Weighted integral solvers for elastic scattering by open arcs in two dimensions
Abstract
We present new methodologies for the numerical solution of problems of elastic scattering by open arcs in two dimensions. The algorithms utilize weighted versions of the classical elastic integral operators associated with Dirichlet and Neumann boundary conditions, where the integral weight accounts for (and regularizes) the singularity of the integral‐equation solutions at the open‐arc endpoints. Crucially, the method also incorporates a certain “open‐arc elastic Calderón relation” introduced in this article, whose validity is demonstrated on the basis of numerical experiments, but whose rigorous mathematical proof is left for future work. (In fact, the aforementioned open‐arc elastic Calderón relation generalizes a corresponding elastic Calderón relation for closed surfaces, which is also introduced in this article, and for which a rigorous proof is included.) Using the open‐surface Calderón relation in conjunction with spectrally accurate quadrature rules and the Krylov‐subspace linear algebra solver GMRES, the proposed overall open‐arc elastic solver produces results of high accuracy in small number of iterations, for both low and high frequencies. A variety of numerical examples in this article demonstrate the accuracy and efficiency of the proposed methodology.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 25, 2021
- Source ID
- 10.1002/nme.6639
Entities
People
- Liwei Xu
- Oscar Bruno
- Tao Yin
Organizations
- Air Force Office of Scientific Research
- California Institute of Technology
- Defense Advanced Research Projects Agency
- National Science Foundation
- Office of Naval Research
- University of Electronic Science and Technology of China