论文标题
通过弱边界条件迈向对称离散方案
Towards symmetric discretization schemes via weak boundary conditions
论文作者
论文摘要
Szymanzik改进量表理论的改进计划最常用于Wilson Action的远期有限差校正。中央对称方案天真地应用，遭受了一倍的自由度，与众所周知的费米昂翻倍现象相同。在添加复杂的威尔逊术语时，费米子的问题不容易转移到实价量规场。在这次演讲中，我报告了最新的进展，以制定简单一维问题的经典作用对称性离散方案。它们通过利用初始/边界条件的弱施加来避免加倍。受到部分微分方程数值分析领域的最新工作的启发，我使用基于仿射坐标的边界数据构建了一个正规求和有限差算子。提出了与二阶导数的经典初始价值问题的应用。
The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom, identical to the well known fermion doubling phenomenon. And while adding a complex Wilson term remedies the problem for fermions, it does not easily transfer to real-valued gauge fields. In this talk I report on recent progress in formulating symmetric discretization schemes for classical actions of simple one-dimensional problems. They avoid doubling by exploiting the weak imposition of initial/boundary conditions. Inspired by recent work in the field of numerical analysis of partial differential equations, I construct a regularized summation-by-parts finite difference operator using boundary data based on affine coordinates. Application to a classical initial value problems with second order derivatives are presented.
