A robust and low frequency stable time domain PMCHWT equation

The time domain PMCHWT equation models transient scattering by piecewise homogeneous dielectrics. After discretization, it can be solved using the marching-on-in-time algorithm. Unfortunately, the PMCHWT equation suffers from DC instability: it supports constant in time regime solutions. Upon discretization, the corresponding poles of the system response function shift into the unstable region of the complex plane, rendering the MOT algorithm unstable. Furthermore, the discrete system becomes ill-conditioned when a large time step is used. This phenomenon is termed low frequency breakdown. In this contribution, the quasi Helmholtz components of the PMCHWT equation are separated using projector operators. Judicially integrating or differentiating these components of the basis and testing functions leads to an algorithm that (i) does not suffer from unstable modes even in the presence of moderate numerical errors, (ii) remains well-conditioned for large time steps, and (iii) can be applied effectively to both simply and multiply connected geometries

High-order div- and quasi curl-conforming basis functions for calderon multiplicative preconditioning of the EFIE

A new high-order Calderon multiplicative preconditioner (HO-CMP) for the electric field integral equation (EFIE) is presented. In contrast to previous CMPs, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of high-order quasi curl-conforming basis functions. Like its predecessors, the HO-CMP can be seamlessly integrated into existing EFIE codes. Numerical results demonstrate that the linear systems of equations obtained using the proposed HO-CMP converge rapidly, regardless of the mesh density and of the order of the current expansion

Calderon multiplicative preconditioner for the PMCHWT equation applied to chiral media

In this contribution, a Calderon preconditioned algorithm for the modeling of scattering of time harmonic electromagnetic waves by a chiral body is introduced. The construction of the PMCHWT in the presence of chiral media is revisited. Since this equation reduces to the classic PMCHWT equation when the chirality parameter tends to zero, it shares its spectral properties. More in particular, it suffers from dense grid breakdown. Based on the work in [1], [2], a regularized version of the PMCHWT equation is introduced. A discretization scheme is described. Finally, the validity and spectral properties are studied numerically. More in particular, it is proven that linear systems arising in the novel scheme can be solved in a small number of iterations, regardless the mesh parameter

Accurate and conforming mixed discretization of the chiral Müller equation

Scattering of time-harmonic fields by chiral objects can be modeled by a second kind boundary integral equation, similar to Muller's equation for scattering by nonchiral penetrable objects. In this contribution, a mixed discretization scheme for the chiral Muller equation is introduced using both Rao-Wilton- Glisson and Buffa-Christiansen funtions. It is shown that this mixed discretization yields more accurate solutions than classical discretizations, and that they can be computed in a limited number of iterations using Krylov type solvers

Job: A Christian Sisyphus? Humor and the Triumph o f Humań Experience

Over the past decades humor and laughter have come to be accepted as serious topics in academic research and a number of diverse theories on humor and the role of laughter have been developed. These theories, however, consider laughter mainly in its daily aspects or in normal life situations. Starting ffom Albert Camus’ concept of the happy Sisyphus, this paper considers whether the figurę of Job, who seems to inhabit a comparably absurd situation, could also be considered as happy, even laughing. The paper concludes with a distinctive reading of the divine words found at the end of The Book of Job that ma> be fundamental in linking Sisyphus w.th Job