Numerical evaluation of Casimir forces using the discontinuous Galerkin time-domain method

TL;DR

This paper introduces a time-domain finite-element method using discontinuous Galerkin techniques to accurately compute Casimir forces in complex geometries and materials, validated against known solutions and applicable to realistic nanostructures.

Contribution

The paper presents a novel time-domain approach leveraging discontinuous Galerkin finite-element methods for calculating Casimir forces, extending applicability to complex geometries and finite temperatures.

Findings

Validated against known Casimir interactions between parallel plates.

Accurately predicts forces in cylindrically symmetric geometries.

Demonstrates potential for realistic nanostructure analysis.

Abstract

We present a time-domain scheme for computing Casimir forces within the Maxwell stress tensor formalism, together with a specific realization using the finite-element-based discontinuous Galerkin time-domain method. The approach enables accurate evaluation of Casimir--Lifshitz interactions for a wide range of geometries and material properties at finite temperature. At the core of the method, the electromagnetic Green's tensor is expressed as the system's response to dipolar excitations, thereby recasting the Maxwell stress tensor into a set of classical scattering problems driven by electric and magnetic dipoles. We validate the approach against reference calculations of the Casimir interaction between parallel half-spaces at both zero and nonzero temperature. We further demonstrate its applicability to finite, cylindrically symmetric geometries for which closed-form solutions are unavailable, obtaining accurate agreement with asymptotic predictions based on physical considerations. These findings illustrate the method's potential for studying Casimir interactions in realistic micro- and nanoscale structures, relevant to nanodevice design and experimental settings.