The Effect of Global Smoothness on the Accuracy of Treecodes  

作　　者：Henry A.Boateng Svetlana Tlupova 

机构地区：[1]Department of Mathematics,San Francisco State University,San Francisco,CA 94132,USA [2]Department of Mathematics,Farmingdale State College,SUNY,Farmingdale,NY 11735,USA

出　　处：《Communications in Computational Physics》2022年第10期1332-1360,共29页计算物理通讯（英文）

基　　金：partially supported by the National Science Foundation grant CHE-2016048 and start-up funds from San Francisco State University;partially supported by the National Science Foundation grant DMS-2012371;the Visiting Faculty Program of the U.S.Department of Energy,Office of Science,Office of Workforce Development for Teachers and Scientists(WDTS).

摘　　要：Treecode algorithms are widely used in evaluation of N-body pairwise interactions in O(N)or O(NlogN)operations.While they can provide high accuracy approximations,a criticism leveled at the methods is that they lack global smoothness.In 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 discontinuous.We 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 treecode.One 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 derivatives.When 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 

分 类 号：O17[理学—数学]