Matrix analysis
SIAM Journal on Scientific and Statistical Computing
On the use of composite grid schemes in computational aerodynamics
Computer Methods in Applied Mechanics and Engineering
The fast Fourier transform and its applications
The fast Fourier transform and its applications
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Hole-Cutting for Three-Dimensional Overlapping Grids
SIAM Journal on Scientific Computing
Microstructural evolution in orthotropic elastic media
Journal of Computational Physics
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps
SIAM Journal on Scientific Computing
Overture: An Object-Oriented Framework for Solving Partial Differential Equations
ISCOPE '97 Proceedings of the Scientific Computing in Object-Oriented Parallel Environments
Mathematics of Computation
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
Journal of Computational Physics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
Compact integration factor methods in high spatial dimensions
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Journal of Computational Physics
Array-representation integration factor method for high-dimensional systems
Journal of Computational Physics
Hi-index | 31.46 |
Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinates, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed.