Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Implicit-Explicit Parallel Asynchronous Solver of Parabolic PDEs
SIAM Journal on Scientific Computing
Fluids in the universe: adaptive mesh refinement in cosmology
Computing in Science and Engineering
A multgrid Newton-Krylov method for multimaterial equilibrium radiation diffusion
Journal of Computational Physics
Time step size selection for radiation diffusion calculations
Journal of Computational Physics
Iterative linear solvers in a 2D radiation-hydrodynamics code: methods and performance
Journal of Computational Physics
Mini review: Computer modeling in cardiac electrophysiology
Journal of Computational Physics
Parallel and Distribution Simulation Systems
Parallel and Distribution Simulation Systems
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps
SIAM Journal on Scientific Computing
Implicit-explicit time stepping with spatial discontinuous finite elements
Applied Numerical Mathematics
Mathematics of Computation
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Adaptive low Mach number simulations of nuclear flame microphysics
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
Spacetime meshing with adaptive refinement and coarsening
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Parallel discrete event simulation with application to continuous systems
Parallel discrete event simulation with application to continuous systems
Journal of Computational Physics
Event-driven, hybrid particle-in-cell simulation: a new paradigm for multi-scale plasma modeling
Journal of Computational Physics
Discrete event solution of gas dynamics within the DEVS framework
ICCS'03 Proceedings of the 2003 international conference on Computational science
Event-driven, hybrid particle-in-cell simulation: a new paradigm for multi-scale plasma modeling
Journal of Computational Physics
Journal of Computational Physics
DAG-guided parallel asynchronous variational integrators with super-elements
Proceedings of the 2007 Summer Computer Simulation Conference
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Journal of Computational Physics
HYPERS: A unidimensional asynchronous framework for multiscale hybrid simulations
Journal of Computational Physics
An asynchronous framework for the simulation of the plasma/flow interaction
Journal of Computational Physics
Time asynchronous relative dimension in space method for multi-scale problems in fluid dynamics
Journal of Computational Physics
Hi-index | 31.48 |
We present a novel, flux-conserving, asynchronous method for the explicit time integration of multi-scale, flux-conservative partial differential equations with source terms. Unlike the conventional explicit and implicit integration schemes, it is based on a discrete-event simulation paradigm, which describes time advance in terms of increments to physical quantities and causality rules rather than time stepping. This method exerts self-adaptive control over local update rates of solution by predicting and correcting changes to simulation variables in accordance with local physical scales. The discrete-event simulation paradigm is independent of the underlying spatial mesh and thus can be incorporated into block-structured and unstructured mesh refinement techniques. The effectiveness and robustness of the new method is demonstrated on a number of one-dimensional, uniform mesh models based on diffusion-convection reaction equations. The event-driven integration reduces numerical approximation errors due to large local time derivatives, prevents explosive numerical instabilities in locally super-Courant calculations and automatically reduces the CPU overhead associated with stiff terms and inactive regions in computation space.