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The Effect of Global Smoothness on the Accuracy of Treecodes

Communications in Computational Physics 2022年第10期32卷 1332-1360页

作者： Henry A.Boateng svetlana tlupova Department of Mathematics San Francisco State UniversitySan FranciscoCA 94132USA Department of Mathematics Farmingdale State CollegeSUNYFarmingdaleNY 11735USA

Treecode algorithms are widely used in evaluation of N-body pairwise interactions in O(N)or O(NlogN)*** they can provide high accuracy approximations,a criticism leveled at the methods is that they lack global *** this work,we study the effect of smoothness on the accuracy of treecodes by comparing three tricubic interpolation based treecodes with differing smoothness properties:a global C^(1) continuous tricubic,and two new tricubic interpolants,one that is globally C^(0) continuous and one that is *** present numerical results which show that higher smoothness leads to higher accuracy for properties dependent on the derivatives of the kernel,nevertheless the global C^(0) continuous and discontinuous treecodes are competitive with the C^(1) continuous *** advantage of the discontinuous treecode over the C^(1) continuous is that,in addition to function evaluations,the discontinuous treecode only requires evaluations of the first derivatives of the kernel while the C^(1) continuous treecode requires evaluations up to third order *** the first derivatives are computed using finite differences,the discontinuous version can be viewed as kernel independent and of utility for a wider array of kernels with minimal effort.

关键词： Fast summation treecode tricubic interpolation

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Nearly Singular Integrals in 3D Stokes Flow

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Communications in Computational Physics 2013年第10期14卷 1207-1227页

作者： svetlana tlupova J.Thomas Beale Department of Mathematics University of MichiganAnn ArborMI 48109-1043USA Department of Mathematics Duke UniversityDurhamNC 27708-0320USA

A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the *** flowquantities arewritten as boundary integrals using the free-spaceGreen’s *** evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate *** order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic *** tests demonstrate the uniform convergence rates of the method.

关键词： Stokes equations boundary integral equation method nearly singular integrals

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