TY - JOUR

T1 - Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

AU - Helsing, Johan

AU - Jiang, Shidong

N1 - Funding Information:
J. Helsing was supported by the Swedish Research Council under contract 2015-03780 . S. Jiang was supported in part by the United States National Science Foundation under grant DMS-1720405 . The authors would like to thank Anders Karlsson at Lund University, Alex Barnett and Leslie Greengard at the Flatiron Institute for helpful discussions.
Funding Information:
J. Helsing was supported by the Swedish Research Council under contract 2015-03780. S. Jiang was supported in part by the United States National Science Foundation under grant DMS-1720405. The authors would like to thank Anders Karlsson at Lund University, Alex Barnett and Leslie Greengard at the Flatiron Institute for helpful discussions.
Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as 1/|r|α with α close to 1, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

AB - A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as 1/|r|α with α close to 1, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

KW - Integral equation method

KW - Linearized BGKW equation

KW - Non-smooth domain

KW - RCIP method

KW - Singular right-hand side

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U2 - 10.1016/j.jcp.2021.110714

DO - 10.1016/j.jcp.2021.110714

M3 - Article

AN - SCOPUS:85115974859

SN - 0021-9991

VL - 448

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 110714

ER -