TY - JOUR
T1 - Determining kernels in linear viscoelasticity
AU - Kaltenbacher, Barbara
AU - Khristenko, Ustim
AU - Nikolić, Vanja
AU - Rajendran, Mabel Lizzy
AU - Wohlmuth, Barbara
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/9/1
Y1 - 2022/9/1
N2 - In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method.
AB - In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method.
KW - Inverse problem
KW - Viscoelasticity
KW - Weakly singular kernels
UR - http://www.scopus.com/inward/record.url?scp=85131224947&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2022.111331
DO - 10.1016/j.jcp.2022.111331
M3 - Article
AN - SCOPUS:85131224947
SN - 0021-9991
VL - 464
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 111331
ER -