2022/11/19 by Alexander Rothkopf, Rothkopf, Alexander
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Boundary value problem #Discretization #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Finite difference #High Energy Physics - Lattice (hep-lat) #Mathematical analysis #Mathematics #Numerical methods for differential equations #Operator (biology) #Partial differential equation
paper · pdf · doi:10.48550/arxiv.2211.10679
openalex publication_date 2022/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.