Local Multiple Traces Formulation for Transmission Problems in Linear Elasticity
Abstract
We investigate the use of the local Multiple Trace Formulation (MTF) in solving time-harmonic elastic wave transmission problems. Originally devised for heterogeneous acoustic media, MTF recasts the boundary value problem as a well-posed system of first-kind boundary integral equations, naturally amenable to parallelization and preconditioning. The formulation takes independent displacement and traction unknowns per subdomain, enforces Calderón identities locally, and imposes transmission conditions weakly across interfaces. We restrict our analysis to single homogeneous scatterers, representing a foundational step toward the application of MTF techniques in heterogeneous elasticity transmission problems. For the sake of clarity, all derivations in the one-dimensional setting are carried out explicitly, with illustrative examples provided in two dimensions. We analyze the effects of frequency and material contrast on the convergence of the GMRES iterative solver. Finally, we present preliminary results for an elastic Calderón preconditioner and discuss its potential to further accelerate iterative solvers.
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BibTeX
@article{chaillat2026local,
title = {{Local Multiple Traces Formulation for Transmission Problems in Linear Elasticity}},
author = {Stéphanie Chaillat and Marion Darbas and Paul Escapil-Inchauspé and Carlos Jerez-Hanckes},
journal = {Computers \& Mathematics with Applications},
year = {2026},
month = aug,
doi = {10.1016/j.camwa.2026.08.005},
url = {https://hal.science/hal-05357974v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Local Multiple Traces Formulation for Transmission Problems in Linear Elasticity
AU - Stéphanie Chaillat
AU - Marion Darbas
AU - Paul Escapil-Inchauspé
AU - Carlos Jerez-Hanckes
PY - 2026
DA - 2026/08/13
JO - Computers & Mathematics with Applications
DO - 10.1016/j.camwa.2026.08.005
UR - https://hal.science/hal-05357974v2
AB - We investigate the use of the local Multiple Trace Formulation (MTF) in solving time-harmonic elastic wave transmission problems. Originally devised for heterogeneous acoustic media, MTF recasts the boundary value problem as a well-posed system of first-kind boundary integral equations, naturally amenable to parallelization and preconditioning. The formulation takes independent displacement and traction unknowns per subdomain, enforces Calderón identities locally, and imposes transmission conditions weakly across interfaces. We restrict our analysis to single homogeneous scatterers, representing a foundational step toward the application of MTF techniques in heterogeneous elasticity transmission problems. For the sake of clarity, all derivations in the one-dimensional setting are carried out explicitly, with illustrative examples provided in two dimensions. We analyze the effects of frequency and material contrast on the convergence of the GMRES iterative solver. Finally, we present preliminary results for an elastic Calderón preconditioner and discuss its potential to further accelerate iterative solvers.
SN - 0898-1221
ER -