Summary Multiphysics simulations are used to solve coupled physics problems found in a wide variety of applications in natural and engineering systems. Combining models of different physical processes into one computational tool is the essence of multiphysics simulation. A general and widely used coupling approach is to combine several ‘single‐physics’ numerical solvers, each already being well developed, mature/sophisticated into an iteration‐based computational package. This approach iterates over the constituent solvers at every time step, to obtain globally converged solutions. During the simulation, each single‐physics component is solved repeatedly until the feedback has been adequately resolved. However, the component problem solution only needs to be as precise as the feedback that it receives from the other component. Thus, computational effort expended to exceed such precision is wasted. This issue is usually called over‐solving. This paper proposes and discusses several methods that circumvent over‐solving. The residual balance, relaxed relative tolerance, alternating nonlinear, and solution interruption methods are described, and their performance is compared with Picard iteration. A steady state problem with coupling along an interface and a transient problem with two fields coupled throughout the spatial domain are solved as examples. These problems demonstrate that the savings associated with eliminating over‐solving can reach at least 30% without any loss in accuracy. Copyright © 2017 John Wiley & Sons, Ltd.

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