Extrapolation methods to compute hypersingular integral in boundary element methods

Jin, Li; Zhang, Xiaoping; Yu, Dehao

doi:10.1007/s11425-013-4593-1

Cited by 12 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where T (0) = a 0 and a j are constant independent of h. In the paper of [14], based on the definition of (4), a generalized trapezoidal rule for numerical computation of hypersingualr integral on interval is given. Then in the recent paper [15], the composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/ sin 2 (x−s) is discussed, and the main part of the asymptotic expansion of error function is obtained. In the reference [18], based on the asymptotic expansion, two extrapolation algorithms are presented for hypersingular integral defined on the interval and their convergence rates are proved, which are the same as the Euler-Maclaurin expansions of classical middle rectangle rule approximations.…”

Section: Introductionmentioning

confidence: 99%

Extrapolation methods for solving hypersingular integral equation of the first kind

2023

Preprint

Self Cite

View full text Add to dashboard Cite

The hypersingular integral equation has been studied widely in boundary element methods, especially in natural boundary element methods. The asymptotic expansion of error function of composite rectangle rule for the computation of Hadamard finite-part integrals with the hypersingular kernel 1/ sin 2 (x − s) is obtained. Extrapolation algorithm is constructed. In order to solve the hypersin-gular integral equation, the superconvergence point is taken as the collocation point, then the extrapolation algorithm is presented and the convergence rate of extrapolation algorithm for hypersingular integral equation is presented. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms. dt − 4f (s) cot ϵ 2 } (3) The equivalent of (2) and (3) can be similarly obtained in [32]. The composite middle rectangle rule is still valid when the singular point is located at the middle rectangle of each subintervals, in the words, the superconvergence phenomenon of the middle rectangle rule appears at this moment, we obtain the error expansion of the error functional. Moreover, we apply the asymptotic expansion results to construct a algorithm scheme for solving hypersingular integral equations. MSC Classification: 65D05 65M70.

show abstract

Section: Introductionmentioning

confidence: 99%

Extrapolation methods for solving hypersingular integral equation of the first kind

2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [31,32], Lyness studied the Euler-Maclaurin expansion technique for the evaluation of two-dimensional Cauchy principal integrals. e extrapolation methods based on Hadamard finite-part integral definition with the trapezoidal rule for the computation of hypersingular integrals on interval and in circle in boundary element methods are presented in [33,34], respectively. e extrapolation methods based on definition of subtraction of singularity are presented in [35,36], respectively.…”

Section: Introductionmentioning

confidence: 99%

Extrapolation Algorithm for Computing Multiple Cauchy Principal Value Integrals

Cheng

2020

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

In this paper, the computation of multiple (including two dimensional and three dimensional) Cauchy principal integral with generalized composite rectangle rule was discussed, with the density function approximated by the middle rectangle rule, while the singular kernel was analytically calculated. Based on the expansion of the density function, the asymptotic expansion formulae of error functional are obtained. A series is constructed to approach the singular point, then the extrapolation algorithm is presented, and the convergence rate is proved. At last, some numerical examples are presented to validate the theoretical analysis.

show abstract

“…The extrapolation method for the computation of Hadamard finite-part integrals on the interval and in a circle is studied in [14] and [15] which focus on the asymptotic expansion of error function. Based on the asymptotic expansion of the error functional, algorithm with theoretical analysis of the generalized extrapolation is given.…”

Section: Introductionmentioning

confidence: 99%

The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle

Li¹,

Gong²,

Liu³

2016

AJCM

Self Cite

View full text Add to dashboard Cite

The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel x s cot 2 − is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.

show abstract

Extrapolation methods to compute hypersingular integral in boundary element methods

Cited by 12 publications

References 18 publications

Extrapolation methods for solving hypersingular integral equation of the first kind

Extrapolation methods for solving hypersingular integral equation of the first kind

Extrapolation Algorithm for Computing Multiple Cauchy Principal Value Integrals

The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle

Contact Info

Product

Resources

About