On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems

DOI10.1137/21M1446289MaRDI QIDQ5886844

Gianluca Ceruti, Jonas Kusch, Lukas Einkemmer

Publication date: 11 April 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.07282

zbMATH Keywords

numerical stabilitykinetic equationsuncertainty quantificationdynamical low-rank approximationunconventional integratorprojector-splitting integrator

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Numerical nonlinear stabilities in dynamical systems (65P40) Numerical analysis (65-XX)

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Uses Software

• GitHub

Cites Work

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• Dynamically orthogonal field equations for continuous stochastic dynamical systems
• Robust and accurate filtered spherical harmonics expansions for radiative transfer
• An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction
• Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions
• Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations
• A rank-adaptive robust integrator for dynamical low-rank approximation
• An unconventional robust integrator for dynamical low-rank approximation
• A low-rank method for two-dimensional time-dependent radiation transport calculations
• An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
• A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
• A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations
• A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps
• Symplectic dynamical low rank approximation of wave equations with random parameters
• A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction
• Filtered stochastic Galerkin methods for hyperbolic equations
• Discretized feedback control for systems of linearized hyperbolic balance laws
• A projector-splitting integrator for dynamical low-rank approximation
• An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime
• Dynamically Orthogonal Numerical Schemes for Efficient Stochastic Advection and Lagrangian Transport
• A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit
• DYNAMICAL LOW-RANK APPROXIMATION FOR BURGERS' EQUATION WITH UNCERTAINTY
• A Low-Rank Algorithm for Weakly Compressible Flow
• Convergence of a Low-Rank Lie--Trotter Splitting for Stiff Matrix Differential Equations
• A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation
• A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations
• Dynamical Low‐Rank Approximation