Robust Scheme Research Articles

AUTOMATIC OPERATION OF ON-GRID SOLAR SYSTEM WITH PROTECTION SCHEME

The on-grid solar energy system is becoming a pivotal component of modern electrical grids due to its potential for sustainable energy production and reduced environmental impact. The integration of automatic operation and protection schemes is essential to ensure optimal performance, reliability, and safety of these systems. This research paper delves into the development and implementation of an automatic operation strategy for an on-grid solar system, incorporating a robust protection scheme to mitigate common operational risks. We explore various components and design considerations, detailing the control strategies employed to achieve seamless system function and high performance. A thorough analysis of the data collected from the implemented system highlights the efficacy and reliability of the proposed method. Additionally, the research compares the findings with existing studies to position the results within the broader academic dialogue. Our findings show significant improvements in both the operational efficiency and protection capabilities of the solar system, thus providing valuable insights for future advancements in renewable energy integration. The developed methodologies could lead to enhanced system durability and energy yield, thereby promoting the broader adoption of renewable energy solutions. As we mentioned in Title, we are going to make the Operation of Solar System Automatic with Protection Scheme. This is very beneficial as point of view to on-Grid Solar Systems which is a Need of Today’s World.

Robust biometric identity authentication scheme using quantum voice encryption and quantum secure direct communications for cybersecurity

A significant problem facing cybersecurity is that most client/server identity authentication schemes depend on computational complexity which is recently challenged by the super exponential computational abilities of quantum computers. Quantum cryptography with its quantum mechanics principles solves this problem and provides mathematically un-hackable secure communication for the quantum computers epoch. Biometric authentication has a big challenge related to its protection as it has to be submitted and stored in encrypted form. Unfortunately, most existing biometric cryptosystems rely on classical cryptography, so they are insecure in quantum era. This problem is solved in this paper by introducing a novel three-factor biometric quantum identity authentication scheme combining something you know (password), something you produce (client’s voice), and something you are (client’s face image) is proposed. The scheme consists of two phases: client enrollment and client login/authentication. The methodology is to use in the enrollment phase, two layers of quantum encryption for the client’s voice signal. Each layer consists of two simple quantum circuits of SWAP and C-NOT quantum gates respectively using a different pseudorandom key obtained from a cellular automata (CA) pseudorandom generator. The proposed scheme has many merits. Firstly, it introduces a new design of muti-factors quantum biometric authentication scheme as the biometric voice data is processed, transmitted, and stored at the server database in an encrypted unconditionally secure quantum form which provides parallel processing, real-time communications, inherent level of security against attacks, tamper-proof security and exponential powerful storage capability due to the quantum properties. Secondly, the proposed scheme achieves double-layers security by combing quantum voice encryption and quantum secure direct communication in one process such that the quantum channel eavesdropper cannot obtain any valuable information in case of information leakage. Thirdly, the distribution and management of encryption key problem is solved as there is no need for key exchange prior to communication. Fourthly, it achieves high communication efficiency as although it is a three-factor biometric identity authentication, only one biometric data is sent in quantum encrypted form to the server. Fifthly, the numerical simulations showed that the proposed scheme has large key space, high key sensitivity and more robust performance against different types of attacks compared to other existing classical and quantum voice encryption schemes. Finally, as an identity authentication method, the proposed scheme achieves identification accuracy of 100% with zero False Rejection Rate (FRR) and zero False acceptance rate (FAR) which is perfect.

High-security multidimensional data protection system based on the Hartley algorithm-driven chaotic scheme

This paper proposes a high-security multidimensional data protection system based on the Hartley algorithm-driven chaotic scheme. We utilize the fast Hartley algorithm instead of the fast fourier computation, and we employ chaotic sequences generated by the multi-winged chaotic system to achieve chaos-driven 3D constellation mapping, effectively integrating the chaotic system with the stochastic amplitude modulator. We reduce the signal’s peak-to-average power ratio (PAPR) by deploying a random amplitude modulator. Simultaneously, this approach enhances the security of the physical layer of the signal. The PAPR reduction can reach up to 2.6 dB, while the most robust and stable modulator scheme can gain 2 dB. Finally, in the Hartley frequency domain, the signal's frequency is disrupted, providing the entire system with a key space of 10131 to resist violent cracking and thus improving the system's overall security. To validate the feasibility of our scheme in comparison to conventional IFFT-based encrypted 3D orthogonal frequency division multiplexing, We achieved a transmission rate of 27.94 Gb/s over a 2 km multicore fiber. Experimental results show that since the random amplitude generator effectively reduces PAPR, our proposed encryption scheme increases the forward error correction threshold range by 1.1 dB, verifying that our proposed scheme has highly reliable security performance.

A novel robust black-box fingerprinting scheme for deep classification neural networks

With the growing value and high training cost of deep neural network (DNN) models, there has been increasing research interest in deep neural network model watermarking. However, the existing literature lacks robust model watermarking methods with retrospective functionality, which hinders multi-user distribution and fine-grained copyright verification of deep neural network models. To achieve the model watermarking with retrospective functionality that is generally denoted the model fingerprinting, this study proposes a novel robust black-box fingerprinting scheme for deep classification neural networks, in which a fingerprint that is unique for each user is inserted in the given DNN. Specifically, a DWT-DCT-SVD-based embedding method is introduced to construct a high-quality poisoned image by spreading the fingerprint as a poisoned trigger to the entire image, which both leads to the traceability of the to-be-protected DNN and significantly enhances the stealthiness and anti-forgery of the embedded poisoned trigger. As the amplitude of the embedded fingerprint is rather small, it poses a challenge that makes the model hard to capture features of the embedded fingerprint during the training process. To tackle this challenge, this study then proposes a poisoned feature enhancement module, which groups classification categories of clean images without the fingerprint as one type while taking the poisoned images with the correct fingerprint and the poisoned adversarial images containing the other incorrect fingerprints as another two different types. This module, which can be removed during fingerprint verification, improves the reliability and fidelity of the model fingerprinting. Accordingly, an adversarial training strategy is designed, aiming at enhancing the effective training of classification neural network models that contain the fingerprint with small embedding strength. Combining these strategies then gives rise to the proposed scheme, which is denoted the UfNet for notational convenience. Extensive experimental simulation results demonstrate the excellent invisibility of the fingerprint in the poisoned image and the desirable verification of the fingerprint in case of even a one-bit difference. Additionally, it also exhibits robustness against the related attacks such as STRIP, Neural Cleanse, Fine-Pruning, and GradCAM, which outperforms the state-of-the-arts (SOTAs). Furthermore, the proposed UfNet is robust to collusion attacks and frame the innocent. These results show the feasibility and effectiveness of the introduced model fingerprinting framework and the proposed implementation methodology in this paper.

Robust predictive control strategy of SCIG-based drive system

This article presents a robust finite control set predictive scheme for a stand-alone squirrel cage induction generator (SCIG) drive. This technique is considered an alternative to the drive system due to the inclusion of system nonlinearities and fast dynamic response. The control objective in the distributed generation environment is to fix the output voltage to follow the stand-alone requirement. The strategy establishes optimized switching instants for cost function minimization for both source and load converter control and diminished cross-coupling amid active and reactive power during transient scenarios. The scheme is designed to achieve the minimal effect caused by the parameter uncertainties. During source and load changes, this work will also address the maintenance of dc-link voltage, machine, and load variables at the set value, supported by machine and load-end converter control to achieve stand-alone load objectives. In addition, the presented scheme is also tested with random variation of speed to check the efficacy of the control configuration. The drive performance is evaluated by simulation using MATLAB/Simulink environment. Comprehensive real-time findings obtained from a scaled laboratory test bench using dSPACE-1104 are provided to verify the feasibility of the predictive solution.

Improved 3D human face reconstruction from 2D images using blended hard edges

This study reports an effective and robust edge-based scheme for the reconstruction of 3D human faces from input of single images, addressing drawbacks of existing methods in case of large face pose angles or noisy input images. Accurate 3D face reconstruction from 2D images is important, as it can enable a wide range of applications, such as face recognition, animations, games and AR/VR systems. Edge features extracted from 2D images contain wealthy and robust 3D geometric information, which were used together with landmarks for face reconstruction purpose. However, the accurate reconstruction of 3D faces from contour features is a challenging task, since traditional edge or contour detection algorithms introduce a great deal of noise, which would adversely affect the reconstruction. This paper reports on the use of a hard-blended face contour feature from a neural network and a Canny edge extractor for face reconstruction. The quantitative results indicate that our method achieves a notable improvement in face reconstruction with a Euclidean distance error of 1.64 mm and a normal vector distance error of 1.27 mm when compared to the ground truth, outperforming both traditional and other deep learning-based methods. These metrics show particularly significant advancements, especially in face shape reconstruction under large pose angles. The method also achieved higher accuracy and robustness on in-the-wild images under conditions of blurring, makeup, occlusion and poor illumination.

An α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation

We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order α∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in (0,1)$$\\end{document}. The basic idea of our scheme is based on local integration followed by linear interpolation. It reduces to the standard Crank–Nicolson scheme in the classical diffusion case, that is, as α→1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 1$$\\end{document}. Using a novel approach, we show that the proposed scheme is α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-robust and second-order accurate in the L2(L2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(L^2)$$\\end{document}-norm, assuming a suitable time-graded mesh. For completeness, we use the Galerkin finite element method for the spatial discretization and discuss the error analysis under reasonable regularity assumptions on the given data. Some numerical results are presented at the end.

A robust unified data-driven protection scheme for hybrid AC/DC transmission lines

To meet rising energy demands, reduce carbon emissions, and address climate change, the importance of hybrid AC/DC transmission has increased. The effective utilization of high-voltage DC in existing AC transmission lines will reduce costs and losses and increase the existing transmission capacity. Therefore, the protection schemes of fault detection, location, and classification are complicated because of the different characteristics of AC and DC in the same transmission network. The existing protection schemes mostly utilize threshold-based criteria and cannot ensure hybrid network protection. To overcome these challenges, a unified data-driven protection scheme (UDDPS) using distinctive features is proposed to detect and identify (either AC or DC) and classify both AC/DC faults of hybrid transmission lines (HTLs). The UDDPS has ensured the protection of AC/DC lines by timely intervening faults and effectively isolating the respective relays of the faulty lines. The fault current data are retrieved during a fault abnormality using distinctive retrieved features from the single end of the HTL. The proposed scheme applies to multi-transmission networks and is independent of the communication channels. Extensive simulation scenarios, such as fault/no-fault, varying fault locations, and near and far locations with low/high impedances, were examined in MATLAB/Simulink to train the UDDPS. The UDDPS successfully detected and identified hybrid AC/DC line faults with 100% accuracy and further classified the AC and DC faults with 97.61 % and 99.20 % accuracy. The efficacy and robustness of the proposed technique were confirmed by comparison with the existing schemes of support vector machine, decision tree, and LSTM. The UDDPS surpassed in terms of the overall model under a normal and noisy environment.

Robust sparse representation based on fitting error decomposition

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.

Induced attack on formation control of multiagent systems with prescribed reference trajectories

AbstractThe induced attack on the formation control of multiagent systems is investigated from the perspective of the attacker, where a new induced attack strategy is proposed to drive the whole formation of multiagent systems to the prescribed reference trajectory. Compared with denial‐of‐service attacks and deception attacks, a desired formation reference trajectory with the stable formation structure is reached by the induced attack instead of disrupting the whole formation. First, the induced attack signal is produced by designing an attack generation exosystem, whose dynamics can be described by the regulated attack matrix and can be adjusted to generate the prescribed reference trajectory. Then, based on the local state information, the formation vector, and the induced attack signal among partial agents, a new distributed induced attack formation protocol is proposed, which is composed of the nominal formation term and the induced attack term. Meanwhile, the induced attack design criterion is proposed by utilizing a robust scheme, where the robust performance bound can be configured by two performance regulating parameters and can be used to design the appropriate regulated attack matrix. Furthermore, by establishing the projection of the induced attack signal onto the formation agreement subspace, an explicit expression of the prescribed reference trajectory is determined, which depicts the movement trajectory of the entire formation of the multiagent system under the induced attack. Finally, a simulation is provided to vindicate the effectiveness of theoretical results.

Enhanced numerical modeling of natural heat convective phase change for generalized non-Newtonian fluids at high Rayleigh number

Numerical modeling of convective heat transfer employing non-Newtonian fluids is a key issue and represent an interesting challenge in many engineering applications. For this reason, this work develops an enhanced numerical model to predict fast and accurately the convective phase change for generalized non-Newtonian fluids. The strongly thermally coupled model is solved by an improved pressure-correction algorithm (SIMPLERnP) and the Finite Volume Method with accuracy of the third order for the transient terms and second order for the convective boundary conditions and the velocity gradients that allows to calculate the apparent viscosity. The study examines the natural heat convective solidification of the ternary Al-27 %Cu-5.25 %Si alloy with the Herschel-Bulkley rheology at a high Rayleigh number (>107). In addressing the main problem, four crucial aspects are discussed: the validation of the numerical scheme with numerical and experimental results; the modeling of the non-linear temperature variation of the liquid phase change fraction; the non-Newtonian effects of the power index (0.1 ≤ n ≤ 1.9) and yield stress (0≤τ0≤5 Pa) on the heat transfer mechanisms; and finally, the time of computation with the high-order numerical scheme and the enhanced pressure-correction algorithm. The main finding is that FVM/SIMPLERnP provides a significant reduction in the time of computation compared to reliable pressure-correction schemes (SIMPLER and IDEAL), being a robust, accurate and efficient scheme to solve complex natural heat convective phase change problems involve generalized non-Newtonian fluids at high-Rayleigh numbers.

A Robust Model Order Reduction Scheme for Lithium-Ion Batteries in Control-Oriented Vehicle Models

The role of batteries in electrification of vehicles is eminent; thus, a dynamic model that represents the physics-based phenomena of the battery system at a minimum computational cost is essential in the model-based design of electrified vehicle control systems. Furthermore, robustness of the reduced-order battery model when maintaining the dominant physics-based phenomena governing the dynamic behavior of the battery system is crucial. Characterization of the power signal applied to the lithium-ion battery in the energy management controller of a plug-in hybrid electric vehicle shows that there is a dominant frequency range in the input signal to the battery. This key feature can be considered as a basis to construct a reduced-order model in which the training input is different from the original power signal. The original idea in this paper is to generate the training input by applying a low-pass filter to the white-noise random signal to maintain the same dominant frequency range observed in the original power signal. Response of the reduced-order model, constructed using the proper orthogonal decomposition, compared to the high-fidelity battery model shows promising results; a maximum relative error of 1% was obtained for the battery state of charge while simulation time was reduced by 42.9%.

Lowest-degree robust finite element schemes for inhomogeneous bi-Laplace problems

In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respectively for an inhomogeneous fourth-order elliptic singular perturbation problem and for the Helmholtz transmission eigenvalue problem. The new methods use the reduced rectangle Morley (RRM for short) element space with piecewise quadratic polynomials, which are of the lowest degree possible. For the finite element space, a discrete analogue of an equality by Grisvard is proved for the stability issue and a locally-averaged interpolation operator is constructed for the approximation issue. Optimal convergence rates of the schemes are proved, and numerical experiments are given to verify the theoretical analysis.

Robust Scheme on 3D Hybrid Meshes with Non-conformity for Maxwell’s Equations in Time Domain

Robust Scheme on 3D Hybrid Meshes with Non-conformity for Maxwell’s Equations in Time Domain

A New Robust Iterative Scheme Applied in Solving a Fractional Diffusion Model for Oxygen Delivery via a Capillary of Tissues

In this paper, we constructed a new and robust fixed point iterative scheme called the UO iterative scheme for the approximation of a contraction mapping. The scheme converges strongly to the fixed point of a contraction mapping. A rate of convergence result is shown with an example, and our scheme, when compared, converges faster than some existing iterative schemes in the literature. Furthermore, the stability and data dependence results are shown. Our new scheme is applied in the approximation of the solution to the oxygen diffusion model. Finally, our results are applied in the approximation of the solution to the boundary value problems using Green’s functions with an example.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Robust inversion of 1D magnetotelluric data using the Huber loss function

In this study, a robust 1D inversion was performed on magnetotelluric (MT) data by utilizing the Huber loss function to avoid misleading interpretation of results, which is caused by the presence of outliers in the data. The MT method utilizes the ratio between the electric field (E) and the magnetic field (H), which are perpendicular to each other, to obtain impedance values (Z). These values are used to extract subsurface information in the form of electrical resistivity variations with depth. In the study, forward modeling of the 1D MT responses was conducted by recursively calculating Z values. Robust inversion was performed using the Huber loss function as an objective function to minimize the difference between the calculated and observed data. The Huber loss function combines the squared loss and the absolute loss to anticipate the presence of outliers in MT observation data. The robust inversion was performed on synthetic data with additional noise and field data. The inversion process utilized 50 layers with a thickness of 500 m, a hyperparameter δ=5×10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\delta }= 5\ imes {10}^{-2}$$\\end{document}, λ=0.01\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =0.01$$\\end{document}, and λt=100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\lambda }_{t}=100$$\\end{document}. The number of iterations used was 500 for inversions that used synthetic data and 3000 for inversions that used field data. The robust inversion scheme using the Huber loss function successfully overcame the presence of outliers and accurately estimated the actual model parameters, both for synthetic data and field data that contained outliers. The misfit was relatively small and close to zero, indicating that the inversion code works well.

Shape optimization of embedded solids using implicit Vertex-Morphing

One of the biggest challenges in optimizing the shape of complex solids is the requirement to maintain a reasonable mesh quality not only at the boundary but also for the bulk discretization of the interior. Thus, additional regularization and, in many cases, re-meshing of the structure during the iterative process is unavoidable with a Lagrangian description. By tracking the shape update using an Eulerian representation, embedded boundary methods are a promising technique for eliminating mesh distortion problems.This work consistently combines the unique features of implicit Vertex-Morphing and embedded boundary methods, facilitating the node-based shape optimization of solids with industrial complexity. One of the crucial elements for solving the primal problem on a fixed background grid is an efficient and robust quadrature scheme. To this end, we incorporate the open-source C++ framework QuESo (https://github.com/manuelmessmer/QuESo) developed for the numerical integration of arbitrarily complex embedded solids defined by oriented boundary meshes, e.g., in STereoLithography (STL) format. Meanwhile, applying the Helmholtz/Sobolev-based (implicit) filter to the vertices of the embedded boundary mesh not only exploits the extensive design space of node-based optimization but also ensures robust control over the feature size. To realize the above methodology, this work introduces a novel sensitivity analysis that yields mesh-independent shape gradients with respect to the immersed boundary. Through a specific sensitivity weighting, we recover a continuous gradient field from discrete values calculated at the nodes of the background grid. In addition, the presented workflow ensures robust enforcement of challenging geometrical constraints, including minimum wall thicknesses and design space limitations.We critically assess our approach with benchmarks and structures of industrial relevance. In all examples, trivariate B-Spline bases span the background grid, providing highly accurate finite element solutions and shape sensitivities at every iteration. Moreover, the elimination of mesh distortion problems enables a successful termination at the local optimum, even for large shape modifications.

A physical tire model for real-time simulations

We present a novel tire brush model with carcass flexibility, primarily designed for real-time applications while preserving the physical significance of its parameters. The tire’s geometry is discretized and represented using a series of ribs, each intersecting the local road surface independently, on the other hand carcass in-plane fore-aft displacement, in-plane deflection, and out-of-plane sidewall torsion are approximated through a second-order polynomial. Forces and torques originating from the tire–road contact area are described using brush mechanics, where bristles’ kinematics is directly linked to carcass deformation. Extensive effort is dedicated to understanding the possible sources of instability, as well as describing and implementing a robust numerical scheme to effectively solve the nonlinear system of equations arising from the modeling. Timing performance results are provided to demonstrate the suitability of the presented model for demanding hard real-time simulations. Finally, validation of the presented tire model is carried out by fitting experimental data and comparing it with the state-of-the-art Magic Formula model, proving its reliability and accuracy in reproducing tire behavior.

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term.

We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.