arXiv subjects

Cedric Münger

Publications and source records attributed to Cedric Münger.

3 recordsLinked to original sources

arXiv2026

Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations

The paper presents a higher-order global multi-trace integral equation for time-harmonic electromagnetic scattering by composite objects. The higher-order multi-trace formulation is preconditioned with a Calderón multiplicative preconditioner using higher-order quasi-Helmholtz projectors. The higher-order quasi-Helmholtz projectors separate the solenoidal and non-solenoidal components of the basis functions. Separate access to the Helmholtz components circumvents the explicit inversion of an ill-conditioned mixed Gram matrix. This enables the application of Calderón multiplicative preconditioning without refining the mesh and resorting to dual basis functions. Furthermore, it enables low-frequency stabilization, as the solenoidal and non-solenoidal components can be rescaled individually. The higher-order quasi-Helmholtz projectors are computed iteratively, enabling iterative solvers to efficiently solve the preconditioned matrix system, yielding accurate solutions in a few dozen iterations. Numerical experiments are conducted for composite dielectric bodies, confirming the effectiveness of the proposed preconditioner for the global multi-trace formulation discretized with higher-order basis functions for dense meshes and at very low frequencies

cs.CE↗

arXiv2026

A Stable, Accurate, and Well-Conditioned Time-Domain PMCHWT Formulation

This paper introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects, based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calderón preconditioner constructed from a modified static electric field integral operator is employed. Large-timestep breakdown and late-time instability are simultaneously resolved through a rescaling of the Helmholtz components using quasi-Helmholtz projectors, with temporal differentiation and integration serving as the rescaling operators. This rescaling additionally balances the loop and star components in the large-timestep regime, thereby preventing loss of accuracy in the secondary quantities caused by numerical cancellation. The resulting discrete system is solved using a marching-on-in-time scheme in conjunction with iterative solvers. Numerical experiments for simply- and multiply-connected dielectric scatterers, including highly non-smooth geometries, corroborate the stability and efficiency of the proposed approach and demonstrate its ability to produce accurate derived quantities in the large-timestep regime.

eess.SY↗

arXiv2020

Dielectric breakdown prediction with GPU-accelerated BEM

The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently compute the electric field at arbitrary points in space. A boundary element method (BEM) based on an indirect formulation, realized with MPI-parallel collocation, has proven to cope very well with this requirement. It deploys surface meshes only, which are easy to generate even for complex industrial geometries. The assembly of the large dense BEM-matrix, as well as the iterative solution process of the resulting system and the evaluation along the field-lines all require us to carry out the same type of calculation many times. Graphical processing units (GPUs) promise to be more efficient than standard processors (CPUs) in these situations. In this paper we investigate if GPU acceleration can speed up the established CPU-parallel BEM solver.

math.NA↗