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The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable coefficient Helmholtz equation including very high frequency problems. The first central idea of this novel approach is to…
A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper [1] where a simpler case of uniform dielectric filling has been considered.…
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
An elegant and convenient rigorous approach for solving circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear…
We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…
Getting standard multigrid to work efficiently for the high-frequency Helmholtz equation has been an open problem in applied mathematics for years. Much effort has been dedicated to finding solution methods which can use multigrid…
The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are…
We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with…
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…
The Transfer Matrix Method is a practical approach for modeling plane wave propagation in one-dimensional waveguides. Its simplicity makes it especially attractive for accounting for viscothermal losses, enabling realistic simulations of…
We propose a new model reduction technique for multiscale scalar transport problems that exhibit dominant axial dynamics. To this aim, we rely on the separation of variables to combine a Hierarchical Model (HiMod) reduction with a two-scale…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous…
We present an exact analytical investigation of the topological properties and edge states of the Haldane model defined on a honeycomb lattice with zigzag edges. By exploiting translational symmetry along the ribbon direction, we perform a…
Turbulent flows, despite their apparent randomness, exhibit coherent structures that underpin their dynamics. Proper orthogonal decomposition (POD) has been widely used to extract these structures from experimental data. While periodic…
A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a…
We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial,…