tost.II: A temporal operator-splitting template library in deal.II

Operator splitting (OS) is a widely used numerical method for solving differential equations by decomposing a problem into simpler sub-problems. OS methods enable consideration of different processes in a problem as separate temporal operators. These temporal operators can be integrated by specialized sub-integrators, often leading to improved computational feasibility or efficiency compared to classical monolithic approaches that treat all the processes as a single operator. This paper describes tost.II, a temporal operator-splitting template library built upon the deal.II finite element library. The tost.II library provides a flexible framework for implementing OS methods in deal.II, including those with real and complex coefficients. We demonstrate the functionality and ease of use of tost.II through three comprehensive examples that illustrate high-order convergence, the tradeoff in efficiency between order and desired accuracy, and the tradeoff in efficiency between the use of real versus complex arithmetic. Furthermore, because tost.II allows users to define any number of operators in any order and with any sub-integrator at any stage of the integration, we perform some less typical experiments with more than two operators and the use of inexpensive explicit sub-integrators for unstable sub-integrations.