principle | Hamiltonian | Fractional derivative | Field equation | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORMULATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2018, Volume 362, pp. 305 - 326

In this paper, an adjoint-based high-order h-adaptive direct discontinuous Galerkin method is developed and analyzed for the two dimensional steady state...

Direct discontinuous Galerkin method | Compressible Navier–Stokes equations | Adjoint-based h-adaptation | Adjoint consistency | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PENALTY DG METHODS | MESH ADAPTATION | ERROR ESTIMATION | FINITE-ELEMENT METHODS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Compressible Navier-Stokes equations | Compressibility | Computational fluid dynamics | Computer simulation | Consistency | Fluid flow | Boundary conditions | Studies | Numerical analysis | Functionals | Models | Galerkin method | Two dimensional analysis | Navier-Stokes equations

Direct discontinuous Galerkin method | Compressible Navier–Stokes equations | Adjoint-based h-adaptation | Adjoint consistency | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PENALTY DG METHODS | MESH ADAPTATION | ERROR ESTIMATION | FINITE-ELEMENT METHODS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Compressible Navier-Stokes equations | Compressibility | Computational fluid dynamics | Computer simulation | Consistency | Fluid flow | Boundary conditions | Studies | Numerical analysis | Functionals | Models | Galerkin method | Two dimensional analysis | Navier-Stokes equations

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 12/2016, Volume 2016, Issue 12, pp. 1 - 40

We test infinite-dimensional extension of algebra s u k , k $$ \mathfrak{s}\mathfrak{u}\left(k,\;k\right) $$ proposed by Fradkin and Linetsky as the candidate...

Conformal Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | SPIN GAUGE-FIELDS | UNITARY REPRESENTATIONS | SYMMETRIES | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Integers | Mathematical analysis | Adjoints | Texts | Systems analysis | Representations | Formulas (mathematics)

Conformal Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | SPIN GAUGE-FIELDS | UNITARY REPRESENTATIONS | SYMMETRIES | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Integers | Mathematical analysis | Adjoints | Texts | Systems analysis | Representations | Formulas (mathematics)

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2010, Volume 51, Issue 2, pp. 023510 - 023510-17

In this paper, a general integrable coupled nonlinear Schrödinger system is investigated. In this system, the coefficients of the self-phase modulation,...

MULTICOMPONENT AKNS EQUATIONS | SOLITONS | ADJOINT SYMMETRY CONSTRAINTS | COLLISION | OPTICAL-FIBERS | PHYSICS, MATHEMATICAL | PROPAGATION

MULTICOMPONENT AKNS EQUATIONS | SOLITONS | ADJOINT SYMMETRY CONSTRAINTS | COLLISION | OPTICAL-FIBERS | PHYSICS, MATHEMATICAL | PROPAGATION

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 02/2019, Volume 88, pp. 222 - 229

In this paper, we propose an imaging technique for the detection of porous inclusions in a stationary flow governed by Stokes–Brinkmann equations. We introduce...

Continuous adjoint method | Function space parametrization technique | Stokes–Brinkmann equations | Shape inverse problem | Shape gradient | MATHEMATICS, APPLIED | Stokes-Brinkmann equations | DERIVATIVES

Continuous adjoint method | Function space parametrization technique | Stokes–Brinkmann equations | Shape inverse problem | Shape gradient | MATHEMATICS, APPLIED | Stokes-Brinkmann equations | DERIVATIVES

Journal Article

SIAM Review, ISSN 0036-1445, 2016, Volume 58, Issue 1, pp. 3 - 33

The study of the sensitivity of the solution of a system of differential equations with respect to changes in the initial conditions leads to the introduction...

Reflected and transposed Runge-Kutta schemes | Symplectic integration | Variational equations | Lagrangian mechanics | Automatic differentiation | Constrained controls | Hamiltonian systems | Adjoint equations | Lagrange multipliers | Differential-algebraic problems | Optimal control | Partitioned Runge-Kutta methods | Computation of sensitivities | Runge-Kutta methods | variational equations | MATHEMATICS, APPLIED | optimal control | constrained controls | differential-algebraic problems | reflected and transposed Runge-Kutta schemes | computation of sensitivities | DISCRETE MECHANICS | automatic differentiation | symplectic integration | adjoint equations | ORDER CONDITIONS | INTEGRATORS | partitioned Runge-Kutta methods

Reflected and transposed Runge-Kutta schemes | Symplectic integration | Variational equations | Lagrangian mechanics | Automatic differentiation | Constrained controls | Hamiltonian systems | Adjoint equations | Lagrange multipliers | Differential-algebraic problems | Optimal control | Partitioned Runge-Kutta methods | Computation of sensitivities | Runge-Kutta methods | variational equations | MATHEMATICS, APPLIED | optimal control | constrained controls | differential-algebraic problems | reflected and transposed Runge-Kutta schemes | computation of sensitivities | DISCRETE MECHANICS | automatic differentiation | symplectic integration | adjoint equations | ORDER CONDITIONS | INTEGRATORS | partitioned Runge-Kutta methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 20, pp. 7643 - 7661

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid...

Mesh refinement | Output functional | Discontinuous Galerkin methods | High-order methods | hp-Multigrid approach | Adjoint-based error estimation | High speed flow | Compressible flow | FINITE-ELEMENT METHODS | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | QUADRATURE-RULES | SYSTEMS | CONSERVATION-LAWS | Mechanical engineering | Methods | Algorithms

Mesh refinement | Output functional | Discontinuous Galerkin methods | High-order methods | hp-Multigrid approach | Adjoint-based error estimation | High speed flow | Compressible flow | FINITE-ELEMENT METHODS | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | QUADRATURE-RULES | SYSTEMS | CONSERVATION-LAWS | Mechanical engineering | Methods | Algorithms

Journal Article

Journal of Geophysical Research: Atmospheres, ISSN 2169-897X, 05/2015, Volume 120, Issue 9, pp. 4017 - 4039

Proper dynamic equation constraints in data assimilation (DA) systems can help improve balance of analyzed atmospheric state. The formulation of...

typhoon forecast | dynamic constraint | hybrid assimilation | PART I | INCREMENTAL APPROACH | METEOROLOGICAL OBSERVATIONS | WEAK CONSTRAINT | KALMAN FILTER | NUMERICAL VARIATIONAL ANALYSIS | 3-DIMENSIONAL WIND | TRACK FORECASTS | SINGLE-DOPPLER RADAR | ADJOINT VORTICITY EQUATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Assimilation | Economic models | Wind | Dynamic tests | Typhoons | Covariance | Dynamics | Mathematical analysis | Radar | Dynamical systems

typhoon forecast | dynamic constraint | hybrid assimilation | PART I | INCREMENTAL APPROACH | METEOROLOGICAL OBSERVATIONS | WEAK CONSTRAINT | KALMAN FILTER | NUMERICAL VARIATIONAL ANALYSIS | 3-DIMENSIONAL WIND | TRACK FORECASTS | SINGLE-DOPPLER RADAR | ADJOINT VORTICITY EQUATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Assimilation | Economic models | Wind | Dynamic tests | Typhoons | Covariance | Dynamics | Mathematical analysis | Radar | Dynamical systems

Journal Article

1996, ISBN 9780849328718, 275

Book

Journal of Computational Physics, ISSN 0021-9991, 2008, Volume 227, Issue 22, pp. 9670 - 9685

In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the...

Compressible Navier–Stokes equations | Discontinuous Galerkin methods | Finite element methods | Adjoint consistency | Compressible Navier-Stokes equations | APPROXIMATIONS | POSTERIORI ERROR ESTIMATION | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DG METHODS | POST-PROCESSING APPROACH | SYSTEMS | FINITE-ELEMENT-METHOD | EULER | Fluid dynamics | Musicians

Compressible Navier–Stokes equations | Discontinuous Galerkin methods | Finite element methods | Adjoint consistency | Compressible Navier-Stokes equations | APPROXIMATIONS | POSTERIORI ERROR ESTIMATION | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DG METHODS | POST-PROCESSING APPROACH | SYSTEMS | FINITE-ELEMENT-METHOD | EULER | Fluid dynamics | Musicians

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 7/2019, Volume 13, Issue 5, pp. 2259 - 2267

In this report we study a fractional analogue of Sturm–Liouville equation. A class of self-adjoint fractional Sturm–Liouville operators is described. We give a...

Riemann–Liouville derivative | The extension theory | Self-adjoint problem | Mathematics | Operator Theory | Conservation law | 47G20 | 34K08 | Analysis | Caputo derivative | Mathematics, general | Fractional kinetic equation | 45J05 | Green’s formula | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Green's formula | Environmental law | Boundary conditions | Kinetic equations | Mathematical analysis | Liouville equations

Riemann–Liouville derivative | The extension theory | Self-adjoint problem | Mathematics | Operator Theory | Conservation law | 47G20 | 34K08 | Analysis | Caputo derivative | Mathematics, general | Fractional kinetic equation | 45J05 | Green’s formula | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Green's formula | Environmental law | Boundary conditions | Kinetic equations | Mathematical analysis | Liouville equations

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2016, Volume 296, pp. 334 - 351

Shape optimization based on surface gradients and the Hadamard-form is considered for a compressible viscous fluid. Special attention is given to the...

Compressible Navier–Stokes equations | Shape derivative | Variational form | Compressible Navier?Stokes equations | MATHEMATICS, APPLIED | HESSIANS | ADJOINT APPROACH | AERODYNAMIC DESIGN | OPTIMIZATION | Compressible Navier-Stokes equations | Fluid dynamics | Derivatives (Financial instruments) | Compressibility | Mathematical analysis | Solvers | Mathematical models | Derivatives | Galerkin methods | Stemming | Navier-Stokes equations

Compressible Navier–Stokes equations | Shape derivative | Variational form | Compressible Navier?Stokes equations | MATHEMATICS, APPLIED | HESSIANS | ADJOINT APPROACH | AERODYNAMIC DESIGN | OPTIMIZATION | Compressible Navier-Stokes equations | Fluid dynamics | Derivatives (Financial instruments) | Compressibility | Mathematical analysis | Solvers | Mathematical models | Derivatives | Galerkin methods | Stemming | Navier-Stokes equations

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7287 - 7306

In this paper, we introduce a q ‐analog of 1‐dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later,...

self‐adjoint operator | Green matrix | eigenfunction expansions | Dirac operator | eigenvalues and eigenfunctions | Eigenfunction expansions | Self-adjoint operator | Eigenvalues and eigenfunctions | Q−Dirac operator | self-adjoint operator | POLYNOMIALS | MATHEMATICS, APPLIED | q-Dirac operator | Eigenvalues | Eigenvectors | Green's functions | Orthogonality | Dirac equation | Uniqueness

self‐adjoint operator | Green matrix | eigenfunction expansions | Dirac operator | eigenvalues and eigenfunctions | Eigenfunction expansions | Self-adjoint operator | Eigenvalues and eigenfunctions | Q−Dirac operator | self-adjoint operator | POLYNOMIALS | MATHEMATICS, APPLIED | q-Dirac operator | Eigenvalues | Eigenvectors | Green's functions | Orthogonality | Dirac equation | Uniqueness

Journal Article