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We present an advection-pressure flux-vector splitting method for the one and two- dimensional shallow water equations following the approach first proposed by Toro and V\'azquez for the compressible Euler equations. The resulting first-order schemes turn out to be exceedingly simple, with accuracy and robustness comparable to that of the sophisticated Godunov upwind method used in conjunction with complete non- linear Riemann solvers. The technique splits the full system into two subsystems, namely an advection system and a pressure system. The sought numerical flux results from fluxes for each of the subsystems. The basic methodology, extended on 2D unstructured meshes, constitutes the building block for the construction of numerical schemes of very high order of accuracy following the ADER approach. The presented numerical schemes are systematically assessed on a carefully selected suite of test problems with reference solutions, in one and two space dimensions.The applicabil- ity of the schemes is illustrated through simulations of tsunami wave propagation in the Pacific Ocean.

We present an accelerated and hardware parallelized integral-equation solver for the problem of acoustic scattering by a two-dimensional surface in three-dimensional space. The approach is based, in part, on the novel Interpolated Factored Green Function acceleration method (IFGF) that, without recourse to the Fast Fourier Transform (FFT), evaluates the action of Green function-based integral operators for an $N$-point surface discretization at a complexity of $\Ord(N\log N)$ operations instead of the $\Ord(N^2)$ cost associated with nonaccelerated methods. The IFGF algorithm exploits the slow variations of factored Green functions to enable the fast evaluation of fields generated by groups of sources on the basis of a recursive interpolation scheme. In the proposed approach, the IFGF method is used to account for the vast majority of the computations, while, for the relatively few singular, nearly-singular and neighboring non-singular integral operator evaluations, a high-order rectangular-polar quadrature approach is employed instead. Since the overall approach does not rely on the FFT, it is amenable to efficient shared- and distributed-memory parallelization; this paper demonstrates such a capability by means of an OpenMP parallel implementation of the method. A variety of numerical examples presented in this paper demonstrate that the proposed methods enable the efficient solution of large problems over complex geometries on small parallel hardware infrastructures. Numerical examples include acoustic scattering by a sphere of up to $128$ wavelengths, an $80$-wavelength submarine, and a turbofan nacelle that is more than $80$ wavelengths in size, requiring, on a 28-core computer, computing times of the order of a few minutes per iteration and a few tens of iterations of the GMRES iterative solver.

The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of metasurfaces. The BEM typically involves the electric and magnetic fields as unknown quantities. Formulations based on electromagnetic potentials rather than fields have garnered interest recently, for two main reasons: (a) they are inherently stable at low frequencies, unlike many field-based approaches, and (b) potentials provide a more direct interface to quantum physical phenomena. Existing potential-based formulations for electromagnetic scattering have been proposed primarily for perfect conductors. We develop a potential-based BEM formulation which can capture both dielectric and conductive losses, and accurately models the skin effect over broad ranges of frequency. The accuracy of the proposed formulation is validated through canonical and realistic numerical examples.

A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM formulations either lead to a poorly conditioned system matrix for multiscale problems, or are computationally expensive for objects embedded in layered substrates. This article presents a new BEM formulation which leverages the surface equivalence principle and Buffa-Christiansen basis functions defined on a dual mesh, to obtain a well-conditioned system matrix suitable for multiscale EM modeling. Unlike existing methods involving dual meshes, the proposed formulation avoids the double-layer potential operator for the surrounding medium, which may be a stratified substrate requiring the use of an advanced Green's function. This feature greatly alleviates the computational expense associated with the use of Buffa-Christiansen functions. Numerical examples drawn from several applications, including remote sensing, chip-level EM analysis, and metasurface modeling, demonstrate speed-ups ranging from 3x to 7x compared to state-of-the-art formulations.

This paper presents a novel approach for the joint design of a reconfigurable intelligent surface (RIS) and a transmitter-receiver pair that are trained together as a set of deep neural networks (DNNs) to optimize the end-to-end communication performance at the receiver. The RIS is a software-defined array of unit cells that can be controlled in terms of the scattering and reflection profiles to focus the incoming signals from the transmitter to the receiver. The benefit of the RIS is to improve the coverage and spectral efficiency for wireless communications by overcoming physical obstructions of the line-of-sight (LoS) links. The selection process of the RIS beam codeword (out of a pre-defined codebook) is formulated as a DNN, while the operations of the transmitter-receiver pair are modeled as two DNNs, one for the encoder (at the transmitter) and the other one for the decoder (at the receiver) of an autoencoder, by accounting for channel effects including those induced by the RIS in between. The underlying DNNs are jointly trained to minimize the symbol error rate at the receiver. Numerical results show that the proposed design achieves major gains in error performance with respect to various baseline schemes, where no RIS is used or the selection of the RIS beam is separated from the design of the transmitter-receiver pair.

This paper introduces novel splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system. This means that the bulk and surface dynamics are modeled separately and connected through a coupling constraint. This allows the implementation of splitting schemes, which show first-order convergence in numerical experiments. On the other hand, acoustic boundary conditions naturally separate bulk and surface dynamics. Here, Lie and Strang splitting schemes reach first- and second-order convergence, respectively, as we reveal numerically.

The prospects of using a reconfigurable intelligent surface (RIS) to aid wireless communication systems have recently received much attention. Among the different use cases, the most popular one is where each element of the RIS scatters the incoming signal with a controllable phase-shift, without increasing its power. In prior literature, this setup has been analyzed by neglecting the electromagnetic interference, consisting of the inevitable incoming waves from external sources. In this letter, we provide a physically meaningful model for the electromagnetic interference that can be used as a baseline when evaluating RIS-aided communications. The model is used to show that electromagnetic interference has a non-negligible impact on communication performance, especially when the size of the RIS grows large. When the direct link is present (though with a relatively weak gain), the RIS can even reduce the communication performance. Importantly, it turns out that the SNR grows quadratically with the number of RIS elements only when the spatial correlation matrix of the electromagnetic interference is asymptotically orthogonal to that of the effective channel (including RIS phase-shifts) towards the intended receiver. Otherwise, the SNR only increases linearly.

The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density, wavespeed and frequency. In particular, high contrast in density and wavespeed across a material interface leads to an ill-conditioned discretisation matrix. Therefore, the convergence of Krylov methods to solve the linear system is slow. Here, specialised boundary integral formulations are designed for the case of acoustic scattering at high-contrast media. The eigenvalues of the resulting system matrix accumulate at two points in the complex plane that depend on the density ratio and stay away from zero. The spectral analysis of the Calder\'on preconditioned PMCHWT formulation yields a single accumulation point. Benchmark simulations demonstrate the computational efficiency of the high-contrast Neumann formulation for scattering at high-contrast media.

Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision operator. In this work, we propose a highly efficient adaptive low rank method for the Boltzmann equation, concerning in particular the steady state computation. This method employs the fast Fourier spectral method (for the collision operator) and the dynamical low rank method to obtain computational efficiency. An adaptive strategy is introduced to incorporate the boundary information and control the computational rank in an appropriate way. Using a series of benchmark tests in 1D and 2D, we demonstrate the efficiency and accuracy of the proposed method in comparison to the full tensor grid approach.

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the physical and velocity/angular variables and the fact that the problem is multiscale in nature. Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test the angular-space reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM). Our method is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an asymptotic preserving upwind discontinuous Galerkin method for the physical space, and an efficient synthetic accelerated source iteration for the resulting linear system. Addressing the challenge of the parameter values (or angular directions) being coupled through an integration operator, the first novel ingredient of our method is an iterative procedure where the macroscopic density is constructed from the RBM snapshots, treated explicitly and allowing a transport sweep, and then updated afterwards. A greedy algorithm can then proceed to adaptively select the representative samples in the angular space and form a surrogate solution space. The second novelty is a least-squares density reconstruction strategy, at each of the relevant physical locations, enabling the robust and accurate integration over an arbitrarily unstructured set of angular samples toward the macroscopic density. Numerical experiments indicate that our method is effective for computational cost reduction in a variety of regimes.