A stable semi-implicit algorithm
This work provides a numerical stability solution for a known bottleneck in simulating systems with mixed singular spectra, relevant to computational physics and plasma modeling.
The authors developed a stable semi-implicit algorithm for evolution operators with mixed singular values (both greater and smaller than one), where neither explicit nor implicit methods alone ensure stability. The method was demonstrated on a two-field model of the tokamak scrape-off layer.
When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one values, neither explicit nor implicit methods insure stabilty. The problem is solved by using a splitting of the evolution operator and a semi-implicit scheme. The method is illustrated in the study of a two-field model of the tokamak scrape-off layer.