Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 03/2017, Volume 27, Issue 3, pp. 549 - 579

In this paper, we develop a second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) scheme for the Kerr-Debye model. By using...

Discontinuous Galerkin | Kerr-Debye model | implicit-explicit | positivity-preserving | stiff systems | Runge-Kutta methods | asymptotic-preserving | NUMERICAL-METHODS | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | DG-IMEX SCHEMES | KINETIC-EQUATIONS | SYMMETRIZABLE SYSTEMS | HIGH-ORDER | RELAXATION APPROXIMATION | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT-METHOD

Discontinuous Galerkin | Kerr-Debye model | implicit-explicit | positivity-preserving | stiff systems | Runge-Kutta methods | asymptotic-preserving | NUMERICAL-METHODS | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | DG-IMEX SCHEMES | KINETIC-EQUATIONS | SYMMETRIZABLE SYSTEMS | HIGH-ORDER | RELAXATION APPROXIMATION | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT-METHOD

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 1/2016, Volume 29, Issue 1, pp. 191 - 206

The aim of this paper is to investigate properties preserved and co-preserved by coarsely n-to-1 functions, in particular by the quotient maps $$X\rightarrow...

Metric sparsification property | Coarse geometry | Asymptotic dimension | Mathematics | Topology | Straight finite decomposition complexity | Asymptotic Property C | Primary 54F45 | Geometry | Secondary 55M10 | Algebra | Analysis | Coarsely n-to-1 functions | Mathematics, general | Applications of Mathematics | Lipschitz maps | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | THEOREM

Metric sparsification property | Coarse geometry | Asymptotic dimension | Mathematics | Topology | Straight finite decomposition complexity | Asymptotic Property C | Primary 54F45 | Geometry | Secondary 55M10 | Algebra | Analysis | Coarsely n-to-1 functions | Mathematics, general | Applications of Mathematics | Lipschitz maps | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | THEOREM

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2013, Volume 253, Issue 15, pp. 138 - 156

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a...

Stiff terms | Transport equations | Asymptotic preserving schemes | Diffusion limit | MICRO-MACRO SCHEMES | TRANSPORT-EQUATIONS | AP SCHEMES | STABILITY | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | RELAXATION SCHEMES | NUMERICAL SCHEMES | BOLTZMANN-EQUATION | Analysis | Boundary layer | Discretization | Asymptotic properties | Mathematical analysis | Mathematical models | Transport | Diffusion | Standards | Preserving | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics | RADIANT HEAT TRANSFER | DIFFUSION EQUATIONS | TRANSPORT THEORY | DECOMPOSITION | BOUNDARY LAYERS | DIFFUSION | MATHEMATICAL METHODS AND COMPUTING | ASYMPTOTIC SOLUTIONS

Stiff terms | Transport equations | Asymptotic preserving schemes | Diffusion limit | MICRO-MACRO SCHEMES | TRANSPORT-EQUATIONS | AP SCHEMES | STABILITY | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | RELAXATION SCHEMES | NUMERICAL SCHEMES | BOLTZMANN-EQUATION | Analysis | Boundary layer | Discretization | Asymptotic properties | Mathematical analysis | Mathematical models | Transport | Diffusion | Standards | Preserving | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics | RADIANT HEAT TRANSFER | DIFFUSION EQUATIONS | TRANSPORT THEORY | DECOMPOSITION | BOUNDARY LAYERS | DIFFUSION | MATHEMATICAL METHODS AND COMPUTING | ASYMPTOTIC SOLUTIONS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 20, pp. 7625 - 7648

In this paper, we propose a general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and...

Boltzmann equation | Stiff source terms | Asymptotic-preserving scheme | NUMERICAL TRANSPORT PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOLTZMANN-EQUATION | SYSTEMS | FINITE-VOLUME SCHEME | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | DIFFUSIVE RELAXATION SCHEMES | OPTICALLY THICK | Fluid dynamics | Asymptotic properties | Mathematical analysis | Nonlinearity | Thermal conductivity | Mathematical models | Density distribution | Collision dynamics | Relaxation time | Navier-Stokes equations | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

Boltzmann equation | Stiff source terms | Asymptotic-preserving scheme | NUMERICAL TRANSPORT PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOLTZMANN-EQUATION | SYSTEMS | FINITE-VOLUME SCHEME | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | DIFFUSIVE RELAXATION SCHEMES | OPTICALLY THICK | Fluid dynamics | Asymptotic properties | Mathematical analysis | Nonlinearity | Thermal conductivity | Mathematical models | Density distribution | Collision dynamics | Relaxation time | Navier-Stokes equations | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

Journal Article

IEEE Transactions on Robotics, ISSN 1552-3098, 04/2018, Volume 34, Issue 2, pp. 317 - 335

Physical compliance can be considered one of the key technical properties a robot should exhibit to increase its mechanical robustness. In addition, the...

Damping | tracking control | Asymptotic stability | Compliant robots | variable stiffness joints | Tracking | passivity-based control | Aerodynamics | Springs | Task analysis | damping control | Robots | FEEDBACK LINEARIZATION | DESIGN | ROBOTICS | IMPEDANCE CONTROL | GLOBAL TRACKING CONTROLLERS | TORQUE | JOINT | Robot arms | Properties (attributes) | Control methods | Robot control | Modulus of elasticity | Stiffness | Elastic properties | Feedback control | Tracking control

Damping | tracking control | Asymptotic stability | Compliant robots | variable stiffness joints | Tracking | passivity-based control | Aerodynamics | Springs | Task analysis | damping control | Robots | FEEDBACK LINEARIZATION | DESIGN | ROBOTICS | IMPEDANCE CONTROL | GLOBAL TRACKING CONTROLLERS | TORQUE | JOINT | Robot arms | Properties (attributes) | Control methods | Robot control | Modulus of elasticity | Stiffness | Elastic properties | Feedback control | Tracking control

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 2, pp. 1064 - 1087

We discuss implicit-explicit (IMEX) Runge Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We consider both the case...

Mathematical problems | Sufficient conditions | Boltzmann equation | Kinetic equations | Mathematical monotonicity | Approximation | Fluid flow | Mathematics | Kinetics | Runge Kutta method | Fluid-dynamical limit | Implicit-explicit Runge-Kutta methods | Stiff differential equations | Asymptotic preserving schemes | MATHEMATICS, APPLIED | implicit-explicit Runge-Kutta methods | HYPERBOLIC SYSTEMS | BOLTZMANN-EQUATION | stiff differential equations | RELAXATION | asymptotic preserving schemes | fluid-dynamical limit | STRONG STABILITY | SCHEMES | Operators | Integrals | Asymptotic properties | Nonlinearity | Collision avoidance | Collision dynamics | Preserving

Mathematical problems | Sufficient conditions | Boltzmann equation | Kinetic equations | Mathematical monotonicity | Approximation | Fluid flow | Mathematics | Kinetics | Runge Kutta method | Fluid-dynamical limit | Implicit-explicit Runge-Kutta methods | Stiff differential equations | Asymptotic preserving schemes | MATHEMATICS, APPLIED | implicit-explicit Runge-Kutta methods | HYPERBOLIC SYSTEMS | BOLTZMANN-EQUATION | stiff differential equations | RELAXATION | asymptotic preserving schemes | fluid-dynamical limit | STRONG STABILITY | SCHEMES | Operators | Integrals | Asymptotic properties | Nonlinearity | Collision avoidance | Collision dynamics | Preserving

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2018, Volume 20, Issue 4, p. 1750027

We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other...

Lyapunov exponents | reduction | Lyapunov regularity | MATHEMATICS | MATHEMATICS, APPLIED

Lyapunov exponents | reduction | Lyapunov regularity | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2014, Volume 276, pp. 380 - 404

In this work, we propose an asymptotic-preserving Monte Carlo method for the Boltzmann equation that is more efficient than the currently available Monte Carlo...

Boltzmann equation | DSMC | Asymptotic preserving scheme | Successive-penalty | EXPONENTIAL RUNGE-KUTTA | KINETIC-EQUATIONS | ELECTRON-BEAM | IMPLEMENTATION | PHYSICS, MATHEMATICAL | SHOCK-WAVES | ARGON | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STATISTICAL ERROR | FLOWS | SCHEMES | Monte Carlo method | Analysis | Methods | Aerodynamics | Monte Carlo methods | Computational fluid dynamics | Computer simulation | Asymptotic properties | Mathematical analysis | Boltzmann transport equation | Mathematical models

Boltzmann equation | DSMC | Asymptotic preserving scheme | Successive-penalty | EXPONENTIAL RUNGE-KUTTA | KINETIC-EQUATIONS | ELECTRON-BEAM | IMPLEMENTATION | PHYSICS, MATHEMATICAL | SHOCK-WAVES | ARGON | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STATISTICAL ERROR | FLOWS | SCHEMES | Monte Carlo method | Analysis | Methods | Aerodynamics | Monte Carlo methods | Computational fluid dynamics | Computer simulation | Asymptotic properties | Mathematical analysis | Boltzmann transport equation | Mathematical models

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 274, pp. 122 - 139

In this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are...

Asymptotic accuracy | Vlasov–BGK–Poisson system | Plasmas simulations | Kinetic-fluid coupling | Asymptotic preservation | Vlasov-BGK-Poisson system | NONLINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | RUNGE-KUTTA SCHEMES | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPLICIT SCHEMES | BOLTZMANN | DISCRETE-VELOCITY MODEL | RELAXATION SCHEMES | FLOWS | EULER EQUATIONS | Plasma physics | Methods | Computer science | Numerical analysis | Fluids | Computer simulation | Asymptotic properties | Fluid flow | Strategy | Mathematical models | Plasmas | Preserving | Numerical Analysis | Mathematics | PLASMA SIMULATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PERFORMANCE | PLASMA FLUID EQUATIONS | BERNSTEIN MODE | COUPLING | EFFICIENCY | PLASMA WAVES | ASYMPTOTIC SOLUTIONS | ACCURACY | COMPUTERIZED SIMULATION

Asymptotic accuracy | Vlasov–BGK–Poisson system | Plasmas simulations | Kinetic-fluid coupling | Asymptotic preservation | Vlasov-BGK-Poisson system | NONLINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | RUNGE-KUTTA SCHEMES | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPLICIT SCHEMES | BOLTZMANN | DISCRETE-VELOCITY MODEL | RELAXATION SCHEMES | FLOWS | EULER EQUATIONS | Plasma physics | Methods | Computer science | Numerical analysis | Fluids | Computer simulation | Asymptotic properties | Fluid flow | Strategy | Mathematical models | Plasmas | Preserving | Numerical Analysis | Mathematics | PLASMA SIMULATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PERFORMANCE | PLASMA FLUID EQUATIONS | BERNSTEIN MODE | COUPLING | EFFICIENCY | PLASMA WAVES | ASYMPTOTIC SOLUTIONS | ACCURACY | COMPUTERIZED SIMULATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2015, Volume 289, Issue C, pp. 35 - 52

In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The...

Uncertainty quantification | Asympotic-preserving | Generalized polynomial chaos | Transport equations | Hyperbolic systems | Diffusion limit | KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COLLOCATION METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | SYSTEMS | CONVERGENCE | CONSERVATION-LAWS | OPTICALLY THICK | Discretization | Asymptotic properties | Mathematical analysis | Preserves | Polynomials | Stochasticity | Diffusion | Galerkin methods

Uncertainty quantification | Asympotic-preserving | Generalized polynomial chaos | Transport equations | Hyperbolic systems | Diffusion limit | KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COLLOCATION METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | SYSTEMS | CONVERGENCE | CONSERVATION-LAWS | OPTICALLY THICK | Discretization | Asymptotic properties | Mathematical analysis | Preserves | Polynomials | Stochasticity | Diffusion | Galerkin methods

Journal Article

11.
Full Text
An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

Journal of Computational Physics, ISSN 0021-9991, 03/2015, Volume 285, pp. 265 - 279

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and...

Grey radiative transfer equations | Unified gas kinetic scheme | Equilibrium diffusion equation | Asymptotic preserving | TRANSPORT-EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFUSION | CONTINUUM | LIMIT | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | Analysis | Force and energy | Asymptotic properties | Mathematical analysis | Mathematical models | Photons | Radiative transfer | Diffusion | Preserving | Radiation transport | RADIANT HEAT TRANSFER | DIFFUSION EQUATIONS | TRANSPORT THEORY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EXACT SOLUTIONS | PHOTON COLLISIONS | TWO-DIMENSIONAL SYSTEMS | ONE-DIMENSIONAL CALCULATIONS | ASYMPTOTIC SOLUTIONS | NONLINEAR PROBLEMS | MEAN FREE PATH | TIME DEPENDENCE | RADIATION TRANSPORT | MATHEMATICAL METHODS AND COMPUTING

Grey radiative transfer equations | Unified gas kinetic scheme | Equilibrium diffusion equation | Asymptotic preserving | TRANSPORT-EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFUSION | CONTINUUM | LIMIT | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | Analysis | Force and energy | Asymptotic properties | Mathematical analysis | Mathematical models | Photons | Radiative transfer | Diffusion | Preserving | Radiation transport | RADIANT HEAT TRANSFER | DIFFUSION EQUATIONS | TRANSPORT THEORY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EXACT SOLUTIONS | PHOTON COLLISIONS | TWO-DIMENSIONAL SYSTEMS | ONE-DIMENSIONAL CALCULATIONS | ASYMPTOTIC SOLUTIONS | NONLINEAR PROBLEMS | MEAN FREE PATH | TIME DEPENDENCE | RADIATION TRANSPORT | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2015, Volume 288, pp. 52 - 65

Asymptotic preserving (AP) schemes target to simulate both continuum and rarefied flows. Many existing AP schemes are capable of recovering the Euler limit in...

Asymptotic preserving schemes | Unified gas kinetic schemes | RUNGE-KUTTA | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | BOLTZMANN | NUMERICAL SCHEMES | STIFF RELAXATION TERMS | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | Kinetic equations | Asymptotic properties | Continuum flow | Continuums | Mathematical models | Convection | Collision dynamics | Preserving | Navier-Stokes equations | Physics - Fluid Dynamics

Asymptotic preserving schemes | Unified gas kinetic schemes | RUNGE-KUTTA | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | BOLTZMANN | NUMERICAL SCHEMES | STIFF RELAXATION TERMS | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | Kinetic equations | Asymptotic properties | Continuum flow | Continuums | Mathematical models | Convection | Collision dynamics | Preserving | Navier-Stokes equations | Physics - Fluid Dynamics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2012, Volume 231, Issue 7, pp. 2724 - 2740

The concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion...

Finite element method | Anisotropic diffusion | Asymptotic preserving scheme | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Anisotropy | Methods | Cartesian | Asymptotic properties | Mathematical analysis | Mathematical models | Diffusion | Preserving | Convergence | Mathematics - Numerical Analysis

Finite element method | Anisotropic diffusion | Asymptotic preserving scheme | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Anisotropy | Methods | Cartesian | Asymptotic properties | Mathematical analysis | Mathematical models | Diffusion | Preserving | Convergence | Mathematics - Numerical Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2015, Volume 302, pp. 222 - 238

This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to...

Optically thick and thin | Unified gas kinetic scheme | Frequency-dependent radiative transfer | Asymptotic preserving scheme | TRANSPORT-EQUATIONS | LIMIT | ACCELERATION METHOD | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | TRANSFER SIMULATIONS | DIFFUSION | CONTINUUM | Analysis | Wave propagation | Radiation | Computer simulation | Mean free path | Asymptotic properties | Mathematical analysis | Mathematical models | Radiative transfer | Opacity | Transport | RADIANT HEAT TRANSFER | MONTE CARLO METHOD | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DISCRETE ORDINATE METHOD | PHOTONS | WAVE PROPAGATION | EQUATIONS | OPACITY | FUNCTIONS | SIMULATION | ASYMPTOTIC SOLUTIONS | MEAN FREE PATH | FREQUENCY DEPENDENCE | CAPTURE

Optically thick and thin | Unified gas kinetic scheme | Frequency-dependent radiative transfer | Asymptotic preserving scheme | TRANSPORT-EQUATIONS | LIMIT | ACCELERATION METHOD | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | TRANSFER SIMULATIONS | DIFFUSION | CONTINUUM | Analysis | Wave propagation | Radiation | Computer simulation | Mean free path | Asymptotic properties | Mathematical analysis | Mathematical models | Radiative transfer | Opacity | Transport | RADIANT HEAT TRANSFER | MONTE CARLO METHOD | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DISCRETE ORDINATE METHOD | PHOTONS | WAVE PROPAGATION | EQUATIONS | OPACITY | FUNCTIONS | SIMULATION | ASYMPTOTIC SOLUTIONS | MEAN FREE PATH | FREQUENCY DEPENDENCE | CAPTURE

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2016, Volume 305, pp. 575 - 588

An asymptotic preserving (AP) scheme is efficient in solving multiscale kinetic equations with a wide range of the Knudsen number. In this paper, we generalize...

Multispecies Boltzmann equation | DSMC | Asymptotic preserving scheme | Multiscale flow | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SMOOTH TRANSITION MODEL | DOMAIN DECOMPOSITION | PHYSICS, MATHEMATICAL | SCHEMES | Monte Carlo method | Aerodynamics | Methods | Monte Carlo methods | Boltzmann equation | Computer simulation | Asymptotic properties | Mathematical analysis | Boltzmann transport equation | Mathematical models | Preserving

Multispecies Boltzmann equation | DSMC | Asymptotic preserving scheme | Multiscale flow | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SMOOTH TRANSITION MODEL | DOMAIN DECOMPOSITION | PHYSICS, MATHEMATICAL | SCHEMES | Monte Carlo method | Aerodynamics | Methods | Monte Carlo methods | Boltzmann equation | Computer simulation | Asymptotic properties | Mathematical analysis | Boltzmann transport equation | Mathematical models | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 17, pp. 6420 - 6437

We present a class of asymptotic-preserving (AP) schemes for the nonhomogeneous Fokker–Planck–Landau (nFPL) equation. Filbet and Jin [16] designed a class of...

Fokker–Planck–Landau equation | Asymptotic-preserving schemes | Fluid dynamic limit | Fokker-Planck-Landau equation | KINETIC-EQUATIONS | POTENTIALS | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | IMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDS | EQUILIBRIUM | SYSTEMS | TREND | ENTROPY | Fluid dynamics | Physicians (General practice) | Fluids | Operators | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Fluid flow | Boltzmann transport equation | Mathematical models

Fokker–Planck–Landau equation | Asymptotic-preserving schemes | Fluid dynamic limit | Fokker-Planck-Landau equation | KINETIC-EQUATIONS | POTENTIALS | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | IMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDS | EQUILIBRIUM | SYSTEMS | TREND | ENTROPY | Fluid dynamics | Physicians (General practice) | Fluids | Operators | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Fluid flow | Boltzmann transport equation | Mathematical models

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 2, pp. A377 - A395

We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late...

Hyperbolic-to-parabolic regime | High-order discretization | Nonlinear hyperbolic system | Late-time limit | Stiff relaxation | late-time limit | MATHEMATICS, APPLIED | stiff relaxation | HYPERBOLIC SYSTEMS | KINETIC-EQUATIONS | HYDRODYNAMICS | LIMIT | RUNGE-KUTTA SCHEMES | DIFFUSIVE RELAXATION | hyperbolic-to-parabolic regime | high-order discretization | ERROR ANALYSIS | NUMERICAL SCHEMES | CONSERVATION-LAWS | nonlinear hyperbolic system | Nonlinear dynamics | Computational fluid dynamics | Computation | Asymptotic properties | Nonlinearity | Mathematical models | Robustness | Dynamical systems

Hyperbolic-to-parabolic regime | High-order discretization | Nonlinear hyperbolic system | Late-time limit | Stiff relaxation | late-time limit | MATHEMATICS, APPLIED | stiff relaxation | HYPERBOLIC SYSTEMS | KINETIC-EQUATIONS | HYDRODYNAMICS | LIMIT | RUNGE-KUTTA SCHEMES | DIFFUSIVE RELAXATION | hyperbolic-to-parabolic regime | high-order discretization | ERROR ANALYSIS | NUMERICAL SCHEMES | CONSERVATION-LAWS | nonlinear hyperbolic system | Nonlinear dynamics | Computational fluid dynamics | Computation | Asymptotic properties | Nonlinearity | Mathematical models | Robustness | Dynamical systems

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 16, pp. 5630 - 5652

This paper deals with the numerical resolution of the Vlasov–Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime,...

Asymptotic-Preserving scheme | Plasma | Quasineutral limit | Debye length | Vlasov–Poisson | Vlasov-Poisson | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | ELECTROMAGNETIC PLASMA SIMULATION | FIELD | CONVERGENCE | PHYSICS, MATHEMATICAL | Stability | Discretization | Asymptotic properties | Computation | Mathematical models | Plasma frequencies | Particle in cell technique | Mathematics | Plasma Physics | Numerical Analysis | Physics

Asymptotic-Preserving scheme | Plasma | Quasineutral limit | Debye length | Vlasov–Poisson | Vlasov-Poisson | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | ELECTROMAGNETIC PLASMA SIMULATION | FIELD | CONVERGENCE | PHYSICS, MATHEMATICAL | Stability | Discretization | Asymptotic properties | Computation | Mathematical models | Plasma frequencies | Particle in cell technique | Mathematics | Plasma Physics | Numerical Analysis | Physics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2019, Volume 376, Issue C, pp. 634 - 659

In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior...

Bipolar Boltzmann-Poisson model | Uncertainty quantification | Stochastic AP scheme | Diffusive scaling | Sensitivity analysis | gPC-SG method | SPECTRAL CONVERGENCE | UNIFORM REGULARITY | AP SCHEMES | GALERKIN METHOD | HYPOCOERCIVITY | LINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | NUMERICAL SCHEMES | UNCERTAINTY | CONSERVATION-LAWS | Electric fields | Analysis | Models | Mathematical analysis | Asymptotic properties | Polynomials | Mathematical models | Galerkin method | Semiconductor doping | Asymptotic methods | Convergence | Mathematics - Numerical Analysis | Physics | Computer Science

Bipolar Boltzmann-Poisson model | Uncertainty quantification | Stochastic AP scheme | Diffusive scaling | Sensitivity analysis | gPC-SG method | SPECTRAL CONVERGENCE | UNIFORM REGULARITY | AP SCHEMES | GALERKIN METHOD | HYPOCOERCIVITY | LINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | NUMERICAL SCHEMES | UNCERTAINTY | CONSERVATION-LAWS | Electric fields | Analysis | Models | Mathematical analysis | Asymptotic properties | Polynomials | Mathematical models | Galerkin method | Semiconductor doping | Asymptotic methods | Convergence | Mathematics - Numerical Analysis | Physics | Computer Science

Journal Article