Convergence Study of Variational Space‐Time Coupled Least‐Squares Frameworks in Simulation of Wave Propagation in Viscoelastic Medium

Abstract

There are many novel applications of space-time decoupled least squares and Galerkin formulations that simulate wave propagation through different types of media. Numerical simulation of stress wave propagation through viscoelastic medium is commonly carried out using the space-time decoupled Galerkin weak form in site response problem, etc. In a recent investigation into accuracy of this formulation in simulating elastic wave propagation, it was shown that the diffusive and dispersive errors are greatly reduced when space-time coupled least squares formulation is used instead in variational form. This paper investigates convergence characteristics of both formulations. To this end, two test cases, which are site response and impact models for viscoelastic medium, are employed, one dominated by dispersive and the other by diffusive numerical error. Convergence studies reveal that, compared to the commonly used space-time decoupled Galerkin and the coupled least squares formulation has much lower numerical errors, higher rates of convergence, and ability to take far larger time increments in the evolution process. In solving such models, coefficient matrices would require updating after each time step, a process that can be very costly. However large time steps allowed by cLs are expected to be a significant feature in reducing the overall computational cost.

A generalized time-domain constitutive finite element approach for viscoelastic materials

“…These approaches are noteworthy since, they enable some beneficial behavior in solving these problems, such as parallel computing [22]. Others handle time domain viscoelasticity, but are formulated for wave propagation [23]. Still others incorporate discontinuous Galerkin schemes, which allow for a range of numerical benefits particularly in regards to convergence rates [24].…”