New mapping properties of the Time Domain Electric Field Integral Equation

TL;DR

This paper investigates enhanced mathematical properties of the Time Domain Electric Field Integral Equation and its discretization, providing sharper stability and error estimates through advanced functional analysis techniques.

Contribution

It introduces improved mapping properties and connects weak distributional solutions with stronger solution classes, leading to more precise stability and error bounds.

Findings

Sharper stability estimates compared to previous literature

Enhanced error bounds for Galerkin semidiscretization

New connections between weak and strong solution frameworks

Abstract

We show some improved mapping properties of the Time Domain Electric Field Integral Equation and of its Galerkin semidiscretization in space. We relate the weak distributional framework with a stronger class of solutions using a group of strongly continuous operators. The stability and error estimates we derive are sharper than those in the literature.