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

Onion gene expression in response to ethylene and 1-MCP

Onion is regarded as a non-climacteric vegetable. In onions, however, ethylene can suppress sprouting while the ethylene binding inhibitor, 1-MCP (1- methylcyclopropene) can also suppress sprout growth yet, it is unknown how ethylene and 1-MCP elicit the same response. In this study, onions were treated with 10 μL L-1 ethylene or 1 μL L-1 1-MCP individually or in combination for 24 h at 20°C before or after curing (six weeks) at 20 or 28°C then stored at 1°C. Following curing, a subset of these same onions was stored separately under continuous air or ethylene (10 μL L- 1) at 1°C Onions treated with ethylene and 1-MCP in combination after curing for 24 h had reduced sprout growth as compared with the control 25 weeks after harvest. Sprout growth following storage beyond 25 weeks was only reduced through continuous ethylene treatment. This observation was supported by a higher proportion of down-regulated genes characterised as being involved in photosynthesis measured using a newly developed onion microarray. Physiological and biochemical data suggested that ethylene was being perceived in the presence of 1-MCP since sprout growth was reduced in onions treated with 1-MCP and ethylene applied in combination but not when applied individually. A cluster of probes representing transcripts up-regulated by 1-MCP alone but down-regulated by ethylene alone or in the presence of 1-MCP support this suggestion. Ethylene and 1-MCP both down52 regulated a probe tentatively annotated as an ethylene receptor as well as EIN3, suggesting that both treatments down-regulate the perception and signalling events of ethylene

On the Hierarchical Preconditioning of the PMCHWT Integral Equation on Simply and Multiply Connected Geometries

We present a hierarchical basis preconditioning strategy for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering both simply and multiply connected geometries.To this end, we first consider the direct application of hierarchical basis preconditioners, developed for the Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found that, whereas for the EFIE a diagonal preconditioner can be used for obtaining the hierarchical basis scaling factors, this strategy is catastrophic in the case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in the case of multiply connected geometries. We then proceed to a theoretical analysis of the effect of hierarchical bases on the PMCHWT operator for which we obtain the correct scaling factors and a provably effective preconditioner for both low frequencies and mesh refinements. Numerical results will corroborate the theory and show the effectiveness of our approach