Why Error Correction Methods Realize Fast Computations

In this paper, deflation method, A-phi method, explicit and implicit error correction (EC) methods and time-periodic explicit error correction (TP-EEC) method are shown to be based on the same mathematical principle that the slowly converging errors are effectively eliminated through the EC process while the fast converging errors are reduced by iterative linear solvers. The properties of the TP-EEC are discussed in detail and the EC is shown to work as an error filter. The numerical experiments show that the error reduction in the time-periodic eddy current problem is in good agreement with those predicted by the present theory.