Open Access
Issue |
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
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Page(s) | 793 - 831 | |
DOI | https://doi.org/10.1051/m2an/2023105 | |
Published online | 24 April 2024 |
- M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. Vol. 55 of National Bureau of Standards Applied Mathematics Series. US Government Printing Office (1964). [Google Scholar]
- F. Alouges and M. Aussal, FEM and BEM simulations with the Gypsilab framework. SMAI J. Comput. Math. 4 (2018) 297–318. [CrossRef] [MathSciNet] [Google Scholar]
- F. Alouges and M. Averseng, New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results. Numer. Math. 148 (2021) 255–292. [Google Scholar]
- F. Alouges, S. Borel and D.P. Levadoux, A stable well-conditioned integral equation for electromagnetism scattering. J. Comput. Appl. Math. 204 (2007) 440–451. [CrossRef] [MathSciNet] [Google Scholar]
- X. Antoine and M. Darbas, Generalized combined field integral equations for the iterative solution of the three-dimensional helmholtz equation. ESAIM: Math. Modell. Numer. Anal. 41 (2007) 147–167. [CrossRef] [EDP Sciences] [Google Scholar]
- M. Averseng, Pseudo-differential analysis of the Helmholtz layer potentials on open curves. Preprint arXiv:1905.13604 (2019). [Google Scholar]
- M. Averseng, Square-root preconditioners for the disk screen in Matlab. https://github.com/MartinAverseng/SqPrecondDiskScreen (2022). DOI: 10.5281/zenodo.7991556. [Google Scholar]
- M. Averseng, Stability of a weighted L2 projection in weighted Sobolev spaces. C. R. Math. 361 (2023) 757–766. [CrossRef] [Google Scholar]
- R.E. Bank and T. Dupont, An optimal order process for solving finite element equations. Math. Comput. 36 (1981) 35–51. [Google Scholar]
- O.P. Bruno and S.K. Lintner, Second-kind integral solvers for TE and TM problems of diffraction by open arcs. Radio Sci. 47 (2012) 1–13. [Google Scholar]
- S.H. Christiansen and J.-C. Nédélec, Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l’acoustique. Comptes Rendus de l’Académie des Sciences-Series I-Mathematics 330 (2000) 617–622. [Google Scholar]
- D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. SIAM (2013). [CrossRef] [Google Scholar]
- M. Costabel, M. Dauge and R. Duduchava, Asymptotics Without Logarithmic Terms for Crack Problems. Taylor & Francis (2003). [Google Scholar]
- C. Flammer, Spheroidal Wave Functions. Courier Corporation (2014). [Google Scholar]
- J. Galkowski, E.H. Muller and E.A. Spence, Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem. Numer. Math. 142 (2019) 329–357. [Google Scholar]
- M.J. Gander, I.G. Graham and E.A. Spence, Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Numer. Math. 131 (2015) 567–614. [Google Scholar]
- Z. Gimbutas and L. Greengard, Computational software: simple fmm libraries for electrostatics, slow viscous flow, and frequency-domain wave propagation. Commun. Comput. Phys. 18 (2015) 516–528. [CrossRef] [MathSciNet] [Google Scholar]
- H. Gimperlein, J. Stocek and C. Urzúa-Torres, Optimal operator preconditioning for pseudodifferential boundary problems. Numer. Math. 148 (2021) 1–41. [Google Scholar]
- I.G. Graham and W. McLean, Anisotropic mesh refinement: the conditioning of Galerkin boundary element matrices and simple preconditioners. SIAM J. Numer. Anal. 44 (2006) 1487–1513. [CrossRef] [MathSciNet] [Google Scholar]
- L. Greengard and V. Rokhlin, A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325–348. [Google Scholar]
- W. Hackbusch, A sparse matrix arithmetic based on H-matrices. Part I: introduction to H-matrices. Computing 62 (1999) 89–108. [CrossRef] [MathSciNet] [Google Scholar]
- N. Hale, N.J. Higham and L.N. Trefethen, Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46 (2008) 2505–2523. [CrossRef] [MathSciNet] [Google Scholar]
- R. Hiptmair, Operator preconditioning. Comput. Math. Appl. 52 (2006) 699–706. [Google Scholar]
- R. Hiptmair, C. Jerez-Hanckes and C. Urzúa-Torres, Mesh-independent operator preconditioning for boundary elements on open curves. SIAM J. Numer. Anal. 52 (2014) 2295–2314. [CrossRef] [MathSciNet] [Google Scholar]
- R. Hiptmair, C. Jerez-Hanckes and C. Urzúa-Torres, Closed-form inverses of the weakly singular and hypersingular operators on disks. Integral Equ.Oper. Theory 90 (2018) 1–14. [CrossRef] [Google Scholar]
- R. Hiptmair, C. Jerez-Hanckes and C. Urzúa-Torres, Optimal operator preconditioning for Galerkin boundary element methods on 3-dimensional screens. SIAM J. Numer. Anal. 58 (2020) 834–857. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holm, M. Maischak and E.P. Stephan, The hp-version of the boundary element method for Helmholtz screen problems. Computing 57 (1996) 105–134. [CrossRef] [MathSciNet] [Google Scholar]
- R. Hurri, The weighted Poincaré inequalities. Math. Scand. 67 (1990) 145–160. [CrossRef] [MathSciNet] [Google Scholar]
- D. Kershaw, Some extensions of W. Gautschi’s inequalities for the gamma function. Math. Comp. 41 (1983) 607–611. [MathSciNet] [Google Scholar]
- Y.Y. Lu, A Padé approximation method for square roots of symmetric positive definite matrices. SIAM J. Matrix Anal. App. 19 (1998) 833–845. [CrossRef] [Google Scholar]
- W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
- F.A. Milinazzo, C.A. Zala and G.H. Brooke, Rational square-root approximations for parabolic equation algorithms. J. Acoust. Soc. Amer. 101 (1997) 760–766. [CrossRef] [Google Scholar]
- N.M. Nachtigal, S.C. Reddy and L.N. Trefethen, How fast are nonsymmetric matrix iterations? SIAM J. Matrix Anal. App. 13 (1992) 778–795. [CrossRef] [Google Scholar]
- J.-C. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems. Vol. 144 of Applied Mathematical Sciences. Springer-Verlag, New York (2001). [Google Scholar]
- C. Pechstein and R. Scheichl, Weighted Poincaré inequalities. IMA J. Numer. Anal. 33 (2013) 652–686. [CrossRef] [MathSciNet] [Google Scholar]
- P. Ramaciotti, Theoretical and numerical aspects of wave propagation phenomena in complex domains and applications to remote sensing. Ph.D. thesis, Université Paris-Saclay (ComUE) (2016). [Google Scholar]
- P. Ramaciotti and J.-C. Nédélec, About some boundary integral operators on the unit disk related to the Laplace equation. SIAM J. Numer. Anal. 55 (2017) 1892–1914. [CrossRef] [MathSciNet] [Google Scholar]
- V. Rokhlin, Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Appl. Comput. Harmonic Anal. 1 (1993) 82–93. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856–869. [CrossRef] [Google Scholar]
- S.A. Sauter and C. Schwab, Boundary Element Methods. Springer Series in Computational Mathematics. Springer-Verlag, Berlin (2011). [CrossRef] [Google Scholar]
- O. Steinbach and W.L. Wendland, The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9 (1998) 191–216. [CrossRef] [MathSciNet] [Google Scholar]
- E.P. Stephan, Boundary integral equations for screen problems in R3. Integral Equ. Oper. Theory 10 (1987) 236–257. [CrossRef] [Google Scholar]
- E.P. Stephan, The hp boundary element method for solving 2-and 3-dimensional problems. Comput. Methods Appl. Mech. Eng. 133 (1996) 183–208. [CrossRef] [Google Scholar]
- A. Veeser, Approximating gradients with continuous piecewise polynomial functions. Found. Comput. Math. 16 (2016) 723–750. [Google Scholar]
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