Operator Splitting Research Articles

Risk Factors for Hardware Removal Following Bimaxillary Surgery: A National Database Analysis.

Orthognathic surgery typically relies on the rigid fixation of fracture fragments using metal hardware. Though hardware is usually intended to be implanted permanently, the removal of hardware (ROH) is sometimes indicated for a variety of reasons. The authors sought to identify risk factors for ROH following orthognathic surgery. The authors conducted a retrospective analysis of the Merative MarketScan Research Databases, 2007-2021 using Current Procedural Terminology (CPT) and International Classification of Disease (ICD-9 and ICD-10) codes to identify patients who underwent an index Le Fort 1 osteotomy and bilateral sagittal split osteotomy operation on the same day. Statistical analysis involved χ2, Shapiro-Wilk, Wilcoxon-Mann-Whitney, Poisson regression, and multivariable logistic regression tests. 4698 patients met the inclusion criteria. The mean age at surgery was 25 years, and 57% were female. ROH occurred in 5.9% of patients. The mean time to hardware removal was 190.5±172.4 days. In a multivariate logistic regression, increased odds of ROH were associated with older patient age [OR: 1.02 (1.01-1.03), P=0.046], sleep apnea [OR: 1.62 (1.13-2.32), P=0.018], and craniofacial syndrome and/or cleft diagnoses [OR: 1.88 (1.14-2.55), P<0.001]. In the same model, postoperative oral antibiotic prophylaxis was not associated with ROH (P=0.494). The incidence of all-cause complications [IRR: 1.03 (1.01-1.05), P<0.001] rose over the study period, while the incidence of ROH did not change significantly (P=0.281). Patients at elevated risk should be counseled on the increased possibility of a second operation for ROH before having orthognathic surgery to ensure expectations and health care utilization decisions align with the evidence.

A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation

In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method.

Incompatible-mode geometrically non-linear finite element for micropolar elasticity

In this work a new three-dimensional geometrically non-linear hexahedral micropolar finite element enhanced with incompatible modes is presented. The analytical model is expressed in terms of Biot-like stress and couple-stress tensors and corresponding Biot-like strain and curvature tensors, with a linear, elastic and isotropic constitutive law. The numerical model is derived based on the principle of virtual work, and the residual derivation together with the linearisation and static condensation procedure is given in detail. The newly developed finite element is tested against the analytical solution of the geometrically non-linear micropolar pure bending problem and the element accuracy and robustness is compared against hexahedral Lagrangian finite elements of first and second order on several numerical examples. It is shown that the newly presented element is fast convergent, more robust and more accurate than the available Lagrangian elements. Moreover, the operator split and static condensation provide for a significantly lower computational cost than standard elements.

WELL-BALANCED ALGORITHM AND HEIGHT FUNCTION METHOD FOR DYNAMIC CONTACT ANGLE IN TWO-PHASE SYSTEMS

The well-balanced algorithm combined with dynamic contact angle was well studied in the literature but was never implemented with the pressure-implicit with splitting of operators (PISO) algorithm in a collocated grid commonly used in an incompressible, transient simulation. This article presents a well-balanced algorithm for PISO schemes coupling with the height function method for curvature estimation. The dynamic contact angle model from Kistler and Cox is also integrated to improve the modelling of the curvature at the wall boundary. In collocated finite volume schemes, the well-balanced PISO algorithm is developed by modifying both the calculation of the gradients in the momentum equation and the Rhie and Chow algorithm. This new gradient calculation method ensures that surface tension force and pressure gradient are identically discretized at the same location. The Rhie and Chow algorithm is also modified by adding the surface tension force to balance the pressure forces. The stationary droplet case in two-dimensions is presented first to validate the proposed methodology. The well-balanced algorithm coupling with the height function method shows its benefits by damping spurious currents by two to three orders of magnitude. The 3D surface-driven flow and water-spreading droplets are then simulated; the results show that the new scheme coupled with dynamic contact angle model outperforms the unbalanced scheme of the smooth void fraction method for theoretical and experimental comparisons.

A fast and efficient numerical algorithm for image segmentation and denoising

&lt;abstract&gt;&lt;p&gt;Image segmentation is the process of partitioning an image into homogenous regions, and represents one of the most fundamental and important procedures in image processing. Image denoising is a process to remove unwanted noise from a digital image, enhancing its visual quality. Various algorithms, like non-local means and deep learning-based approaches, have been developed to remove noise while preserving important image details. Currently, the prevalent application of pattern recognition technology is achieved through the implementation of image segmentation algorithms. In this study, we present a new, highly efficient, and fast computational scheme specifically developed for a phase-field mathematical model of image segmentation. The numerical methodology is based on an operator splitting method (OSM). The split operators are solved by using closed-form analytic solutions and a finite difference method (FDM) with an alternating direction explicit (ADE) method. To show the notable efficiency and rapid computational performance of the proposed computational algorithm, we conduct a series of numerical experiments. Through these computational tests, we confirm a significant contribution to the advancement of methodologies employed in the critical domain of image processing.&lt;/p&gt;&lt;/abstract&gt;

A combined first and fractional order regularization method for mixed Poisson-white spike noisy image restoration

In this paper we study the problem of restoring images affected by mixed Poisson-Square Cauchy noise. A multi-convex variational model is derived by integrating infimal convolution likelihood into a process of joint maximum a posteriori estimation, where a modified four-directional fractional-order total variation is united with the first order total variation to characterize the image prior. To solve the proposed model numerically, a block coefficient descent based algorithm is derived, in which variable splitting and alternating direction minimization of multipliers are utilized along with anisotropic diffusion and additive operator splitting to gain efficiency and quality. The obtained numerical results are compared with results obtained from two other total variation regularized models with different fidelities. The numerical discuss confirms the flexibility and validity of the proposed model.

Data transfers for full core heterogeneous reactor high-fidelity multiphysics studies

Multiphysics simulations for nuclear reactor analysis are usually performed by resorting to operator splitting and fixed point iterations between single-physics solvers. This enables the separate solution of each physics, such as neutronics, fuel performance, and thermal hydraulics, on meshes tailored to the requirements of the respective numerical discretizations of the equations. As the equations are coupled, several fields must be transferred between singlephysics solves. Projecting fields between meshes while preserving order of accuracy, conservation properties, and mapping non-overlapping geometries is a complex endeavour. This conference paper will present the transfers as implemented in MOOSE, which can handle arbitrary meshes, arbitrary mappings, conservation of integral quantities, and are made to scale with distributed simulations on both ends of the transfers. Their adequacy for advanced nuclear reactor multiphysics coupling is shown through examples and numerical studies.

The ADMM algorithm for audio signal recovery and performance modification with the dual Douglas-Rachford dynamical system

&lt;abstract&gt;&lt;p&gt;Practitioners employ operator splitting methods—such as alternating direction method of multipliers (ADMM) and its "dual" Douglas-Rachford method (DR)—to solve many kinds of optimization problems. We provide a gentle introduction to these algorithms, and illustrations of their duality-like relationship in the context of solving basis pursuit problems for audio signal recovery. Recently, researchers have used the dynamical systems associated with the iterates of splitting methods to motivate the development of schemes to improve performance. These developments include a class of methods that act by iteratively minimizing surrogates for a Lyapunov function for the dynamical system. An exemplar of this class is currently state-of-the-art for the feasibility problem of finding wavelets with special structure. Early experimental evidence has also suggested that, when implemented in a primal-dual (ADMM and DR) framework, this exemplar may provide improved performance for basis pursuit problems. We provide a reasonable way to compute the updates for this exemplar, and we study the application of this method to the aforementioned basis pursuit audio problems. We provide experimental results and visualizations of the dynamical system for the dual DR sequence. We observe that for highly structured problems with real data, the algorithmic behavior is noticeably different than for randomly generated problems.&lt;/p&gt;&lt;/abstract&gt;

SOD2D: A GPU-enabled Spectral Finite Elements Method for compressible scale-resolving simulations

As new supercomputer architectures become more heavily focused on using hardware accelerators, in particular general-purpose graphical processors, it is therefore relevant that algorithms for computational fluid dynamics, especially those targeting scale-resolving simulations, be designed in such a way as to make efficient use of such hardware.In this paper, we propose one such hardware-accelerated Continuous Galerkin Finite Elements model, aimed at handling simulations of turbulent compressible flows over complex geometries. As this model is intended for use in Large-Eddy and Direct Numerical simulations, it is necessary that the resulting scheme introduces only small amounts of artificial (numerical) diffusion for stabilization purposes. We achieve this through a combination of Spectral Finite Elements, operator splittings on the convective term, and the use of the Entropy Viscosity stabilization model adapted to spectral elements scheme.The paper will present the resulting algorithm, how it is made to work efficiently on the accelerators, and results obtained that demonstrate its high-accuracy capabilities.

An endeavor from the Glowinski-Le Tallec splitting for approximating the solution of Kawarada equation

This paper studies an extended application of the Glowinski-Le Tallec splitting for approximating solutions of linear and nonlinear partial differential equations. It is shown that the three-level, six-component operator decomposition, originally designed for Lagrangian optimizations, provides a stable second-order operator splitting approximation for the solutions of evolutional partial differential equations. It is also found that the Glowinski-Le Tallec formula not only provides an effective enhancement to conventional two-level, four-component ADI and LOD methods, but also introduces a flexible way for constructing multi-parameter operator splitting strategies in respective spaces where broad spectrums of mathematical models may exist for important natural phenomena and applications. The extended operator splitting is utilized for solving a singular and nonlinear Kawarada problem satisfactorily. Multiple simulation results are presented.

Solving inverse problems with sparse noisy data, operator splitting and physics-constrained machine learning

Solving inverse problems with sparse noisy data, operator splitting and physics-constrained machine learning

Energy dissipation and maximum bound principle preserving scheme for solving a nonlocal ternary Allen-Cahn model

We present a new energy dissipation and maximum bound principle preserving scheme for solving a nonlocal ternary Allen-Cahn (NtAC) model, where the standard Laplace operator is deliberately replaced with a spatial convolution term that aims at describing long-range interactions among particles and the structure-preserving scheme is obtained based on the operator splitting method. The discrete maximum bound principle and global convergence of the new scheme are analyzed rigorously. Moreover, the scheme is strictly dissipative for a modified energy, which coincides with the original energy up to O(τ), where τ is the time step. To the best of our knowledge, this is the first work to show that the operator splitting method can guarantee the maximum bound principle for a ternary Allen-Cahn model. Various 2D/3D numerical experiments including the NtAC model with mass conservation are tested to verify the bound-preserving and energy-stable properties of the resulted scheme.

Weed Identification Using Convolution Neural Networks

Deep learning is the core component of the machine learning field which employs knowledge representation for learning. Learning can be supervised or unsupervised. More deep learning techniques can be used which will contain deep belief, deep neural, recurrent neural networks in it which will be used in many fields. The most commonly used applications in deep learning are vision, audio, video, language processing, social media, medical, gaming and there are so many other programs where this deep learning has already produced very perfect results when compared to other cases and in a very little number of cases with superior to experts i.e. humans. Techno Agriculture is the domain where the farmers will get benefited from these latest improvements in the expert system. One of main objectives is that in order to remove weeds or unwanted plants by reduction in the usage of herbicides and to decrease the pollution in both crop and water. One of the Neural Networks i.e. CNN uses a flexible layer with the function of a ReLU to extract image elements and then uses a high-resolution and fully integrated RELU layer to separate weeds from the plant. The image which was processed previously is used on the convolution neural network which in return gives an image from the Region of Interest (ROI) from where it will extract the image and remove the certain aspects of the image in the training phase, after the training a splitting operation will be performed and the weeds are therefore classified by using the deep learning technique. In this scenario we trained 100 images in order to increase the accuracy of the model.

A conformal beam splitter with polarization transformation operation

A multifunctional beam splitting frequency selective surface (FSS) is modeled, analyzed, and tested in transmission and reflection modes. The proposed FSS comprises a C-shaped split-ring resonator designed and fabricated on an ultrathin, flexible polyimide material. When a linearly polarized incident wave interacts with the unit cell of the proposed FSS, half of the wave is reflected, and the other half is transmitted at two frequency bands from 5.8–6.2 GHz and 18.5–22 GHz. Moreover, the proposed FSS is angularly stable upto 40° and also performs simultaneous beam splitting and quarter-wave operation within one of its two bands of operation i.e., from 16.5–18.2 GHz. Such flexible beam splitting FSSs with polarization transformation operation and having angular stability, size miniaturization and multi-band operation is a specialized component having potential to be used for electromagnetic wave manipulation in antenna systems, radar technology, stealth technology, wireless communication, satellite communication, medical imaging, security and surveillance, aerospace and defense, and automotive radar.

A semi-Lagrangian Splitting framework for the simulation of non-hydrostatic free-surface flows

Incorporation of the free-surface dynamics plays an important role in the numerical modelling of non-hydrostatic flows. In the present work a novel semi-Lagrangian splitting (SLS) scheme for the free-surface Euler system is proposed.Using the operator splitting technique, the three main components emerge: the multilayer Shallow Water Equations (mSWE) (enforcing the free-surface kinematics), the Vertical Remeshing Operator (VRO) (that blends the Eulerian and Lagrangian techniques) and the Pressure Correction Operator (PCO) (that is a classic elliptic equation used in projection-type pressure coupling schemes). The first two are solved by two separate Finite Volume schemes, while the latter is resolved in a Finite Difference manner.In order to assess the SLS’s performance, numerical simulations of periodic waves and solitons propagating over variable bathymetry are performed. The last case concerns the propagation of waves on top of a shear current, showcasing the use of the SLS on rotational flows. The results are compared with experiments and analytic relations and the method is proven to be robust and efficient.

Convergence analysis of operator splitting methods for Maxwell’s equations in dispersive media of Debye type

Convergence analysis of operator splitting methods for Maxwell’s equations in dispersive media of Debye type

A Multiobjective Optimization Application to Control the Aedes Aegypti Mosquito using a Two-Dimensional Diffusion-Reaction Model

Aedes aegypti is the main vector of multiple diseases, such as dengue, yellow fever, Zika, and chikungunya. Diseases associated with mosquitoes have been growing in recent years, with more than one-third of the world population at risk. Control techniques have been studied to prevent the spread of the Aedes aegypti, such that new formula and how to use adulticides and larvicides, among others. This paper proposes a novel approach in the field of partial differential equations and optimization. We consider a two-dimensional diffusion-reaction model that describes the interaction between aquatic and adult female stages spreading across a domain with parameters dependent on rainfall and temperature. We also formulate a mono-objective and multiobjective optimization problem to minimize the Aedes aegypti populations and the control, considering the application of adulticides and larvicides, using actual data from the city of Lavras/Brazil. The operator splitting technique is used to solve the diffusion-reaction system, coupling finite difference and the fourth-order Runge-Kutta method and optimal solutions were searched by using the Real-Biased Genetic Algorithm and Non-dominated Sorting Genetic Algorithm -II. Numerical results show significant reduction of the Aedes aegypti population.

A variational driven optimization framework for pansharpening of multispectral images

ABSTRACT Pansharpening is an established remote sensing image fusion technique that yields a high-resolution multispectral (HRMS) image. Despite the fact that the advanced technologies like sparse coding and deep learning have achieved a remarkable improvement in solving the pansharpening problem, a unified model is required to further enhance the fusion quality. The variational optimisation (VO) mechanism has gained interest of most of the researchers in recent years. In this article, pansharpening is designated as a constrained optimisation problem with a data generative term and two regularisers to ameliorate spatial details and spectral information. The gradient information is exploited to impart the spatial details from the panchromatic image to the fused image. The correlation among multispectral image bands inspired to promote the spectral quality of the HRMS image as well as to reduce the distortion. Consequently, the optimisation problem is efficiently solved for the required HRMS image using the operator splitting approach. The extensive experiments performed in accordance with the well-known protocols rationalise that the proposed model outperforms most of the state-of-the-art methods in terms of objective metrics and visual outcomes.

An interwoven composite tailored finite point method for two dimensional unsteady Burgers' equation

This paper centers on constructing a lucid and utilitarian approach to tackle linear and non-linear two-dimensional partial differential equations. To test the applicability of the proposed algorithm a variant of the classical two-dimensional unsteady Burgers' equation is set up as a testing ground. The method in a nutshell reduces to solving one-dimensional Burgers' equations resulting from the application of appropriate operator splitting techniques in the temporal direction. In solving these one-dimensional Burgers' equations a refined tailored finite point method in conjunction with an apposite linearization to the purpose is employed. The conditional stability, consistency, and convergence of the method are established theoretically and the method is found to be first-order convergent in time and second-order convergent in space. To illustrate the accuracy of the scheme, divers examples have been solved and the results obtained prove that this method is top-notch in terms of cost-cutting and time efficiency through the sufficiency of coarse meshes.

Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type

The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and parabolic type comprise the Laplacian, a potential acting as multiplication operator, and a cubic nonlinearity. Moreover, an invariance principle is deduced that has a significant impact on the efficient realisation of the resulting modified operator splitting methods for the Schrödinger case.Numerical illustrations for the time-dependent Gross–Pitaevskii equation in the physically most relevant case of three space dimensions and for its parabolic counterpart related to ground state and excited state computations confirm the benefits of the proposed fourth-order modified operator splitting method in comparison with standard splitting methods.The presented results are novel and of particular interest from both, a theoretical perspective to inspire future investigations of modified operator splitting methods for other classes of nonlinear evolution equations and a practical perspective to advance the reliable and efficient simulation of Gross–Pitaevskii systems in real and imaginary time.