Adaptive Integration and Singular Boundary Transformations
Adaptive Integration and Singular Boundary Transformations
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自适应积分和奇异边界变换
DOI：
10.1016/j.procs.2016.05.462
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
John Kapenga and Fola Olagbemi
中科院分区：
文献类型：
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作者：
Elise de Doncker;Fukuko Yuasa;Tadashi Ishikawa;John Kapenga and Fola Olagbemi
我们应用和比较结果的变换用于零化边界奇点的多元集成超矩形和单纯域。虽然经典的这些变换与产品梯形规则，我们使用自适应方法的PARINT软件包，根据规则的更高的多项式次数的子域上的集成。PARINT在MPI环境（消息传递接口）上分层，并部署高级并行计算技术，例如分布在节点网络上的进程之间的负载平衡。消息传递以非阻塞和异步的方式执行，并且允许计算和通信的重叠。使用长双精度与双精度的计算时间比较证实，扩展格式不会显著增加长双精度的时间。我们进一步应用所提出的方法所产生的问题，从自能费曼回路图与无质量的内部线路，特别是在相应的被积函数的积分域的边界上有奇点。
We apply and compare results of transformations used to annihilate boundary singularities for multivariate integration over hyper-rectangular and simplicial domains. While classically these transformations are applied with a product trapezoidal rule, we use adaptive methods in the PARINT software package, based on rules of higher polynomial degree for the integration over subdomains. PARINT is layered over the MPI environment (Message Passing Interface) and deploys advanced parallel computation techniques such as load balancing among processes that are distributed over a network of nodes. The message passing is performed in a non-blocking and asynchronous manner, and permits overlapping of computation and communication. Comparisons of computation times using long double vs. double precision confirm that the extended format does not considerably increase the time for long doubles. We further apply the proposed methods to problems arising from self-energy Feynman loop diagrams with massless internal lines, in particular where the corresponding integrand has singularities on the boundaries of the integration domain.