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

Casimir forces dominate the interaction between electrically neutral macroscopic objects at nanoscale separations, making their quantitative description highly relevant to modern technology and fundamental physics. In this work, we present a time-domain scheme for computing Casimir forces between vacuum-separated bodies based on the Maxwell stress tensor formalism. In particular, we provide a concrete implementation using the finite-element-based discontinuous Galerkin time-domain method. The approach enables accurate evaluation of finite-temperature Casimir–Lifshitz interactions in arbitrary geometries and for general material models. At the core of the method, the electromagnetic Green 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 finite temperature. We further demonstrate its applicability to the interaction between a finite cylindrical object and a half-space, for which semi-analytical expressions are not available, showing excellent agreement with both asymptotic predictions based on physical considerations and alternative numerical approaches. These findings illustrate the method's potential for studying Casimir interactions in micro- and nanoscale structures of relevance to nanodevice design and experimental settings.