# Alternating Directions Implicit Integration in a General Linear Method Framework

@article{Sarshar2021AlternatingDI, title={Alternating Directions Implicit Integration in a General Linear Method Framework}, author={Arash Sarshar and Adrian Sandu}, journal={J. Comput. Appl. Math.}, year={2021}, volume={387}, pages={112619} }

## Figures from this paper

## 4 Citations

A unified formulation of splitting-based implicit time integration schemes

- Computer ScienceJ. Comput. Phys.
- 2022

Parallel implicit-explicit general linear methods

- Computer ScienceArXiv
- 2020

This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel based on diagonally implicit multistage integration methods (DIMSIMs) of types 3 and 4.

CSL-TR-19-12 April 22 , 2020

- 2020

This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel based on diagonally implicit multistage integration methods (DIMSIMs) of types 3 and 4.

CSL-TR-19-12 February 4 , 2020

- Computer Science
- 2020

This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel based on diagonally implicit multistage integration methods (DIMSIMs) of types 3 and 4.

## References

SHOWING 1-10 OF 36 REFERENCES

AMF-type W-methods for Parabolic Problems with Mixed Derivatives

- MathematicsSIAM J. Sci. Comput.
- 2018

A stability analysis, based on a scalar test equation that is relevant for the class of problems when periodic or homogeneous Dirichlet boundary conditions are considered, is presented and unconditional stability, independent of the number of space dimensions m, is proved for a variety of AMF-type W-methods.

Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations

- Mathematics
- 1996

Rosenbrock-type methods with Inexact AMF for the time integration of advection-diffusion-reaction PDEs

- Computer ScienceJ. Comput. Appl. Math.
- 2014

High Order Implicit-explicit General Linear Methods with Optimized Stability Regions

- Computer ScienceSIAM J. Sci. Comput.
- 2016

This work shows that IMEX general linear methods (GLMs) are competitive alternatives to classic IMEX schemes for large problems arising in practice, and are superior in terms of accuracy and efficiency.

Runge-Kutta methods for partial differential equations and fractional orders of convergence

- Mathematics
- 1992

We apply Runge-Kutta methods to linear partial differential equations of the form u¡(x, t) =5?(x, d)u(x, t)+f(x, t). Under appropriate assumptions on the eigenvalues of the operator 5C and the…

Construction of highly stable implicit-explicit general linear methods

- Mathematics
- 2015

This paper deals with the numerical solution of systems of differential equations with a stiff part and a non-stiff one, typically arising from the semi-discretization of certain partial differential…

A Class Of Implicit-Explicit Two-Step Runge-Kutta Methods

- MathematicsSIAM J. Numer. Anal.
- 2015

This work develops new implicit-explicit time integrators based on two-step Runge--Kutta methods that offers extreme flexibility in the construction of partitioned integrators since no coupling conditions are necessary.

Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods

- Computer ScienceJ. Comput. Appl. Math.
- 2015

A Second-order Diagonally-Implicit-Explicit Multi-Stage Integration Method

- Computer ScienceICCS
- 2012