Boundary integral equation methods for Lipschitz domains in linear elasticity
A review of stable boundary integral equation methods for solving the Navier equation with either Dirichlet or Neumann boundary conditions in the exterior of a Lipschitz domain is presented. The conventional combined-field integral equation (CFIE) formulations, that are used to avoid spurious resona...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-05-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.317/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206268424355840 |
|---|---|
| author | Le Louër, Frédérique |
| author_facet | Le Louër, Frédérique |
| author_sort | Le Louër, Frédérique |
| collection | DOAJ |
| description | A review of stable boundary integral equation methods for solving the Navier equation with either Dirichlet or Neumann boundary conditions in the exterior of a Lipschitz domain is presented. The conventional combined-field integral equation (CFIE) formulations, that are used to avoid spurious resonances, do not give rise to a coercive variational formulation for nonsmooth geometries anymore. To circumvent this issue, either the single layer or the double layer potential operator is composed with a compact or a Steklov–Poincaré type operator. The later can be constructed from the well-know elliptic boundary integral operators associated to the Laplace equation and Gårding’s inequalities are satisfied. Some Neumann interior eigenvalue computations for the unit square and cube are presented for forthcoming numerical investigations. |
| format | Article |
| id | doaj-art-d7ee66a199bf4e348864c4c26304132d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d7ee66a199bf4e348864c4c26304132d2025-02-07T11:20:52ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G445346710.5802/crmath.31710.5802/crmath.317Boundary integral equation methods for Lipschitz domains in linear elasticityLe Louër, Frédérique0Alliance Sorbonne Université, Université de Technologie de Compiègne, LMAC EA2222 Laboratoire de Mathématiques Appliquées de Compiègne - CS 60319 - 60203 Compiègne cedex, FranceA review of stable boundary integral equation methods for solving the Navier equation with either Dirichlet or Neumann boundary conditions in the exterior of a Lipschitz domain is presented. The conventional combined-field integral equation (CFIE) formulations, that are used to avoid spurious resonances, do not give rise to a coercive variational formulation for nonsmooth geometries anymore. To circumvent this issue, either the single layer or the double layer potential operator is composed with a compact or a Steklov–Poincaré type operator. The later can be constructed from the well-know elliptic boundary integral operators associated to the Laplace equation and Gårding’s inequalities are satisfied. Some Neumann interior eigenvalue computations for the unit square and cube are presented for forthcoming numerical investigations.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.317/Boundary integral equationLinear elasticityLipschitz domainsGårding’s inequalityEigenvalues |
| spellingShingle | Le Louër, Frédérique Boundary integral equation methods for Lipschitz domains in linear elasticity Comptes Rendus. Mathématique Boundary integral equation Linear elasticity Lipschitz domains Gårding’s inequality Eigenvalues |
| title | Boundary integral equation methods for Lipschitz domains in linear elasticity |
| title_full | Boundary integral equation methods for Lipschitz domains in linear elasticity |
| title_fullStr | Boundary integral equation methods for Lipschitz domains in linear elasticity |
| title_full_unstemmed | Boundary integral equation methods for Lipschitz domains in linear elasticity |
| title_short | Boundary integral equation methods for Lipschitz domains in linear elasticity |
| title_sort | boundary integral equation methods for lipschitz domains in linear elasticity |
| topic | Boundary integral equation Linear elasticity Lipschitz domains Gårding’s inequality Eigenvalues |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.317/ |
| work_keys_str_mv | AT lelouerfrederique boundaryintegralequationmethodsforlipschitzdomainsinlinearelasticity |