Stability of explicit subcycling time integration with linear interpolation for first-order finite element semidiscretizations

An explicit subcycling time integration algorithm based on an element partition is presented for first-order finite element systems. This method uses linear interpolation to compute intermediate values at nodes in the subdomains integrated with the larger time steps. Stability of the algorithm for the two partition cases is analyzed by showing that the eigenvalues of the amplification matrix for the total integration cycle are not greater than one in absolute value. Using this stability criterion, critical time steps for the element subdomains are derived in terms of element eigenvalues. Several numerical examples are considered to compare the accuracy of the method with previously developed subcycling algorithms to numerically verify the stability analysis.

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