Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators
نویسندگان
چکیده
A high-order accurate quadrature rule for the discretization of boundary integral equations (BIEs) on closed smooth contours in plane is introduced. This can be viewed as a hybrid spectral Kress (Math. Comput. Model. 15(3-5), 229–243 1991) and locally corrected trapezoidal Kapur Rokhlin (SIAM J. Numer. Anal. 34(4), 1331–1356, 1997). The new technique combines strengths both methods, attains convergence, numerical stability, ease implementation, compatibility with “fast” algorithms (such Fast Multipole Method or Direct Solvers). Important connections between punctured Riemann zeta function are introduced, which enable complete convergence analysis lead to remarkably simple procedures constructing corrections. paper reports detailed comparison method methods Kress, Rokhlin, Alpert Sci. 20(5), 1551–1584, 1999).
منابع مشابه
a new approach to credibility premium for zero-inflated poisson models for panel data
هدف اصلی از این تحقیق به دست آوردن و مقایسه حق بیمه باورمندی در مدل های شمارشی گزارش نشده برای داده های طولی می باشد. در این تحقیق حق بیمه های پبش گویی بر اساس توابع ضرر مربع خطا و نمایی محاسبه شده و با هم مقایسه می شود. تمایل به گرفتن پاداش و جایزه یکی از دلایل مهم برای گزارش ندادن تصادفات می باشد و افراد برای استفاده از تخفیف اغلب از گزارش تصادفات با هزینه پائین خودداری می کنند، در این تحقیق ...
15 صفحه اولLocally Corrected Multidimensional Quadrature Rules for Singular Functions
Accurate numericalintegrationof singularfunctions usually requireseither adaptivity or product integration. Both interfere with fast summation techniques and thus hamper large-scale computations. This paper presents a method for computing highly accurate quadrature formulas for singular functions which combine well with fast summation methods. Given the singularity and the N nodes, we rst const...
متن کاملHybrid Gauss-Trapezoidal Quadrature Rules
A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily high-order convergence. The quadratures result from alterations to the trapezoidal rule, in which a small number of nodes and weights at the ends of the integration interval are repla...
متن کاملEfficient quadrature rules for a class of cordial Volterra integral equations: A comparative study
A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations. The equations of this class appear in heat conduction problems with mixed boundary conditions. The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes. A comparative stud...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2021
ISSN: ['1019-7168', '1572-9044']
DOI: https://doi.org/10.1007/s10444-021-09872-9