Journal of Computational Physics, ISSN 0021-9991, 03/2015, Volume 284, pp. 367 - 388

We build a simple and general class of finite difference schemes for first order Hamiltonâ€“Jacobi (HJ) Partial Differential Equations. These filtered schemes...

Fully nonlinear elliptic partial differential equations | Monotone schemes | Eikonal equation | Hamiltonâ€“Jacobi equations | Upwind schemes | Nonlinear finite difference methods | Viscosity solutions | Hamilton-Jacobi equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHMS | PHYSICS, MATHEMATICAL | SEMI-LAGRANGIAN SCHEMES | Interpolation | Construction | Hamilton-Jacobi equation | Computation | Mathematical analysis | Two dimensional | Standards | Finite difference method

Fully nonlinear elliptic partial differential equations | Monotone schemes | Eikonal equation | Hamiltonâ€“Jacobi equations | Upwind schemes | Nonlinear finite difference methods | Viscosity solutions | Hamilton-Jacobi equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHMS | PHYSICS, MATHEMATICAL | SEMI-LAGRANGIAN SCHEMES | Interpolation | Construction | Hamilton-Jacobi equation | Computation | Mathematical analysis | Two dimensional | Standards | Finite difference method

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 1, pp. 423 - 444

The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear partial differential equations such...

Viscosity | Approximation | Mathematical monotonicity | Partial differential equations | Numerical methods | Elliptic equations | Boundary conditions | Monge Ampere equation | Stencils | Fully nonlinear elliptic partial differential equations | Monotone schemes | Monge-AmpÃ¨re equations | Nonlinear finite difference methods | Viscosity solutions | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | nonlinear finite difference methods | CONSTRUCTION | Monge Ampere equations | HAMILTON-JACOBI EQUATIONS | viscosity solutions | ALGORITHMS | SOLVERS | fully nonlinear elliptic partial differential equations | monotone schemes | Accuracy | Construction | Asymptotic properties | Mathematical analysis | Mathematical models | Convergence

Viscosity | Approximation | Mathematical monotonicity | Partial differential equations | Numerical methods | Elliptic equations | Boundary conditions | Monge Ampere equation | Stencils | Fully nonlinear elliptic partial differential equations | Monotone schemes | Monge-AmpÃ¨re equations | Nonlinear finite difference methods | Viscosity solutions | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | nonlinear finite difference methods | CONSTRUCTION | Monge Ampere equations | HAMILTON-JACOBI EQUATIONS | viscosity solutions | ALGORITHMS | SOLVERS | fully nonlinear elliptic partial differential equations | monotone schemes | Accuracy | Construction | Asymptotic properties | Mathematical analysis | Mathematical models | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2016, Volume 307, pp. 423 - 445

In this paper, we present a class of new Hermite weighted essentially non-oscillatory (HWENO) schemes based on finite volume framework to directly solve the...

Monotone modification | Finite volume method | HWENO method | Hamiltonâ€“Jacobi equation | Hamilton-Jacobi equation | TRIANGULAR MESHES | EFFICIENT IMPLEMENTATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | Reconstruction | Discontinuity | Discretization | Mathematical analysis | Mathematical models | Derivatives | Fluxes | Two dimensional

Monotone modification | Finite volume method | HWENO method | Hamiltonâ€“Jacobi equation | Hamilton-Jacobi equation | TRIANGULAR MESHES | EFFICIENT IMPLEMENTATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | Reconstruction | Discontinuity | Discretization | Mathematical analysis | Mathematical models | Derivatives | Fluxes | Two dimensional

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 3/2015, Volume 62, Issue 3, pp. 772 - 802

We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual...

Hyperbolic conservation laws | Computational Mathematics and Numerical Analysis | Algorithms | Time-dependent problems | Rungeâ€“Kutta time-stepping | Residual distribution | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Second order schemes | MATHEMATICS, APPLIED | MONOTONE | CONSERVATION-LAWS | FORMULATION | Runge-Kutta time-stepping | MULTIDIMENSIONAL UPWIND | FLOW | IMPLICIT | Environmental law | Analysis | Linear systems | Approximation | Blending | Partial differential equations | Computation | Nonlinearity | Mathematical models | Runge-Kutta method | Temporal logic | Modeling and Simulation | Numerical Analysis | Computer Science | Mechanics | Mechanics of the fluids | Physics

Hyperbolic conservation laws | Computational Mathematics and Numerical Analysis | Algorithms | Time-dependent problems | Rungeâ€“Kutta time-stepping | Residual distribution | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Second order schemes | MATHEMATICS, APPLIED | MONOTONE | CONSERVATION-LAWS | FORMULATION | Runge-Kutta time-stepping | MULTIDIMENSIONAL UPWIND | FLOW | IMPLICIT | Environmental law | Analysis | Linear systems | Approximation | Blending | Partial differential equations | Computation | Nonlinearity | Mathematical models | Runge-Kutta method | Temporal logic | Modeling and Simulation | Numerical Analysis | Computer Science | Mechanics | Mechanics of the fluids | Physics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 04/2019, Volume 266, Issue 9, pp. 5625 - 5663

In this paper, we show that solutions of stochastic nonlinear SchrÃ¶dinger (NLS) equations can be approximated by solutions of coupled splitting systems. Based...

Non-monotone coefficients | Stochastic nonlinear SchrÃ¶dinger equation | Strong convergence rate | Exponential integrability | Splitting scheme | MATHEMATICS | UP METHOD | ORDER | WHITE | Stochastic nonlinear Schrodinger equation | APPROXIMATIONS | Military electronics industry

Non-monotone coefficients | Stochastic nonlinear SchrÃ¶dinger equation | Strong convergence rate | Exponential integrability | Splitting scheme | MATHEMATICS | UP METHOD | ORDER | WHITE | Stochastic nonlinear Schrodinger equation | APPROXIMATIONS | Military electronics industry

Journal Article

Handbook of Numerical Analysis, ISSN 1570-8659, 12/2016, Volume 17, pp. 467 - 493

We review the topic of entropy stability of discrete schemes, finite-difference and finite-volume schemes, for the approximate solution of nonlinear systems of...

Monotone schemes | Unstructured grids | Numerical viscosity | High-order methods | Euler and Navierâ€“Stokes equations | Entropy stability | Entropy inequality | Entropy conservative schemes | E-schemes

Monotone schemes | Unstructured grids | Numerical viscosity | High-order methods | Euler and Navierâ€“Stokes equations | Entropy stability | Entropy inequality | Entropy conservative schemes | E-schemes

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2015, Volume 166, Issue 3, pp. 930 - 948

In this paper, we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued...

Monotone inclusion | 65K05 | Fitzpatrick function | Mathematics | Theory of Computation | Backward penalty algorithm | Optimization | Maximally monotone operator | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Convex subdifferential | Applications of Mathematics | Engineering, general | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONICITY | PENALIZATION | FORWARD-BACKWARD | Algorithms | Studies | Set theory | Mathematical analysis | Operators | Inclusions

Monotone inclusion | 65K05 | Fitzpatrick function | Mathematics | Theory of Computation | Backward penalty algorithm | Optimization | Maximally monotone operator | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Convex subdifferential | Applications of Mathematics | Engineering, general | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONICITY | PENALIZATION | FORWARD-BACKWARD | Algorithms | Studies | Set theory | Mathematical analysis | Operators | Inclusions

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 07/2017, Volume 72, Issue 1, pp. 198 - 230

We analyse two practical aspects that arise in the numerical solution of Hamilton-Jacobi-Bellman equations by a particular class of monotone approximation...

Semi-Lagrangian schemes | Fully non-linear PDEs | Monotone approximation schemes | Multigrid | Wide stencils | CONVECTION-DIFFUSION EQUATIONS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | ALGORITHM | NONSYMMETRIC LINEAR-SYSTEMS

Semi-Lagrangian schemes | Fully non-linear PDEs | Monotone approximation schemes | Multigrid | Wide stencils | CONVECTION-DIFFUSION EQUATIONS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | ALGORITHM | NONSYMMETRIC LINEAR-SYSTEMS

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2017, Volume 165, Issue 1, pp. 113 - 149

We propose a novel stochastic method, namely the stochastic accelerated mirror-prox (SAMP) method, for solving a class of monotone stochastic variational...

68Q25 | Theoretical, Mathematical and Computational Physics | Stochastic variational inequalities | Mathematics | 90C15 | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Mirror-prox method | 90C25 | Numerical Analysis | Extragradient method | Combinatorics | 62L20 | SAMPLE AVERAGE APPROXIMATION | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | STOCHASTIC MATHEMATICAL PROGRAMS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | COMPLEXITY | EQUILIBRIUM CONSTRAINTS | SELECTION | SADDLE-POINT | MONOTONE-OPERATORS | Algorithms | Iterative methods | Inequalities | Complexity

68Q25 | Theoretical, Mathematical and Computational Physics | Stochastic variational inequalities | Mathematics | 90C15 | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Mirror-prox method | 90C25 | Numerical Analysis | Extragradient method | Combinatorics | 62L20 | SAMPLE AVERAGE APPROXIMATION | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | STOCHASTIC MATHEMATICAL PROGRAMS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | COMPLEXITY | EQUILIBRIUM CONSTRAINTS | SELECTION | SADDLE-POINT | MONOTONE-OPERATORS | Algorithms | Iterative methods | Inequalities | Complexity

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2015, Volume 25, Issue 3, pp. 1912 - 1943

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built...

Forwardbackward splitting | Peaceman-Rachford splitting | Nonexpansive operator | Primal-dual algorithms | Douglas-Rachford splitting | Convergence rates | Forward-backward-forward splitting | Averaged operator | Fixed-point algorithm | Proximal point algorithm | MATHEMATICS, APPLIED | forward-backward splitting | forward-backward-forward splitting | DECOMPOSITION | primal-dual algorithms | SUM | ALGORITHMS | CONVEX-OPTIMIZATION | COMPOSITE | averaged operator | MONOTONE INCLUSIONS | MINIMIZATION | SYSTEMS | convergence rates | nonexpansive operator | OPERATORS | proximal point algorithm | fixed-point algorithm

Forwardbackward splitting | Peaceman-Rachford splitting | Nonexpansive operator | Primal-dual algorithms | Douglas-Rachford splitting | Convergence rates | Forward-backward-forward splitting | Averaged operator | Fixed-point algorithm | Proximal point algorithm | MATHEMATICS, APPLIED | forward-backward splitting | forward-backward-forward splitting | DECOMPOSITION | primal-dual algorithms | SUM | ALGORITHMS | CONVEX-OPTIMIZATION | COMPOSITE | averaged operator | MONOTONE INCLUSIONS | MINIMIZATION | SYSTEMS | convergence rates | nonexpansive operator | OPERATORS | proximal point algorithm | fixed-point algorithm

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2018, Volume 177, Issue 2, pp. 413 - 447

We propose a new iterative algorithm for the numerical approximation of the solutions to convex optimization problems and constrained variational inequalities,...

Penalization | Forwardâ€“backward | Mathematics | Theory of Computation | Convex programming | Optimization | Calculus of Variations and Optimal Control; Optimization | Lagrange multipliers | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | Forward-backward | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | NOISE | DESCENT | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PENALTY | IMAGES | CONVERGENCE | SEPARABLE CONVEX MINIMIZATION | MONOTONE-OPERATORS | Analysis | Algorithms | Computational geometry | Newtonian fluids | Computational fluid dynamics | Non Newtonian fluids | Iterative algorithms | Mathematical models | Convexity | Iterative methods | Convex analysis | Convergence

Penalization | Forwardâ€“backward | Mathematics | Theory of Computation | Convex programming | Optimization | Calculus of Variations and Optimal Control; Optimization | Lagrange multipliers | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | Forward-backward | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | NOISE | DESCENT | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PENALTY | IMAGES | CONVERGENCE | SEPARABLE CONVEX MINIMIZATION | MONOTONE-OPERATORS | Analysis | Algorithms | Computational geometry | Newtonian fluids | Computational fluid dynamics | Non Newtonian fluids | Iterative algorithms | Mathematical models | Convexity | Iterative methods | Convex analysis | Convergence

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 12/2017, Volume 57, Issue 12, pp. 1994 - 2004

New second-order accurate monotone difference schemes on nonuniform spatial grids for two-dimensional stationary and nonstationary convectionâ€“diffusion...

twosided estimate | Computational Mathematics and Numerical Analysis | Mathematics | monotone difference scheme | convectionâ€“diffusion equation | maximum principle | nonuniform grids | convection-diffusion equation | MATHEMATICS, APPLIED | two-sided estimate | PHYSICS, MATHEMATICAL | Algorithms | Resveratrol | Diffusion | Boundary conditions | Convection

twosided estimate | Computational Mathematics and Numerical Analysis | Mathematics | monotone difference scheme | convectionâ€“diffusion equation | maximum principle | nonuniform grids | convection-diffusion equation | MATHEMATICS, APPLIED | two-sided estimate | PHYSICS, MATHEMATICAL | Algorithms | Resveratrol | Diffusion | Boundary conditions | Convection

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 16, pp. 5653 - 5691

In this paper, we construct spatially consistent explicit second order discretizations for time dependent hyperbolic problems, starting from a given residual...

Hyperbolic conservation laws | Rungeâ€“Kutta time-stepping | Residual distribution | Explicit schemes | Second order schemes | Time dependent problems | Runge-Kutta time-stepping | SEMIDISCRETE | DISCONTINUOUS GALERKIN METHOD | FORMULATION | PHYSICS, MATHEMATICAL | FLOW | STABILIZED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ACCURATE MONOTONE | CONSTRUCTION | CONSERVATION-LAWS | FOURIER-ANALYSIS | DIFFUSIVE-REACTIVE EQUATION | Operators | Approximation | Discretization | Mathematical analysis | Stabilization | Matrices | Runge-Kutta method | Galerkin methods

Hyperbolic conservation laws | Rungeâ€“Kutta time-stepping | Residual distribution | Explicit schemes | Second order schemes | Time dependent problems | Runge-Kutta time-stepping | SEMIDISCRETE | DISCONTINUOUS GALERKIN METHOD | FORMULATION | PHYSICS, MATHEMATICAL | FLOW | STABILIZED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ACCURATE MONOTONE | CONSTRUCTION | CONSERVATION-LAWS | FOURIER-ANALYSIS | DIFFUSIVE-REACTIVE EQUATION | Operators | Approximation | Discretization | Mathematical analysis | Stabilization | Matrices | Runge-Kutta method | Galerkin methods

Journal Article

Electronics Letters, ISSN 0013-5194, 1/2014, Volume 50, Issue 1, pp. 22 - 23

A novel low-energy hybrid capacitor switching scheme for a low-power successive approximation register (SAR) analogue-to-digital converter (ADC) is presented....

Circuits and systems | low-energy monotonic procedure | low energy-efficient hybrid capacitor switching scheme | SAR ADC | analogue-digital conversion | capacitor switching | energy saving | low-power successive approximation register analogue-to-digital converter | average switching energy | ENGINEERING, ELECTRICAL & ELECTRONIC

Circuits and systems | low-energy monotonic procedure | low energy-efficient hybrid capacitor switching scheme | SAR ADC | analogue-digital conversion | capacitor switching | energy saving | low-power successive approximation register analogue-to-digital converter | average switching energy | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

15.
Full Text
How to construct a verifiable multi-secret sharing scheme based on graded encoding schemes

IET Information Security, ISSN 1751-8709, 7/2019, Volume 13, Issue 4, pp. 343 - 351

In a verifiable multi-secret sharing scheme, a dealer distributes multiple secrets between a group of participants and also additional information is given...

Research Article | verifiable multisecret sharing scheme | graded decision-Diffie-Hellman problem | graded encoding schemes | COMPUTER SCIENCE, INFORMATION SYSTEMS | cryptography | monotone span programs | COMPUTER SCIENCE, THEORY & METHODS | VMSS scheme | general access structure | computational security

Research Article | verifiable multisecret sharing scheme | graded decision-Diffie-Hellman problem | graded encoding schemes | COMPUTER SCIENCE, INFORMATION SYSTEMS | cryptography | monotone span programs | COMPUTER SCIENCE, THEORY & METHODS | VMSS scheme | general access structure | computational security

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 10/2015, Volume 65, Issue 1, pp. 110 - 137

We construct a class of convergent high order schemes for time dependent Hamiltonâ€“Jacobi equations. In general, high order schemes such as WENO scheme achieve...

First order monotone scheme | Computational Mathematics and Numerical Analysis | Algorithms | WENO scheme | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Nonconvex Hamiltonian | Mathematics | Hamiltonâ€“Jacobi equations | High order scheme | Convergence | Hamilton-Jacobi equations | WEIGHTED ENO SCHEMES | HERMITE WENO SCHEMES | VISCOSITY SOLUTIONS | TRIANGULAR MESHES | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | APPROXIMATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD

First order monotone scheme | Computational Mathematics and Numerical Analysis | Algorithms | WENO scheme | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Nonconvex Hamiltonian | Mathematics | Hamiltonâ€“Jacobi equations | High order scheme | Convergence | Hamilton-Jacobi equations | WEIGHTED ENO SCHEMES | HERMITE WENO SCHEMES | VISCOSITY SOLUTIONS | TRIANGULAR MESHES | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | APPROXIMATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | CONSERVATION-LAWS | FINITE-ELEMENT-METHOD

Journal Article

Information Sciences, ISSN 0020-0255, 02/2017, Volume 378, pp. 99 - 108

A publicly verifiable secret sharing allows anyone to detect the cheating of dealer or participants only from the public information. In this paper, by using...

Standard model | Monotone span program | Proactive scheme | Publicly verifiable secret sharing | Bilinear pairing | Robust | COMPUTER SCIENCE, INFORMATION SYSTEMS | Computer information security

Standard model | Monotone span program | Proactive scheme | Publicly verifiable secret sharing | Bilinear pairing | Robust | COMPUTER SCIENCE, INFORMATION SYSTEMS | Computer information security

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 351, pp. 80 - 107

In the present work, we deal with the convergence of cell-centered nonlinear finite volume schemes for anisotropic and heterogeneous diffusion operators. A...

Monotone | Multi-point flux approximation | Heterogeneous anisotropic diffusion | Finite volume methods | Convergence analysis | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | Anisotropy | Analysis | Numerical analysis | Numerical Analysis | Mathematics

Monotone | Multi-point flux approximation | Heterogeneous anisotropic diffusion | Finite volume methods | Convergence analysis | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | Anisotropy | Analysis | Numerical analysis | Numerical Analysis | Mathematics

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 06/2017, Volume 127, Issue 6, pp. 1738 - 1762

We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo (2014) for viscosity solutions to...

Monotone schemes | Path-dependent PDE | Numerical analysis | Viscosity solution | VISCOSITY SOLUTIONS | ALGORITHM | EQUATIONS | DISCRETE-TIME APPROXIMATION | BSDES | STATISTICS & PROBABILITY

Monotone schemes | Path-dependent PDE | Numerical analysis | Viscosity solution | VISCOSITY SOLUTIONS | ALGORITHM | EQUATIONS | DISCRETE-TIME APPROXIMATION | BSDES | STATISTICS & PROBABILITY

Journal Article