Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 9 min ago
PreprintCC BY-NC-ND 4.0arXiv

CQ-collocation BEMs for exterior wave propagation problems: the 3D Neumann case

  • Davide Collato
  • Silvia Falletta
  • Giovanni Monegato
  • Letizia Scuderi
Open at sourcePDFDOICite

Abstract

In this paper, we consider three-dimensional exterior wave propagation problems with non-homogeneous Neumann boundary conditions. We reformulate the problem as a space-time boundary integral equation involving a hypersingular operator. To solve the resulting formulation, we combine Lubich's convolution quadrature with a shifted collocation boundary element discretization and investigate numerically the efficiency, stability, and convergence of the resulting numerical scheme. Numerical tests show that the proposed approach achieves an accuracy comparable to that of Lubich's convolution quadrature combined with a Galerkin boundary element method, and provide numerical evidence of the unconditional stability of the collocation scheme.

Related

  1. Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth
    Michael Bildhauer Martin Fuchs
    arXivPreprintCC0Full textAnalysis & PDEsarXiv
  2. Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions
    Somnath Giri, Muslim Malik, Rishikesh Yadav
    arXivPreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingComputational physicsarXiv
  3. Advancements in Spectral Collocation Methods for High-Order Eigenvalue Problems
    Sameh Gana
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Well-Conditioned Birkhoff-Collocation Methods for Elliptic-type Problems in Multiple Dimensions
    Shunchang Li, Zixuan Gao, Yujian Jiao +1
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  5. A Shifted Balanced Polynomial Collocation Framework for Variable-Coefficient Multi-Term Time-Fractional Convection–Diffusion–Reaction Problems
    Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Naher Mohammed A. Alsafri +3
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref

Cite

BibTeXRIS
BibTeX
@misc{collato2026cqcollocation,
  title = {{CQ-collocation BEMs for exterior wave propagation problems: the 3D Neumann case}},
  author = {Davide Collato and Silvia Falletta and Giovanni Monegato and Letizia Scuderi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05226},
  eprint = {2611.05226},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05226},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - CQ-collocation BEMs for exterior wave propagation problems: the 3D Neumann case
AU  - Davide Collato
AU  - Silvia Falletta
AU  - Giovanni Monegato
AU  - Letizia Scuderi
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05226
UR  - https://arxiv.org/abs/2611.05226
AB  - In this paper, we consider three-dimensional exterior wave propagation problems with non-homogeneous Neumann boundary conditions. We reformulate the problem as a space-time boundary integral equation involving a hypersingular operator. To solve the resulting formulation, we combine Lubich's convolution quadrature with a shifted collocation boundary element discretization and investigate numerically the efficiency, stability, and convergence of the resulting numerical scheme. Numerical tests show that the proposed approach achieves an accuracy comparable to that of Lubich's convolution quadrature combined with a Galerkin boundary element method, and provide numerical evidence of the unconditional stability of the collocation scheme.
ER  -