arXiv subjects

Lorenzo Codecasa

Publications and source records attributed to Lorenzo Codecasa.

5 recordsLinked to original sources

arXiv2026

A higher-order dual cell method for time-domain Maxwell equations

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and generalises a previously developed two-dimensional high-order formulation. The electric and magnetic fields are discretised on mutually dual barycentric grids using curl-conforming polynomial spaces constructed via tensor-product Gauss--Radau interpolation. The resulting semi-discrete formulation yields block-diagonal mass matrices and sparse discrete curl operators, enabling explicit time integration while preserving a discrete energy identity. Special attention is devoted to the construction of compatible approximation spaces on the three-dimensional primal and dual meshes, the reference-to-physical element mappings, and the preservation of tangential continuity. We show that the method achieves arbitrary-order convergence, avoids spurious modes, and maintains optimal sparsity properties. Numerical experiments confirm spectral correctness, high-order accuracy, and computational efficiency on unstructured tetrahedral meshes.

math.NA↗

arXiv2026

Uncertainty Quantification of Radio Wave Propagation over Irregular Terrains Using Adaptive Polynomial Chaos Expansion

Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within deterministic models. In this paper, we present, to the best of our knowledge, the first uncertainty quantification (UQ) study of realistic antenna configurations for irregular-terrain propagation. An adaptive polynomial chaos expansion (APCE) method is improved and coupled with a two-way parabolic wave equation (PWE) method to address this problem efficiently. The polynomial basis is extended according to variance contributions and terminated by a composite criterion combining validation error and sample-to-basis ratio, enabling stable coefficient estimations via least-square regression without additional regularization. Convergence analysis shows a monotonic error decay with increasing training samples, producing compact, low-interaction models and improved accuracy and robustness over the previous APCE methods. For two realistic terrain profiles, the proposed method accurately predicts the mean and the 5th-95th percentile range of the path loss, matching Monte Carlo (MC) references using only 30 PWE simulations. Using a fixed sampling budget, APCE outperforms standard and sparse PCE, with the largest gains observed for the 5th and 95th percentile estimates; as the sample size increases, APCE maintains low errors with reduced trial-to-trial variability.

eess.SP↗

arXiv2023

Mass lumping the dual cell method to arbitrary polynomial degree for acoustic and electromagnetic waves

We present a fundamental improvement of a high polynomial degree time domain cell method recently introduced by the last three authors. The published work introduced a method featuring block-diagonal system matrices where the block size and conditioning scaled poorly with respect to polynomial degree. The issue is herein bypassed by the construction of new basis functions exploiting quadrature rule based mass lumping techniques for arbitrary polynomial degrees in two dimensions for the Maxwell equations and the acoustic wave equation in the first order velocity pressure formulation. We characterize the degrees of freedom of all new discrete approximation spaces we employ for differential forms and show that the resulting block diagonal (inverse) mass matrices have block sizes independent of the polynomial degree. We demonstrate on an extensive number of examples how the new technique is applicable and efficient for large scale computations.

math.NA↗

arXiv2020

An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations

We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and on approximating two unknown fields with integral quantities on geometric entities of the two dual complexes. A careful choice of basis-functions yields cheaply invertible block-diagonal system matrices for the discrete time-stepping scheme. The main novelty of the present contribution lies in incorporating arbitrary polynomial degree in the approximating functional spaces, defined through a new reference cell. The presented method, albeit a kind of Discontinuous Galerkin approach, requires neither the introduction of user-tuned penalty parameters for the tangential jump of the fields, nor numerical dissipation to achieve stability. In fact an exact electromagnetic energy conservation law for the semi-discrete scheme is proved and it is shown on several numerical tests that the resulting algorithm provides spurious-free solutions with the expected order of convergence.

physics.comp-ph↗

arXiv2015

Modeling of anechoich chambers with equivalent materials and equivalent sources

Numerical simulation of anechoic chambers is a hot topic since it can provide useful data about the performance of the EMC site. However, the mathematical nature of the problem, the physical dimensions of the simulated sites and the frequency ranges pose nontrivial challenges to the simulation. Computational requirements in particular will quickly become unmanageable if adequate techniques are not employed. In this work we describe a novel approach, based on equivalent elements, that enables the simulation of large chambers with modest computational resources. The method is then validated against real measurement results.

cs.CE↗