Stability analysis of space-time finite integration schemes

Abstract

Purpose

The purpose of this paper is to examine the numerical stability of a space-time finite integration (FI) method. A symmetric correction is proposed to give an accurate constitutive relation at the subgrid connections.

Design/methodology/approach

A scheme for the numerical stability analysis of the space-time FI method is presented, where the growth rate of instability is evaluated by a numerical eigenvalue analysis formulated from an explicit time-marching scheme.

Findings

The 3D and 4D subgrid schemes using the space-time FI method are conditionally stable, where a symmetric correction does not induce numerical instability. The staircase-type 4D space-time subgrid allows a larger time-step than the straight-type subgrid.

Originality/value

The numerical stability of space-time FI method is proven by an eigenvalue analysis, which provides 3D and 4D stable subgrid schemes.

Citation

Matsuo, T., Kawahara, J., Shimoi, T. and Mifune, T. (2015), "Stability analysis of space-time finite integration schemes", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 5, pp. 1609-1622. https://doi.org/10.1108/COMPEL-02-2015-0074