An efficient time-domain perfectly matched layers formulation for elastodynamics on spherical domains

Sagiyama, K.; Govindjee, S.; Persson, P. -O.

doi:10.1002/nme.4740

An efficient time-domain perfectly matched layers formulation for elastodynamics on spherical domains

Journal Article · Tue Jul 15 00:00:00 EDT 2014 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.4740· OSTI ID:1523916

Sagiyama, K. ^[1]; Govindjee, S. ^[1]; Persson, P. -O. ^[1]

Univ. of California, Berkeley, CA (United States). Dept. of Civil Engineering

Many practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain. One widely used approach for truncating the infinite domain is the so called method of perfectly matched layers (PMLs). Most existing PML formulations are developed for finite difference methods based on the first-order velocity-stress form of the elasticity equations, and they are not straight-forward to implement using standard finite element methods (FEMs) on unstructured meshes. Some of the problems with these formulations include the application of boundary conditions in half-space problems and in the treatment of edges and/or corners for time-domain problems. Several PML formulations, which do work with FEMs have been proposed, although most of them still have some of these problems and/or they require a large number of auxiliary nodal history/memory variables. Here in this work, we develop a new PML formulation for time-domain elastodynamics on a spherical domain, which reduces to a two-dimensional formulation under the assumption of axisymmetry. Our formulation is well-suited for implementation using FEMs, where it requires lower memory than existing formulations, and it allows for natural application of boundary conditions. We solve example problems on two-dimensional and three-dimensional domains using a high-order discontinuous Galerkin (DG) discretization on unstructured meshes and explicit time-stepping. We also study an approach for stabilization of the discrete equations, and we show several practical applications for quality factor predictions of micromechanical resonators along with verifying the accuracy and versatility of our formulation.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1523916

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 6 Vol. 100; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Discontinuous Galerkin
PML
elastodynamics
perfectly matched layer
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An efficient time-domain perfectly matched layers formulation for elastodynamics on spherical domains

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