Fourier spectral methods for nonlinear Boltzmann equations

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Boltzmann equations (35Q20)

Cites Work

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Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit
Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
Mathematics of granular materials
Mathematical modeling of collective behavior in socio-economic and life sciences
Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
The mathematical theory of dilute gases
A quadrature formula for the sphere of the 131st algebraic order of accuracy
An efficient numerical method for solving the Boltzmann equation in multidimensions
Galerkin-Petrov approach for the Boltzmann equation
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A fast spectral algorithm for the quantum Boltzmann collision operator
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A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation
On steady-state preserving spectral methods for homogeneous Boltzmann equations
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An adaptive dynamical low rank method for the nonlinear Boltzmann equation
A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases
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On the stability of spectral methods for the homogeneous Boltzmann equation
A numerical scheme for the quantum Boltzmann equation with stiff collision terms
Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
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Spectral Methods for Time-Dependent Problems
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Solving the Boltzmann Equation in N log₂N
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Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator
Efficient Spherical Designs with Good Geometric Properties
A Polynomial Spectral Method for the Spatially Homogeneous Boltzmann Equation
Numerical methods for kinetic equations
An Entropic Fourier Method for the Boltzmann Equation
Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I
On Deterministic Approximation of the Boltzmann Equation in a Bounded Domain
A Fast Petrov--Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions
Burnett Spectral Method for High-Speed Rarefied Gas Flows
A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels
A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation
Asymptotic-preserving schemes for multiscale physical problems

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