A High-Order Fast Boundary Element Method with Near-Boundary Stability for Field Emission from Nanoscale Structures (Communications in Computational Physics, 2024)
Advancing electron beam applications require pushing toward the quantum degeneracy limit. Nanoscale structured cathodes are a promising electron sourcefor this regime, but the numerical tools for studying these designs remain limited.A previous paper detailed the implemented of a flat-panel fast-multipole-acceleratedboundary element method, which solves the relevant Poisson problem. However, flatpanels are inadequate and inefficient for representing curved surfaces at the high precision necessary for many applications. Additionally, the boundary element methodhas an established numerical instability when evaluated near the domain boundary.To resolve this, a general high-order curvilinear element interpolation and modifiedquadrature method is developed utilizing a differential algebraic mapping for greateraccuracy in the boundary surface representation. The boundary instability effect ismitigated by devising local corrections to the quadrature scheme in the form of Cartesian Taylor expansions. This approach is suitably general, requiring only small modifications for application to other kernels, and can easily be incorporated into a fastmultipole accelerated framework. The refined algorithm is evaluated with respect toboth accuracy and efficiency using several analytic structures and the performance capacity is highlighted by the capability of accurately determining the field enhancementfactor for a single nanotip electron cathode.
Keywords: Quadrature by expansion; high-order boundary interpolation; fast-multipole accelerated boundary element method; differential algebraic framework.