Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After possible semi-discretization space, class under consideration is modeled by system ordinary differential equations where right-hand side summation component functions, each corresponding to given set processes. The partitioned-exponential methods proposed herein evolve via an integrator, information between partitions exchanged coupling terms. traditional constructing methods, based on variation-of-constants formula, not directly applicable systems. Rather, our developing families general-structure additive formulation schemes. Two method formulations considered, one linear-nonlinear splitting right hand another approximate Jacobians. paper classical (non-stiff) order conditions theory schemes particular T-trees B-series theory. Several practical third constructed that extend Rosenbrock-type EPIRK integrators. implementation optimizations specific application these reaction-diffusion systems also discussed. Numerical experiments reveal can perform better than unpartitioned some