Physics-Based Multi-Time Stepping Algorithm for Three-Dimensional Quasi-Static Electroporoelasticity Equations

Abstract

Electroporoelasticity equations comprise of Maxwell’s equations and Biot’s equations, playing an important role in geophysical areas such as oil-gas exploration and earthquake early warning. The development of electromagnetic waves and elastic waves presents distinct time scales due to the multi-physics nature. In this paper, we propose a multi-time stepping numerical algorithm to approximate electroporoelasticity equations, in which we use a smaller time step to compute Maxwell’s equations and a larger time step to calculate Biot’s equations. We prove the stability of this algorithm and derive its error estimates. Numerical experiments are conducted to demonstrate the theoretical analysis.