论文信息 - Numerical integration of 2‐D integrals based on local bivariate C1 quasi‐interpolating splines

Numerical integration of 2‐D integrals based on local bivariate C1 quasi‐interpolating splines

In this paper cubature formulas based on bivariate C1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.

Catterina Dagnino | Paola Lamberti

[1] Giovanni Monegato,et al. Numerical evaluation of hypersingular integrals , 1994 .

[2] G. Evans. Practical Numerical Integration , 1993 .

[3] F. Rizzo,et al. A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations , 1992 .

[4] Giovanni Monegato,et al. The numerical evaluation of a 2-D Cauchy principal value integral arising in boundary integral equation methods , 1994 .

[5] P. Theocaris,et al. On the numerical evaluation of two‐dimensional principal value integrals , 1980 .

[6] Cui Jin-Tai,et al. ON A BIVARIATE B-SPLINE BASIS , 1984 .

[7] C. Dagnino,et al. Numerical evaluation of Cauchy principal value integrals based on local spline approximation operators , 1996 .

[8] P. Zwart. Multivariate Splines with Nondegenerate Partitions , 1973 .

[9] P. Rabinowitz. Numerical integration based on approximating splines , 1990 .

[10] Ren-Hong Wang,et al. Multivariate B-splines on triangulated rectangles☆ , 1983 .

[11] B. Irons,et al. Over-relaxation and subspace iteration , 1979 .

[12] Ayse Alaylioglu,et al. Product integration of logarithmic singular integrands based on cubic splines , 1984 .

[13] Catterina Dagnino,et al. Product integration of singular integrands using quasi-interpolatory splines , 1997 .

[14] Massimo Guiggiani,et al. A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method , 1990 .