RT info:eu-repo/semantics/article
T1 A unified formulation of splitting-based implicit time integration schemes
A1 Hernández Abreu, Domingo
A1 González Pinto, Severiano
A1 Pérez-Rodríguez, María S.
A1 Sarshar, Arash
A1 Roberts, Steven
A1 Sandu, Adrian
A2 Análisis Matemático
A2 Grupo de investigación ULL:
"Métodos numéricos en ecuaciones diferenciales"
K1 General-structure additive
K1 Runge–Kutta methods
K1 Alternating direction implicit
K1 Implicit-explicit
K1 Implicit-implicit methods
AB Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. This work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.
YR 2022
FD 2022
LK http://riull.ull.es/xmlui/handle/915/39016
UL http://riull.ull.es/xmlui/handle/915/39016
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 18-dic-2024