A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces

Wu, Bowei; Martinsson, Per-Gunnar

doi:10.1137/22m1520372

A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces

Journal Article · 28 September 2023 · SIAM Journal on Numerical Analysis

DOI:https://doi.org/10.1137/22m1520372· OSTI ID:2422114

^[1]; ^[2]

Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712 USA.; OSTI
Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712 USA.

Not provided.

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0022251

OSTI ID:: 2422114

Journal Information:: SIAM Journal on Numerical Analysis, Journal Name: SIAM Journal on Numerical Analysis Journal Issue: 5 Vol. 61; ISSN 0036-1429

Publisher:: Society for Industrial and Applied Mathematics (SIAM)

Country of Publication:: United States

Language:: English

References (29)

Zur Theorie allgemeiner Zetafunktionen. II Epstein, Paul Mathematische Annalen, Vol. 63, Issue 2 https://doi.org/10.1007/BF01449900	journal	June 1906
On the Interaction of Electrons in Metals Wigner, E. Physical Review, Vol. 46, Issue 11 https://doi.org/10.1103/PhysRev.46.1002	journal	December 1934
Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme Wu, Bowei; Zhu, Hai; Barnett, Alex Journal of Computational Physics, Vol. 410 https://doi.org/10.1016/j.jcp.2020.109361	journal	June 2020
Euler–Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities Sidi, Avram Mathematics of Computation, Vol. 81, Issue 280 https://doi.org/10.1090/S0025-5718-2012-02597-X	journal	April 2012
The Curious History of Faa di Bruno's Formula Johnson, Warren P. The American Mathematical Monthly, Vol. 109, Issue 3 https://doi.org/10.2307/2695352	journal	March 2002
Arbitrarily high-order trapezoidal rules for functions with fractional singularities in two dimensions Jiang, Senbao; Li, Xiaofan Applied Mathematics and Computation, Vol. 429 https://doi.org/10.1016/j.amc.2022.127236	journal	September 2022
Evaluation of near-singular integrals with application to vortex sheet flow Nitsche, Monika Theoretical and Computational Fluid Dynamics, Vol. 35, Issue 5 https://doi.org/10.1007/s00162-021-00577-9	journal	July 2021
Corrected trapezoidal rules for a class of singular functions Marin, O.; Runborg, O.; Tornberg, A. -K. IMA Journal of Numerical Analysis, Vol. 34, Issue 4 https://doi.org/10.1093/imanum/drt046	journal	November 2013
Zur Theorie allgemeiner Zetafunctionen Epstein, Paul Mathematische Annalen, Vol. 56, Issue 4 https://doi.org/10.1007/BF01444309	journal	December 1903
Fast direct solvers for integral equations in complex three-dimensional domains Greengard, Leslie; Gueyffier, Denis; Martinsson, Per-Gunnar Acta Numerica, Vol. 18 https://doi.org/10.1017/S0962492906410011	journal	May 2009
Euler–Maclaurin Expansions for Integrals with Arbitrary Algebraic-Logarithmic Endpoint Singularities Sidi, Avram Constructive Approximation, Vol. 36, Issue 3 https://doi.org/10.1007/s00365-011-9140-0	journal	September 2011
Richardson Extrapolation on Some Recent Numerical Quadrature Formulas for Singular and Hypersingular Integrals and Its Study of Stability Sidi, Avram Journal of Scientific Computing, Vol. 60, Issue 1 https://doi.org/10.1007/s10915-013-9788-7	journal	October 2013
On lattice sums and Wigner limits Borwein, David; Borwein, Jonathan M.; Straub, Armin Journal of Mathematical Analysis and Applications, Vol. 414, Issue 2 https://doi.org/10.1016/j.jmaa.2014.01.008	journal	June 2014
Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow Nitsche, Monika Advances in Computational Mathematics, Vol. 48, Issue 5 https://doi.org/10.1007/s10444-022-09973-z	journal	September 2022
High-order corrected trapezoidal quadrature rules for the coulomb potential in three dimensions Aguilar, J. C.; Chen, Yu Computers & Mathematics with Applications, Vol. 49, Issue 4 https://doi.org/10.1016/j.camwa.2004.01.018	journal	February 2005
High-order quadratures for the solution of scattering problems in two dimensions Duan, Ran; Rokhlin, Vladimir Journal of Computational Physics, Vol. 228, Issue 6 https://doi.org/10.1016/j.jcp.2008.11.033	journal	April 2009
Boundary Integral Equations Hsiao, George C.; Wendland, Wolfgang L. Applied Mathematical Sciences https://doi.org/10.1007/978-3-540-68545-6	book	January 2008
Shape optimization of Stokesian peristaltic pumps using boundary integral methods Bonnet, Marc; Liu, Ruowen; Veerapaneni, Shravan Advances in Computational Mathematics, Vol. 46, Issue 2 https://doi.org/10.1007/s10444-020-09761-7	journal	February 2020
Hybrid Gauss-Trapezoidal Quadrature Rules Alpert, Bradley K. SIAM Journal on Scientific Computing, Vol. 20, Issue 5 https://doi.org/10.1137/S1064827597325141	journal	January 1999
High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions Kapur, Sharad; Rokhlin, Vladimir SIAM Journal on Numerical Analysis, Vol. 34, Issue 4 https://doi.org/10.1137/S0036142995287847	journal	August 1997
A fast direct solver for two dimensional quasi-periodic multilayered media scattering problems Zhang, Yabin; Gillman, Adrianna BIT Numerical Mathematics, Vol. 61, Issue 1 https://doi.org/10.1007/s10543-020-00818-z	journal	July 2020
Compact Numerical Quadrature Formulas for Hypersingular Integrals and Integral Equations Sidi, Avram Journal of Scientific Computing, Vol. 54, Issue 1 https://doi.org/10.1007/s10915-012-9610-y	journal	June 2012
An Extension of the Euler‐Maclaurin Summation Formula to Functions with a Branch Singularity Navot, Israel Journal of Mathematics and Physics, Vol. 40, Issue 1-4 https://doi.org/10.1002/sapm1961401271	journal	April 1961
A Further Extension of the Euler‐Maclaurin Summation Formula Navot, Israel Journal of Mathematics and Physics, Vol. 41, Issue 1-4 https://doi.org/10.1002/sapm1962411155	journal	April 1962
A high-order accurate accelerated direct solver for acoustic scattering from surfaces Bremer, James; Gillman, Adrianna; Martinsson, Per-Gunnar BIT Numerical Mathematics, Vol. 55, Issue 2 https://doi.org/10.1007/s10543-014-0508-y	journal	July 2014
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators Wu, Bowei; Martinsson, Per-Gunnar Advances in Computational Mathematics, Vol. 47, Issue 3 https://doi.org/10.1007/s10444-021-09872-9	journal	May 2021
A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications Bruno, Oscar P.; Kunyansky, Leonid A. Journal of Computational Physics, Vol. 169, Issue 1 https://doi.org/10.1006/jcph.2001.6714	journal	May 2001
Corrected trapezoidal rules for boundary integral equations in three dimensions Wu, Bowei; Martinsson, Per-Gunnar Numerische Mathematik, Vol. 149, Issue 4 https://doi.org/10.1007/s00211-021-01244-1	journal	November 2021
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane Gopal, Abinand; Martinsson, Per-Gunnar Advances in Computational Mathematics, Vol. 48, Issue 4 https://doi.org/10.1007/s10444-022-09963-1	journal	June 2022

Similar Records

An overview of integration methods for hypersingular boundary integrals

Conference · 1990 · OSTI ID:6129096

Singular symmetries of integrable curves and surfaces

Journal Article · 1982 · J. Math. Phys. (N.Y.); (United States) · OSTI ID:5632453

A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory

Journal Article · 2008 · Computational Mechanics · OSTI ID:952512

Related Subjects

Mathematics

A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces

Citation Formats

References (29)

Similar Records

Related Subjects