Spurious Reflections Research Articles

Meshless method for wave propagation in poroelastic transversely isotropic half‐space with the use of perfectly matched layer

AbstractNumerical investigation of wave propagation in transversely isotropic poroelastic half‐space with the use of a new stretched coordinate system through the Meshless Local Petrov–Galerkin (MLPG) formulation is presented in this paper. To this end, the u−p formulation of Biot is adopted as the framework of the porous media. One approach to numerically solve the infinite domain problems is the use of an absorber layer in which the whole half‐space is divided into two parts, that is (i) a finite part, in which the responses are interested, and (ii) the remaining semi‐infinite part, which is replaced by a Perfectly Matched Layer (PML). The stretched coordinates in the PML are introduced in such a way that the wave propagating in it does not generate spurious reflection to the finite part. Comparing the numerical results with some existing exact solutions and evaluating the norm of error demonstrate that the response functions in the finite part are achievable as precise as desired. Some new results are also presented which show the validity of the numerical approach in poroelastic transversely isotropic domain.

Improved accuracy and robustness of electron density profiles from JET's X-mode frequency-modulated continuous-wave reflectometers.

JET's frequency-modulated continuous wave (FMCW) reflectometers have been operating well with the current design since 2005, and density profiles have been automatically calculated intershot since then. However, the calculated profiles had long suffered from several shortcomings: poor agreement with other diagnostics, sometimes inappropriately moving radially by several centimeters, elevated levels of radial jitter, and persistent wriggles (strong unphysical oscillations). In this research, several techniques are applied to the reflectometry data analysis, and the shortcomings are significantly improved. Starting with improving the equilibrium reconstruction that estimates the background magnetic field, adding a ripple correction in the reconstructed magnetic field profile, and adding new inner-wall reflection positions estimated through ray-tracing, these changes not only improve the agreement of reconstructed profiles to other diagnostics but also solve density profile wriggles that were present during band transitions. Other smaller but also persistent wriggles were also suppressed by applying a localized correction to the measured beat frequency where persistent oscillations are present. Finally, the burst analysis method, as introduced by Varela etal. [Nucl. Fusion 46 S693 (2006)], has been implemented to extract the beat frequency from stacked spectrograms. Due to the strong suppression of spurious reflections, the radial jitter that sometimes would span several centimeters has been strongly reduced. The stacking of spectrograms has also been shown to be very useful for stacking recurring events, like small gas puff modulations, and extracting transport coefficients that would otherwise be below the noise level.

An Efficient Local Artificial Boundary Condition for Infinite Long Finite Element Euler–Bernoulli Beam

To solve the wave propagation problems of the Euler–Bernoulli beam in an unbounded domain effectively and efficiently, a new local artificial boundary condition technology is proposed. It replaces the residual right-hand side of the truncated discrete equation with an equivalent linear algebraic system. First, the equivalent Schrodinger equation is discussed. Its artificial boundary condition is obtained by first rationalizing the Dirichlet-to-Neumann condition in the frequency domain with a Pade approximation and then inverse transforming each Pade term back into the time domain by introducing auxiliary degrees of freedom. Frequency shifting is employed such that it performs better near a prescribed frequency. Then, the artificial boundary condition of the finite element Euler–Bernoulli beam is obtained by simple algebraic manipulations on that of the corresponding Schrodinger equation. This method only makes local changes to the original truncated discrete dynamic system and thus is very efficient and easy to use. The accuracy of the proposed method can be improved by using more Pade terms and a proper shift frequency. The numerical example shows, with only a few additional degrees of freedom, the proposed artificial boundary condition effectively eliminates the spurious reflection. The idea of the proposed method can also be used in other dispersive wave systems.

Numerical investigation of flow past a cylinder using cumulant lattice Boltzmann method

This paper presents simulations of flow past a circular cylinder within the subcritical Reynolds number (Re) range from 3900 to 2 × 105, utilizing the parameterized cumulant lattice Boltzmann model. In this study, a three-dimensional characteristic boundary condition for incompressible flow has been integrated into the lattice Boltzmann method at the outflow boundary to minimize spurious reflection. The flow field, wake statistics, hydrodynamic force, and power spectra results of Re = 3900 from the cumulant lattice Boltzmann model are exhaustively compared with the laboratory data and other numerical models. Relative to other numerical models employing turbulence closure, the cumulant lattice Boltzmann simulations demonstrate enhanced agreement with the experimental data even with relatively coarser grid resolution. The resolution-spanning feature for the cumulant lattice Boltzmann model in turbulent flows, without using explicit turbulence model, aligns with the previous benchmark case studies. The stability-preserving regularization process in the present model is analyzed. Results indicate that the influence of the regularization parameter is mitigated with improved grid resolution. A specific regularization parameter for flow around cylinder simulations is recommended. Variations in flow properties and hydrodynamic forces within the subcritical Reynolds number range of 3900 to 2 × 105 are analyzed. The results confirm that the parameterized cumulant lattice Boltzmann model can accurately simulate practical engineering flows, characterized by complex separation and recirculation, within the subcritical range. Moreover, the computational efficiency and parallel scalability are compared with other numerical methods.

Non-reflective hard source method for multiple physically extended sources and scattering bodies

In this paper, we focus on methodologies to inject a noise source in a numerical model of noise propagation in confined domains. This is a problem of primary importance when dealing with propagation of fluid-dynamic induced noise in confined basins, like ships at sea or wind farms. We first assess the performance of the literature hard source (HS) and transparent source methods; successively, we propose a novel method named the non-reflective HS (NRHS) method. It takes advantage of the linearity of the equation governing the propagation of acoustic waves in fluids and is based on the decomposition of the total signal in the sum of direct and reflected signals. It presents the advantages of the hard source method removing the main drawback consisting of the well-known problem of spurious reflections. To check the reliability of the HS vs the NRHS, a non-dimensional parameter (the encumbrance) has been defined, which gives a measure of the extension of the generation domain with respect to the propagation domain in relation to the principal wavelength of the acoustic waves and the presence of reflecting surfaces. The method herein developed gives accurate results in the case of a single-point source, where the literature methods behave well; more importantly, the NRHS method maintains its own accuracy when a noise source needs to be represented by a large number of points in space, situations of very practical importance where the standard methods may exhibit inaccuracy. This is a point of importance since the use of large generation domains is in favor of the accuracy of the source characterization, which can exhibit a complex directivity. The new method has been tested in a number of archetypal situations characterized by the presence of a reflecting plane, a scattering body close to the source location, and two sources placed side by side. In all cases, the method has shown its own superiority with respect to the standard HS method, still preserving the flexibility and simplicity of the latter.

A generating absorbing boundary condition for simulating wave interaction with maritime structures in current or at forward speed

The lack of suitable boundary conditions in practical surface wave simulations with maritime structures in current or at forward speed may cause energy in the computational domain to accumulate due to spurious wave reflection. The common way to prevent wave reflection is to use passive wave absorbers, such as damping zones or relaxation zones, which requires larger domains at the cost of computational effort. Our goal is to derive a local generating absorbing boundary condition (GABC) for long-crested irregular waves on top of a mean flow, using the flow to model the forward speed of a structure such as a ship. Earlier work has demonstrated that a local GABC for free surface waves has a performance similar to passive wave absorbers, but at a reduced computational effort. New in the present work is that we extend, verify and validate the GABC in the presence of a nonzero mean flow. The GABC is designed to be accurate for a range of wave components in irregular sea states, with the resulting reflection coefficients for each component lower than a chosen value, say 5%. Having used potential flow theory for its derivation means that the boundary should not be placed at the exact location where wave breaking is expected, such as very close to the structure in the domain, or in the surf zone in coastal modeling. For the application with ships in this article that does not pose a limitation. The performance is demonstrated for a range of dimensionless wave number between 0 and 6. Such a boundary condition is obtained through a rational approximation of the linear dispersion relation with a mean flow, in combination with vertical derivatives of the solution variables along the boundary. Local linearization means that the GABC incorrectly considers bound, nonlinear wave components to be freely propagating wave components. Bound components, however, tend to have smaller amplitudes and do not appear to affect performance for the considered cases. Results of simulations with regular and irregular waves, on top of flows with different magnitudes and directions, are found to agree with the theory. The main source of differences is the implementation of the second derivate in the GABC near the free surface. Simulations of a Wigley hull at forward speed in irregular waves are compared to an experiment that was conducted specifically for validating the ABC. The data of the experiment are available as open data through doi: 10.4121/21320604. The comparison between simulation and experiment demonstrates that the GABC with a mean flow can be applied not only for theoretical simulations with propagating waves, but also for more practical applications with a structure in the domain.

An unsplit-field viscoelastic complex-frequency-shifted perfectly matched layer for analysis of transient waves in heterogeneous media based on an efficient voxel element method

Wave propagation analysis of heterogeneous unbounded media employing domain discretization methods necessitates truncation of the finite computational domain at its truncation boundaries. The Perfectly Matched Layer (PML) is a robust absorbing boundary condition, which is extensively employed to favorably absorb outgoing scattered waves from the interior computational domain, regardless of frequencies and directions of outgoing waves. Nonetheless, most available PMLs are developed for elastic domains, while their developments in domain discretization methods, which consider damping using the Rayleigh damping formulation, are insufficient. In this study, a viscoelastic PML formulation is developed that accommodates the Rayleigh-type damping. The PMLs are basically developed from a coordinate transformation concept using a complex stretching function. Suitable stretching functions can efficiently control the absorptive properties and the spectral character of the PML. Besides, the stretching functions play a crucial role in the long-time stability of transient wave simulations. The standard stretching function usually results in spurious reflections, especially when propagating waves incident to the truncation boundary at near-grazing incidence. On the other hand, the complex-frequency-shifted (CFS) stretching function has been shown to mitigate long-time instability. Therefore, the proposed viscoelastic PML in the time-domain and frequency-domain are derived using the CFS stretching function for the first time. Comprehensive formulations of the proposed viscoelastic CFS-PML are given, where the displacement field is represented as the sole unknown variable of the problem. Hence, the proposed CFS-PML can be incorporated into any domain discretization method. However, the proposed CFS-PML is further developed in the context of the voxel element method, where element-by-element iterative strategies are implemented to solve the governing equations without storing global matrices in the computer memory. Comprehensive numerical experiments are conducted to demonstrate the validity and efficiency of the proposed viscoelastic CFS-PML formulation in analyzing soil profiles with various damping ratios and properties. Moreover, long-time stability for problems involving waveguides and near-grazing wave incidence is studied, where no instabilities are detected.

Hermetic Package for MEMS Mirror

Applications for optical scanning and 3D sensing, mostly related to the consumer electronics and automotive markets, are becoming more and more demanding in terms of performance and power consumption. When using a MEMS based Laser Beam Scanning, enclosing the mirrors into a hermetic package helps to address these requirements. Two MEMS mirrors with different sizes and performance have been selected for this study. A unique package, suitable for both mirrors, has been properly designed. The package is based on a ceramic chip carrier with a soldering ring on the top surface. A metal cap with a sintered optical window is attached to the ceramic substrate. The optical window is tilted with respect to the mirror to avoid spurious reflections. The MEMS mirrors have been integrated onto the ceramic substrate by standard die attach and wirebonding technologies. Hermetic sealing has been developed under nitrogen atmosphere to guarantee the MEMS stable operation against humidity and contaminants. Flux-less SnAgCu solder preforms have been selected as sealing material. The solder reflow profile has been optimized in order to obtain a uniform solder fillet at the sealing region while minimizing the thermal stress to the mirrors. The hermeticity of the assemblies has been proved by fine and gross leak testing. The packages show a leak rate < 1.5 E-8 atm cc/s and pass the fine and gross leak test, defined accordingly to MIL-STD-883 TM 1014.18.

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

AbstractWe introduce an extended discontinuous Galerkin discretization of hyperbolic–parabolic problems on multidimensional semi‐infinite domains. Building on previous work on the one‐dimensional case, we split the strip‐shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and nonlinear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi‐infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single‐domain discontinuous finite element techniques.

Enhanced intensity of Raman signals from hexagonal boron nitride films

Optical spectroscopy is commonly used to study the properties of 2D materials. In order to obtain the best signal-to-noise ratio, it is important to optimize the incoupling of the excitation laser and, at the same time, reduce spurious light reflection. We performed Raman spectroscopy on exfoliated hexagonal boron nitride (hBN) flakes of different thicknesses, placed on a 300 nm SiO2 on Si substrate. By changing the hBN layer thickness, we found a specific thickness, where the Raman signals from the substrate and the hBN showed maximum intensity, whereas the backscattered laser light was suppressed. To explain the increased emission, we calculated the reflectivity and transmissivity of the full layer system (air, hBN, SiO2, and Si) as a function of hBN layer thicknesses for different excitation wavelengths (457, 532, and 633 nm), using the transfer-matrix algorithm. To compare theory with the experiment, we performed Raman measurements with these three different excitation wavelengths on different flakes and determined their thicknesses with AFM measurements. The experimental results are in good agreement with the calculations, which shows the importance of thin film interference to obtain optimum spectroscopic conditions. Since interference colors are easily visible in an optical microscope, this facilitates the choice of optimum flakes for a wide range of optical characterization techniques, including Raman, photoluminescence, and single defect spectroscopy.

Hybrid Artificial Boundary Conditions for the Application of Blunt-Body Aerodynamic Noise Prediction

A hybrid artificial boundary condition (HABC) that combines the volume-based acoustic damping layer (ADL) and the local face-based characteristic boundary condition (CBC) is presented to enhance the absorption of acoustic waves near the computational boundaries. This method is applied to the prediction of aerodynamic noise from a circular cylinder immersed in uniform compressible viscous flow. Different ADLs are designed to assess their effectiveness whereby the effect of the mesh-stretch direction on wave absorption in the ADL is analysed. Large eddy simulation (LES) and FW-H acoustic analogy method are implemented to predict the far-field noise, and the sensitivities of each approach to the HABC are compared. In the LES computed propagation field of the fluctuation pressure and the frequency-domain results, the spurious reflections at edges are found to be significantly eliminated by the HABC through the effective dissipation of incident waves along the wave-front direction in the ADL. Thereby, the LES results are found to be in a good agreement with the acoustic pressure predicted using FW-H method, which is observed to be just affected slightly by reflected waves.

Local wall heating effects on aeroacoustic field radiated by an isolated square cylinder in a laminar flow

The aim of this work is to gain an insight on the effect of the wall heating on the aeroacoustic sound radiated by bluff bodies in laminar flows. In particular, the local thermal treatment of the wall boundary was investigated as a possible method for active controlling the emitted noise. This technique was studied performing direct numerical simulations of the aeroacoustic noise produced by an isolated square cylinder operating at a Reynolds and Mach numbers equal to 150 and 0.2, respectively. In the considered case, the Karman vortex street deriving by the flow/cylinder interaction, produces a lift and drag pulsation on the body surface, leading to a dipolar-like noise emission. In this context, different local thermal fluxes were applied to the cylinder wall in order to reduce its aerodynamic forces fluctuation and, consequently, the associated pressure disturbance that produces the radiated sound. The computations are performed using an OpenFOAM solver that adopts an explicit Runge-Kutta scheme for time integration and a second-order, energy conserving scheme for the convective part of the Eulerian flux. Moreover, the spurious numerical waves reflections at the far-field boundary are damped adopting a sponge-layer approach.

Cross‐impact of beam local wavenumbers on the efficiency of self‐adaptive artificial boundary conditions for two‐dimensional nonlinear Schrödinger equation

In this paper, we propose self‐adaptive artificial boundary conditions (ABCs) for the two‐dimensional (2D) time‐dependent nonlinear Schrödinger equation and studied their efficiency. This equation describes the laser pulse interaction with a semiconductor layer under laser‐induced plasma generation. Because of its nonlinearity, the interaction process is very sensitive to the appearance of the optical beam spurious reflection; therefore, highly transparent ABCs are urgently required to avoid disturbing the interaction process by an unphysical reflected wave. This can be achieved by using time‐ and spatial‐dependent local wavenumbers computed near the artificial boundaries. We claim that it is necessary to account for both wavenumbers in each of the adaptive ABCs stated on both spatial coordinates. Based on computer simulation, we demonstrate an increase in the efficiency of the adaptive ABC stated on the coordinate along which the optical pulse propagates by involving both local wavenumbers. The accuracy of the developed approach is verified using a well‐known analytical solution of the linear Schrödinger equation as well as the reference problem solution, obtained by solving the problem with zero‐value boundary conditions on the extended spatial domain. For computer modeling, the finite‐difference scheme, possessing asymptotic stability, is applied together with a two‐stage iterative process for its realization. The algorithm and peculiarities of the local wavenumber computation are discussed in detail. The applicability of the developed approach is also demonstrated via the solution of both linear and nonlinear problems. The proposed method has widespread application for solving various laser physics problems governed by the Schrödinger equation.

Investigating shock wave propagation, evolution, and anisotropy using a moving window concurrent atomistic–continuum framework

Despite their success in microscale modeling of materials, atomistic methods are still limited by short time scales, small domain sizes, and high strain rates. Multiscale formulations can capture the continuum-level response of solids over longer runtimes, but using such schemes to model highly dynamic, nonlinear phenomena is very challenging and an active area of research. In this work, we develop novel techniques within the concurrent atomistic–continuum (CAC) multiscale framework to simulate shock wave propagation through a two-dimensional, single-crystal lattice. The technique is described in detail, and two moving window methods are incorporated to track the shock front through the domain and thus prevent spurious wave reflections at the atomistic–continuum interfaces. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of two materials. We then use the moving window techniques to perform parametric studies which analyze the shock front’s structure. Finally, we compare the efficiency of our model to molecular dynamics simulations. This work showcases the framework’s capability for simulating dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and alloys.

Hybrid 3D-plane finite element modeling for elastodynamics

The coupling of three-dimensional (3D) and plane (2D) finite element (FE) models to form a single hybrid 3D–2D model is considered for linear elastodynamic problems. The 2D model is used to represent a large thin 3D computational domain where the solution behaves approximately in a 2D (plane-elasticity) way. Problems where the normal displacement is important in the thin region (bending) are excluded. The hybrid model, if designed properly, is a more efficient way to solve the full 3D model over the entire problem. This paper focuses on the way the 3D–2D coupling is performed, and on the coupling error generated. The Panasenko technique is used to couple the 3D and 2D models. This method has been used previously for mixed-dimensional coupling in steady-state problems, as well as for 2D–1D coupling of acoustic waves. Here it is being used for the first time for the 3D–2D coupling of time-dependent elastic problems. The hybrid formulation is derived, and is shown to be well-posed. It is shown that the Panasenko method is extremely simple to implement in the framework of FE analysis, yet the resulting coupling yields a rather small error level, provided the 3D–2D interface is sensibly placed. The numerical accuracy and efficiency of the method are explored for a couple of example problems. In particular, it is shown that spurious reflections from the interface back into the 3D region are negligible. • A hybrid 3D–2D model is constructed for elastodynamics. • The 3D–2D coupling is performed using the Panasenko technique. • The hybrid formulation is shown to be well posed. • Numerical experimentation is performed with a few configurations. • Excellent agreement is obtained between the proposed and reference models.

Design of a simple radio frequency circuit for implementing the open-ended coaxial probe method for permittivity measurement.

The development of electromagnetic (EM)-based therapeutic and diagnostic tools, as well as safety assessment of EM interactions with the human body, requires adequate measurement of the complex permittivity of different biological tissues. Such measurement techniques must be low-cost, readily available, and easy to implement. In this study, a simple circuit with basic radio frequency electronics was used to implement the open-ended coaxial probe method for permittivity measurement, as opposed to the widely used vector network analyzers. The non-ideal behavior of the circuit due to spurious reflections and ohmic losses was accounted for by a scattering matrix (SM) that relates the measured reflection coefficient to the true reflection coefficient at the probe tip. Parameters of SM were obtained using three calibration standards, and the circuit was used to measure the complex permittivity of a standard, tissue-equivalent, American Society of Testing Materials (ASTM) polymer gel. A more intuitive approach to circuit analysis is also introduced. For both methods, the dielectric constant and electrical conductivity of the gel were found to agree with the recommended uncertainties of the ASTM standard and validate the utility of the circuit at the test frequency.

Superconducting gravimeters based on advanced nanomaterials and quantum neural network

The paper is focused on a new concept of a cryogenic-optical sensor intended for use in the space industry, geodynamics, and fundamental experiments. The basis of the sensor is a magnetic suspension with a levitating test body, a high-precision optical recorder of mechanical coordinates of the levitating body, and a signal-processing system. A Michelson-type interferometer with a laser diode and a single-mode optical fiber was used to measure the test body's displacements. The coordination of the laser diode coherence length and the difference in the interferometer optical lengths of the arms made it possible to eliminate coherent noise caused by interference from spurious reflections. The minimum recorded shift of the test body was 0.1 nm. The design of the sensor and the mathematical model of the superconducting suspension dynamics are presented. The results of experimental studies of a magnetic suspension together with an optical interferometric displacement sensor having a subnanometer sensitivity are shown.

Hollow-Waveguide Tri-Band Shared-Aperture Full-Corporate-Feed Continuous Transverse Stub Antenna

This article presents a tri-band shared-aperture full-corporate-feed continuous transverse stub (CTS) antenna based on hollow-waveguide. The multiband operation is enabled by a broadband CTS radiator and a novel six-port parallel-plate waveguide (PPW) multiplexer. The CTS radiation slot is fed by a broadband vertical PPW power divider. The six-port multiplexer is composed of three diplexers, which defines the three frequency bands—Ku, K, and Ka. The quasi-TEM mode in the PPW structure is generated by single-layer linear source generators (LSGs). Four such LSGs operating at three different bands are used to feed into the multiplexer. The amplitude and phase precompensation method is applied in the LSG to overcome the imbalance and spurious reflection caused by the metal walls at the terminal ends of the PPW. This has resulted in improved radiation performance in all three bands. A prototype antenna is designed, fabricated, and measured. Good agreement between simulation and measurement has been shown. The peak gains of the antenna over the frequency range of 11.25–15 GHz, 17.7–22 GHz, and 27.5–32 GHz are better than 24.7, 28.2, and 32.1 dBi, respectively. Over 80% antenna efficiency has been achieved in all three frequency bands.

Turbulent Non-Stationary Reactive Flow in a Cement Kiln

The reduction of emissions from large industrial furnaces critically relies on insights gained from numerical models of turbulent non-premixed combustion. In the article Mitigating Thermal NOx by Changing the Secondary Air Injection Channel: A Case Study in the Cement Industry, the authors present the use of the open-source OpenFoam software environment for the modeling of the combustion of Dutch natural gas in a cement kiln operated by our industrial partner. In this paper, various model enhancements are discussed. The steady-state Reynolds-Averaged Navier-Stokes formulation is replaced by an unsteady variant to capture the time variation of the averaged quantities. The infinitely fast eddy-dissipation combustion model is exchanged with the eddy-dissipation concept for combustion to account for the finite-rate chemistry of the combustion reactions. The injection of the gaseous fuel through the nozzles occurs at such a high velocity that a comprehensive flow formulation is required. Unlike in Mitigating Thermal NOx by Changing the Secondary Air Injection Channel: A Case Study in the Cement Industry, wave transmissive boundary conditions are imposed to avoid spurious reflections from the outlet patch. These model enhancements result in stable convergence of the time-stepping iteration. This in turn increases the resolution of the flow, combustion, and radiative heat transfer in the kiln. This resolution allows for a more accurate assessment of the thermal NO-formation in the kiln. Results of a test case of academic interest are presented. In this test case, the combustion air is injected at a low-mass flow rate. Numerical results show that the flow in the vicinity of the hot end of the kiln is unsteady. A vortex intermittently transports a fraction of methane into the air stream and a spurious reaction front is formed. This front causes a transient peak in the top wall temperature. The simulated combustion process is fuel-rich. All the oxygen is depleted after traveling a few diameters into the kiln. The thermal nitric oxide is formed near the burner and diluted before reaching the outlet. At the outlet, the simulated thermal NO concentration is equal to 1 ppm. The model is shown to be sufficiently mature to capture a more realistic mass inflow rate in the next stage of the work.

High harmonic spectra computed using time-dependent Kohn–Sham theory with Gaussian orbitals and a complex absorbing potential

High harmonic spectra for H2 and H2 + are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.