Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
Journal of Computational Physics
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Microstructural evolution in orthotropic elastic media
Journal of Computational Physics
Exponential time differencing for stiff systems
Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Compact integration factor methods in high spatial dimensions
Journal of Computational Physics
Journal of Computational Physics
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
Journal of Computational Physics
A robust and efficient method for steady state patterns in reaction-diffusion systems
Journal of Computational Physics
Circuit simulation via matrix exponential method for stiffness handling and parallel processing
Proceedings of the International Conference on Computer-Aided Design
A fast time-domain EM-TCAD coupled simulation framework via matrix exponential
Proceedings of the International Conference on Computer-Aided Design
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth
Journal of Scientific Computing
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Hi-index | 31.48 |
When explicit time discretization schemes are applied to stiff reaction-diffusion equations, the stability constraint on the time step depends on two terms: the diffusion and the reaction. The part of the stability constraint due to diffusion can be totally removed if the linear diffusions are treated exactly using integration factor (IF) or exponential time differencing (ETD) methods. For systems with severely stiff reactions, those methods are not efficient because the reaction terms in IF or ETD are still approximated with explicit schemes. In this paper, we introduce a new class of semi-implicit schemes, which treats the linear diffusions exactly and explicitly, and the nonlinear reactions implicitly. A distinctive feature of the scheme is the decoupling between the exact evaluation of the diffusion terms and implicit treatment of the nonlinear reaction terms. As a result, the size of the nonlinear system arising from the implicit treatment of the reactions is independent of the number of spatial grid points; it only depends on the number of original equations, unlike the case in which standard implicit temporal schemes are directly applied to the reaction-diffusion system. The stability region for this class of methods is much larger than existing methods using an explicit treatment of reaction terms. In particular, the one with second order accuracy is unconditionally linearly stable with respect to both diffusion and reaction. Direct numerical simulations on test equations, as well as morphogen systems from developmental biology, show the new semi-implicit schemes are efficient, robust and accurate.