Recent zbMATH articles in MSC 78Mhttps://zbmath.org/atom/cc/78M2024-04-15T15:10:58.286558ZWerkzeugProperties of generalized magnetic polarizability tensorshttps://zbmath.org/1530.352942024-04-15T15:10:58.286558Z"Ledger, Paul David"https://zbmath.org/authors/?q=ai:ledger.paul-david"Lionheart, William R. B."https://zbmath.org/authors/?q=ai:lionheart.william-robert-breckon(no abstract)Heat generation using Lorentzian nanoparticles: estimation via time-domain techniqueshttps://zbmath.org/1530.352952024-04-15T15:10:58.286558Z"Mukherjee, Arpan"https://zbmath.org/authors/?q=ai:mukherjee.arpan"Sini, Mourad"https://zbmath.org/authors/?q=ai:sini.mouradSummary: We analyze the mathematical model that describes the heat generated by electromagnetic nanoparticles. We use the known optical properties of the nanoparticles to control the support and amount of the heat needed around a nanoparticle. Precisely, we show that the dominant part of the heat around the nanoparticle is the electric field multiplied by a constant which is explicitly and solely dependent on the permittivity and quantities related to the eigenvalues and eigenfunctions of the magnetization (or the Newtonian) operator, defined on the nanoparticle, and inversely proportional to the distance to the nanoparticle. The nanoparticles are described via the Lorentz model. If the used incident frequency is chosen related to the plasmonic frequency \(\omega_p\) (via the magnetization operator), then the nanoparticle behaves as a plasmonic one; if it is chosen related to the undamped resonance frequency \(\omega_0\) (via the Newtonian operator), then it behaves as a dielectric one. The two regimes exhibit different optical behaviors. In both cases, we estimate the generated heat and discuss advantages of each incident frequency regime. The analysis is based on time-domain integral equation techniques, avoiding the use of (formal) Fourier type transformations.Asymptotic expansion for solution of Maxwell equation in domain with highly oscillating boundaryhttps://zbmath.org/1530.352962024-04-15T15:10:58.286558Z"Boujemaa, Saoussen"https://zbmath.org/authors/?q=ai:boujemaa.saoussen"Khelifi, Abdessatar"https://zbmath.org/authors/?q=ai:khelifi.abdessatarSummary: In this paper, we derive high-order terms in the asymptotic expansions of the boundary perturbations for the electric field by taking into account of highly oscillating perturbations of an inhomogeneity with regular boundary. We show then that the asymptotic expansions depend on some parameter \(\gamma\), that describes the depth \(O(\delta^\gamma)\) of irregularity. Our study is rigorous and is founded on Field expansion method.
{\copyright} 2023 Wiley-VCH GmbH.\textit{A priori} error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell's equationshttps://zbmath.org/1530.651182024-04-15T15:10:58.286558Z"Cockburn, Bernardo"https://zbmath.org/authors/?q=ai:cockburn.bernardo"Du, Shukai"https://zbmath.org/authors/?q=ai:du.shukai"Sánchez, Manuel A."https://zbmath.org/authors/?q=ai:sanchez.manuel-aThe first a priori error analysis of a class of space discretizations by hybridizable discontinuous Galerkin (HDG) methods for the time-dependent Maxwell's equations is given. The article is outlined as follows. Section 1 is an introduction. The main result is presented in Section 2. The class of HDG semi-discretizations as well as the choice of the approximation to the initial condition are described and error estimates are discussed in this section, too. Then, in Section 3 it's detailed proofs are given. In Section 4, the fully discrete method is presented. Section 5 contains numerical experiments with figures and tables which validate theoretical results. Finally, some concluding remarks are given in Section 6.
Reviewer: Temur A. Jangveladze (Tbilisi)Analysis of a direct discretization of the Maxwell eigenproblemhttps://zbmath.org/1530.651512024-04-15T15:10:58.286558Z"Du, Zhijie"https://zbmath.org/authors/?q=ai:du.zhijie"Duan, Huoyuan"https://zbmath.org/authors/?q=ai:duan.huoyuanSummary: A direct discretization is analyzed for the computation of the eigenvalues of the Maxwell eigenproblem, where the finite element space \((P_k)^d + \nabla P_{k + 1}\) with the pair of the \(k\)th order \(P_k\) and \((k + 1)\)th order \(P_{k + 1}\) Lagrange element spaces (\(k \geq 1\)) on generic simplexes are used. The finite element space directly mimics the Hodge decomposition of the second-kind \(k\)th order Nédélec \((P_k)^d\) elements while the finite element formulation directly uses the classical variational formulation. We prove the convergence of the resulting finite element solutions.An adaptive and quasi-periodic HDG method for Maxwell's equations in heterogeneous mediahttps://zbmath.org/1530.651552024-04-15T15:10:58.286558Z"Camargo, Liliana"https://zbmath.org/authors/?q=ai:camargo.liliana"López-Rodríguez, Bibiana"https://zbmath.org/authors/?q=ai:lopez-rodriguez.bibiana"Osorio, Mauricio"https://zbmath.org/authors/?q=ai:osorio.mauricio-a"Solano, Manuel"https://zbmath.org/authors/?q=ai:solano.manuel-eSummary: With the aim to continue developing a hybridizable discontinuous Galerkin (HDG) method for problems arisen from photovoltaic cells modeling, in this manuscript we consider the time harmonic Maxwell's equations in an inhomogeneous bounded bi-periodic domain with quasi-periodic conditions on part of the boundary. We propose an HDG scheme where quasi-periodic boundary conditions are imposed on the numerical trace space. Under regularity assumptions and a proper choice of the stabilization parameter, we prove that the approximations of the electric and magnetic fields converge, in the \(L^2\)-norm, to the exact solution with order \(h^{k+1}\) and \(h^{k+1/2}\), resp., where \(h\) is the meshsize and \(k\) the polynomial degree of the discrete spaces. Although, numerical evidence suggests optimal order of convergence for both variables. An \textit{a posteriori} error estimator for an energy norm is also proposed. We show that it is reliable and locally efficient under certain conditions. Numerical examples are provided to illustrate the performance of the quasi-periodic HDG method and the adaptive scheme based on the proposed error indicator.Well-posedness and convergence analysis of PML method for time-dependent acoustic scattering problems over a locally rough surfacehttps://zbmath.org/1530.780032024-04-15T15:10:58.286558Z"Guo, Hongxia"https://zbmath.org/authors/?q=ai:guo.hongxia"Hu, Guanghui"https://zbmath.org/authors/?q=ai:hu.guanghuiSummary: We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of the wave equation in a truncated bounded domain through a well-defined transparent boundary condition. Well-posedness and stability of the reduced problem are established. Numerically, we adopt the perfect matched layer (PML) scheme for simulating the propagation of perturbed waves. By designing a special absorbing medium in a semi-circular PML, we show the well-posedness and stability of the truncated initial-boundary value problem. Finally, we prove that the PML solution converges exponentially to the exact solution in the physical domain. Numerical results are reported to verify the exponential convergence with respect to absorbing medium parameters and thickness of the PML.