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This study investigates the decomposition of bath correlation functions (BCFs) in terms of complex exponential functions, with an eye on the realistic modeling of open quantum systems based on the hierarchical equations of motion. We introduce the theoretical background of various decomposition schemes in both time and frequency domains and assess their efficiency and accuracy by demonstrating the decomposition of various BCFs. We further develop a new procedure for the decomposition of BCFs originating from highly structured spectral densities with a high accuracy and compare it with existing fitting techniques. Advantages and disadvantages of each methodology are discussed in detail with special attention to their application to the corresponding quantum dynamical problem. This work provides fundamental tools for choosing and using a variety of decomposition techniques of BCFs for the study of open quantum systems in structured environments. [ABSTRACT FROM AUTHOR]

One of the most common shoulder injuries is the rotator cuff tear (RCT). The risk of RCTs increases with age, with a prevalence of 9.7 % in those under 20 years old and up to 62 % in individuals aged 80 years and older. In this article, we present first a microwave digital twin prototype (MDTP) for RCT detection, based on machine learning (ML) and advanced numerical modeling of the system. We generate a generalizable dataset of scattering parameters through flexible numerical modeling in order to bypass real-world data collection challenges. This involves solving the linear system as a result of finite element discretization of the forward problem with use of the domain decomposition method to accelerate the computations. We use a support vector machine (SVM) to differentiate between injured and healthy shoulder models. This approach is more efficient in terms of required memory resources and computing time compared with traditional imaging methods. [ABSTRACT FROM AUTHOR]

The phase field modeling of fracture is able to simulate the nucleation and the propagation of complex crack patterns. However, the relatively small internal lengths that are required usually lead to very fine meshes and high computational costs, especially for three‐dimensional applications. In the present work, additional cost also comes from the implicit dynamics regularization of unstable crack propagations which potentially leads to a large variation of time steps when switching from quasi‐static to dynamic regimes. To reduce the time to solution in this context, this study proposes a domain decomposition framework and acceleration techniques for the phase field fracture staggered solver. The displacement subproblem and the phase field one are solved with parallel domain decomposition solvers. Dual domain decomposition methods provide low cost preconditioner well adapted to the phase field subproblem. For displacement subproblems undergoing unstable crack propagations, primal domain decomposition methods are preferred to be less sensitive to the treatment of floating substructures. Preconditioners performances are assessed and scalability studies over academic test cases, up to 324 subdomains, are presented. Finally, the robustness of the approach is illustrated on two semi‐industrial simulations. [ABSTRACT FROM AUTHOR]

The physics-informed neural networks (PINNs) have shown great potential in solving a variety of high-dimensional partial differential equations (PDEs), but the complexity of a realistic problem still restricts the practical application of the PINNs for solving most complicated PDEs. In this paper, we propose a parallel framework for PINNs that is capable of modeling two-phase flows with complicated interface evolution. The proposed framework divides the problem into several simplified subproblems and solves them through training several PINNs on corresponding subdomains simultaneously. To enhance the accuracy of the parallel training framework in two-phase flow, the overlapping domain decomposition method is adopted. The optimal subnetwork sizes and partitioned method are systematically discussed, and a series of cases including a bubble rising, droplet splashing, and the Rayleigh–Taylor instability are applied for quantitative validation. The maximum relative error of quantitative values in these cases is 0.1319. Our results show that the proposed framework not only can accelerate the training procedure of PINNs, but also can capture the spatiotemporal evolution of the interface between various phases. This framework overcomes the difficulties of training PINNs to solve a forward problem in two-phase flow, and it is expected to model more realistic dynamic systems in nature. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid approach, merging the two-grid and domain decomposition strategies, to address the coupled Navier-Stokes-Darcy challenge, which is then elaborated and examined. First, the current Robin boundary condition-based domain decomposition technique is used to get the approximate solution on the coarse grid. Following the substitution of certain interface elements with coarse meshbased functions, an improved fine grid problem is obtained. [ABSTRACT FROM AUTHOR]

This paper presents an electromagnetic finite element analysis method using domain decomposition based on the Finite Element Tearing and Interconnecting (FETI) method. This method specifically addresses the extended FETI techniques of FETI-dual, FETI-DP, and FETI-H. The accuracy of the solutions obtained from each method was validated using the electromagnetic scattering field and the Radar Cross Section (RCS) of a PEC cube. It was demonstrated that the FETI-H method, which employs a First-Order Transmission Condition (FOTC) at the subdomain boundaries, exhibits improved convergence and computation speed. [ABSTRACT FROM AUTHOR]

The Neumann–Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann–Neumann methods that have better convergence properties and require fewer computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov–Poincaré operators. [ABSTRACT FROM AUTHOR]

The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Schur complement of the finite element stiffness matrix with respect to the interior variables. Since both matrices correctly approximate the same object, the Steklov-Poincaré operator, it is natural to assume that the matrices corresponding to the same fine boundary discretization are similar. However, this note shows that the distribution of the spectrum of the boundary element stiffness matrix is significantly better conditioned than the finite element Schur complement. The effect of the favorable conditioning of BETI clusters is demonstrated by solving huge problems by H-TBETI-DP and H-TFETI-DP. [ABSTRACT FROM AUTHOR]

We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination method) is based on the Uzawa method by decoupling the linear system, while the second algorithm (Global inversion) is based on the overall resolution of the system by the GMRES method. A detailed implementation is proposed and some numerical tests are carried out in two and three dimensions and where the domain is multiply connected. [ABSTRACT FROM AUTHOR]

We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm. [ABSTRACT FROM AUTHOR]

With the aid of hardware and software developments, there has been a surge of interest in solving PDEs by deep learning techniques, and the integration with domain decomposition strategies has recently attracted considerable attention due to its enhanced representation and parallelization capacity of the network solution. While there are already several works that substitute the numerical solver of overlapping Schwarz methods with the deep learning approach, the nonoverlapping counterpart has not been thoroughly studied yet because of the inevitable interface overfitting problem that would propagate the errors to neighboring subdomains and eventually hamper the convergence of outer iteration. In this work, a novel learning approach, i.e., the compensated deep Ritz method using neural network extension operators, is proposed to enable the flux transmission across subregion interfaces with guaranteed accuracy, thereby allowing us to construct effective learning algorithms for realizing the more general nonoverlapping domain decomposition methods in the presence of overfitted interface conditions. Numerical experiments on a series of elliptic boundary value problems, including the regular and irregular interfaces, low and high dimensions, and smooth and high-contrast coefficients on multi domains, are carried out to validate the effectiveness of our proposed domain decomposition learning algorithms. [ABSTRACT FROM AUTHOR]

We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semidiscretization, we use the Lagrange multiplier approach to derive a coupled forward-backward optimality system, which can then be solved using a time domain decomposition. Due to the forwardbackward structure of the optimality system, three variants can be found for the Dirichlet-Neumann and Neumann-Dirichlet algorithms. We analyze their convergence behavior and determine the optimal relaxation parameter for each algorithm. Our analysis reveals that the most natural algorithms are actually only good smoothers, and there are better choices which lead to efficient solvers. We illustrate our analysis with numerical experiments. [ABSTRACT FROM AUTHOR]

We introduce a new overlapping domain decomposition method (DDM) to solve fully nonlinear elliptic partial differential equations (PDEs) approximated with monotone schemes. While DDMs have been extensively studied for linear problems, their application to fully nonlinear PDEs remains limited in the literature. To address this gap, we establish a proof of global convergence of these new iterative algorithms using a discrete comparison principle argument. We also provide a specific implementation for the Monge-Ampére equation. Several numerical tests are performed to validate the convergence theorem. These numerical experiments involve examples of varying regularity. Computational experiments show that method is efficient, robust, and requires relatively few iterations to converge. The results reveal great potential for DDM methods to lead to highly efficient and parallelizable solvers for large-scale problems that are computationally intractable using existing solution methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the use of vibration measurements for the purpose of cost-effective performance evaluation for the safety management and maintenance of Japan's social infrastructure like bridges. Since modal properties are often used to diagnose damage of structures by analysing their changes, various modal identification methods have been developed in the past few decades. Among these, the FDD method has still attractive attention because of its simplicity and practicality. It is also highly applicable to simultaneous observation at multiple points and even complex modes can be identified instantly. On the other hand, the applicability of this method to impact tests applied to evaluate the condition of structures has not been sufficiently discussed to date. In this study, we will clarify the applicability to impact tests by reconstructing the theoretical background of the FDD method. Furthermore, we will show from theory that when there is a correlation between inputs, higher-order singular values, which should be noted when applied to impact tests, will be affected. The conclusions obtained from the reconstruction of the theoretical background will be verified based on numerical experiments and actual observation records. [ABSTRACT FROM AUTHOR]

To address the efficiency bottleneck encountered in reactor design calculations for the newly developed lead-based reactor neutronics analysis code system MOSASAUR, we recently developed acceleration functions based on various coarse-mesh finite difference (CMFD) methods and spatial domain decomposition parallel algorithm. However, the applicability of these improvements to different lead-based reactors remains to be analyzed. This work collected and established core models for various types of lead-based reactor. Based on different SN nodal transport solvers, we analyzed the acceleration performance of different CMFD methods, different CPU cores, and the combination of CMFD and parallel calculation. The results indicated that the impact of different CMFD acceleration or parallel acceleration on the calculation accuracy was negligible; the rCMFD method had good stability and convergence rate, achieving speedup of several to dozens; parallel efficiency was related to the number of meshes, and for large reactor cores, superlinear speedup was achieved with 200 CPU cores; rCMFD and parallel computing could achieve combined speedup, with 200 cores achieving speedup of hundreds to thousands, typically completing a reactor core transport calculation in 1 min. [ABSTRACT FROM AUTHOR]

The high-resolution 3D groundwater flow and transport simulation problem requires massive discrete linear systems to be solved, leading to significant computational time and memory requirements. The domain decomposition method is a promising technique that facilitates the parallelization of problems with minimal communication overhead by dividing the computation domain into multiple subdomains. However, directly utilizing a domain decomposition scheme to solve massive linear systems becomes impractical due to the bottleneck in algebraic operations required to coordinate the results of subdomains. In this paper, we propose a two-level domain decomposition method, named dual-domain decomposition, to efficiently solve the massive discrete linear systems in high-resolution 3D groundwater simulations. The first level of domain decomposition partitions the linear system problem into independent linear sub-problems across multiple subdomains, enabling parallel solutions with significantly reduced complexity. The second level introduces a domain decomposition preconditioner to solve the linear system, known as the Schur system, used to coordinate results from subdomains across their boundaries. This additional level of decomposition parallelizes the preconditioning of the Schur system, addressing the bottleneck of the Schur system solution while improving its convergence rates. The dual-domain decomposition method facilitates the partition and distribution of the computation to be solved into independent finely grained computational subdomains, substantially reducing both computational and memory complexity. We demonstrate the scalability of our proposed method through its application to a high-resolution 3D simulation of chromium contaminant transport in groundwater. Our results indicate that our method outperforms both the vanilla domain decomposition method and the algebraic multigrid preconditioned method in terms of runtime, achieving up to 8.617× and 5.515× speedups, respectively, in solving massive problems with approximately 108 million degrees of freedom. Therefore, we recommend its effectiveness and reliability for high-resolution 3D simulations of groundwater flow and transport. [ABSTRACT FROM AUTHOR]

Polarizable continuum solvation models are popular in both, quantum chemistry and in biophysics, though typically with different requirements for the numerical methods. However, the recent trend of multiscale modeling can be expected to blur field‐specific differences. In this regard, numerical methods based on domain decomposition (dd) have been demonstrated to be sufficiently flexible to be applied all across these levels of theory while remaining systematically accurate and efficient. In this contribution, we present ddX, an open‐source implementation of dd‐methods for various solvation models, which features a uniform interface with classical as well as quantum descriptions of the solute, or any hybrid versions thereof. We explain the key concepts of the library design and its application program interface, and demonstrate the use of ddX for integrating into standard chemistry packages. Numerical tests illustrate the performance of ddX and its interfaces. This article is categorized under:Software > Quantum ChemistrySoftware > Simulation Methods [ABSTRACT FROM AUTHOR]

This paper derives optimized coefficients for optimized Schwarz iterations for the time-dependent Stokes–Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and discretization parameters that characterize the coupled problem, and they guarantee the robustness of the associated domain decomposition method. Numerical results validate the proposed approach in several test cases with physically relevant parameters. [ABSTRACT FROM AUTHOR]

It is known that physics‐informed learning become a new learning philosophy that has been applied in many scientific domains. However, this approach often struggles to achieve optimal performance in addressing the issue of multiphysics coupling. Here, for the first time, we extend this approach to modeling chemical reactor systems. We design a new decoupling–coupling training framework, which consists of decoupling pre‐training and multiphysics coupling training steps. With decoupling pre‐training, the complex physical domain is decomposed into subdomains of fluid flow, heat transfer, and mass transfer combined with reaction kinetics. Each subdomain is represented by a specialized neural network that can provide a coarse but reasonable distribution of network parameters for initializing the sub‐networks for the subsequent multiphysics coupling training. The capabilities of this approach, in comparison with the traditional CFD simulation, are demonstrated through an example of a plate reactor system with a heating cylinder. [ABSTRACT FROM AUTHOR]

Low-pressure discharge events have a major impact on a satellite's electrical performance. Most notably, a number of serious issues arise from the inability to directly modify satellite systems that operate in orbit. Accurate analysis of electrical performance is crucial for mitigating the issues arising from the low-pressure discharge phenomenon. Complex structures, such as intricate features and curved structures, are frequently used in satellite systems' enormous microwave components. In this case, the finite-difference time-domain (FDTD) approach proposes the hybrid implicit–explicit (HIE) algorithm with a domain decomposition method to effectively simulate complex structures under the low-pressure discharge phenomenon. The bilinear transform method is adjusted in accordance with the implicit equations for the anisotropic magnetized plasma environment caused by the discharge. To end unbounded lattices, a higher-order perfectly matched layer is used at the boundary. An example of a microwave connector structure is used to show how well the algorithm performs electrically. According to the findings, the suggested algorithm behaves in a way that is consistent with both the traditional algorithm and the experiments. Furthermore, the phenomenon of low-pressure discharge has a notable impact on the electrical performance of microwave components. [ABSTRACT FROM AUTHOR]

Nonequilibrium dynamics governed by electron–phonon (e-ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport equation (rt-BTE) with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations (phonons). Yet, a bottleneck of these simulations is the calculation of e–ph scattering integrals on dense momentum grids at each time step. Here we show a data-driven approach based on dynamic mode decomposition (DMD) that can accelerate the time propagation of the rt-BTE and identify dominant electronic processes. We apply this approach to two case studies, high-field charge transport and ultrafast excited electron relaxation. In both cases, simulating only a short time window of ~10% of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD extrapolation. Analysis of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or equilibrium. The combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials. [ABSTRACT FROM AUTHOR]

A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed finite element pair in the Darcy domain. Due to this choice, the method conserves linear momentum and mass locally in the Stokes domain and exhibits local mass conservation in the Darcy domain. The MAC scheme is reformulated as a mixed finite element method on a staggered grid, which allows for the proposed scheme to be analyzed as a mortar mixed finite element method. We show that the discrete system is well-posed and derive a priori error estimates that indicate first order convergence in all variables. The system can be reduced to an interface problem concerning only the mortar variables, leading to a non-overlapping domain decomposition method. Numerical examples are presented to illustrate the theoretical results and the applicability of the method. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Aluminum honeycomb sandwich structure with panels made of carbon fiber reinforced polymer (CFRP) are widely used in aerospace and other fields. Simulation of the eddy current (EC) testing of the sandwich structure using the finite element (FE) method is challenging as the traditional FE method has difficulties in mesh division and the solution of the algebraic equations. This paper proposes to use the domain decomposition FE method to solve such problems. The top CFRP panel, the aluminum honeycomb core, and the bottom CFRP panel of the sandwich structure and the ferrite core of the coil are placed in different subdomains and the subdomains are meshed independently. This method simplifies the mesh generation and does not require regenerating the meshes when simulating the scanning testing with the ferrite-core coil. In this way, the efficiency of simulation is greatly improved. The EC distributions in the sandwich structure are computed and the influence of defect on EC distribution is analyzed. The C scans of the sandwich structures are simulated. The images of the EC responses to the defects, such as wall fracture, node disconnection, and core wrinkle, are obtained. The simulation results are validated by experiments. [ABSTRACT FROM AUTHOR]

We aim to develop efficient and robust algorithms for nonsmooth nonlinear systems arising from complementarity problems. The semismooth Newton algorithm is popular due to its reliability and efficiency. However, it struggles with issues with imbalanced nonlinearities of the problems, leading to degraded convergence rates or failure despite help from the globalization techniques like linesearch or trust region. We introduce a right nonlinearly preconditioned semismooth Newton algorithm to address this difficulty. The critical success ingredient is that before each global Newton update, a nonlinear preconditioning step implicitly removes the so-called 'bad components' causing trouble via nonlinear subspace correction, inspired by Gaussian elimination but adapted nonlinearly to balance system nonlinearities. Additionally, our method integrates with a domain decomposition framework, enhancing parallelism. Numerical results on two classes of problems demonstrate significantly improved convergence over standard semismooth Newton methods. [ABSTRACT FROM AUTHOR]

In view of the problem that the output thrust of the solenoid actuator is affected by various factors and is difficult to calculate in actual working conditions, this paper proposes a semi-analytical model constructed by magnetic field subdomain method with internal and external boundary conditions in a cylindrical coordinate system for calculation, and the general solution equations of magnetic vector potential for each subdomain are derived and solved by MATLAB. Taking a push–pull electromagnet as an example, the finite element simulation and experimental comparative analysis are carried out. The correctness and applicable conditions of the subdomain method are illustrated by comparing the gradient plot of magnetic vector potential, inductance curve and electromagnetic force. It is shown that the results calculated by the subdomain method are very close to the finite element method when the magnetic saturation problem is neglected. However, when the nonlinearity of core permeability is considered, the magnetic saturation gradually deepens with the increase in current, and the error of the subdomain method calculation results gradually increases. Through simulation and experimental verification at slight magnetic saturation, the output thrust after considering the core gravity, spring force and electromagnetic force, it is shown that this method has the advantage of computational flexibility compared with the finite element method, and it is easier to write special algorithms according to various working conditions to calculate the important parameters in engineering applications. [ABSTRACT FROM AUTHOR]

The introduction of Bioresorbable Stents (BRS) in angioplasty (the clinical operation to reopen an occluded coronary with intravascular procedures), originally saluted as an important innovation, was a failure for many associated adverse events. Yet, the clinical community advocates for BRS as an unmet clinical need. The reason for the failures can be associated with the special size of the bioresorbable scaffold: the absence of a metallic core calls for an increased thickness, suspected of triggering abnormal flow patterns and biological inflammations, leading to adverse events. Accurate mathematical modeling of the fluid-wall-strut interaction and the related elution of the struts can provide a breakthrough for rigorous shape optimization. Here, we model in 3D the elution process involving all three domains (fluid, wall, and struts) coexisting together. Previous studies involved only two domains. Real cases show that the stent, the lumen, and the wall are in contact with every other subdomain. The multidomain case presents nontrivial challenges. We propose a domain decomposition approach for the numerical solution using an iterative-by-subdomain method. We prove the convergence of the iterative method. We provide preliminary results in idealized yet realistic 3D geometries. Results demonstrate that the iterative method is independent of the mesh size. [ABSTRACT FROM AUTHOR]

In this work, we propose a parallel grad‐div stabilized finite element algorithm for the Navier–Stokes equations attached with a nonlinear damping term, using a fully overlapping domain decomposition approach. In the proposed algorithm, we calculate a local solution in a defined subdomain on a global composite mesh which is fine around the defined subdomain and coarse in other regions. The algorithm is simple to carry out on the basis of available sequential solvers. By a local a priori estimate of the finite element solution, we deduce error bounds of the approximations from our presented algorithm. We perform also some numerical experiments to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature has focused on devising accurate numerical integration methods for neural networks (NNs), which is essential for getting accurate solutions. In this work, we propose adaptive quadratures for the accurate integration of neural networks and apply them to loss functions appearing in low-dimensional PDE discretisations. We show that at opposite ends of the spectrum, continuous piecewise linear (CPWL) activation functions enable one to bound the integration error, while smooth activations ease the convergence of the optimisation problem. We strike a balance by considering a CPWL approximation of a smooth activation function. The CPWL activation is used to obtain an adaptive decomposition of the domain into regions where the network is almost linear, and we derive an adaptive global quadrature from this mesh. The loss function is then obtained by evaluating the smooth network (together with other quantities, e.g., the forcing term) at the quadrature points. We propose a method to approximate a class of smooth activations by CPWL functions and show that it has a quadratic convergence rate. We then derive an upper bound for the overall integration error of our proposed adaptive quadrature. The benefits of our quadrature are evaluated on a strong and weak formulation of the Poisson equation in dimensions one and two. Our numerical experiments suggest that compared to Monte-Carlo integration, our adaptive quadrature makes the convergence of NNs quicker and more robust to parameter initialisation while needing significantly fewer integration points and keeping similar training times. [ABSTRACT FROM AUTHOR]

In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is characterized by a surface particle density and an out-of-plane dielectric permittivity in the region surrounding the single-layer. To avoid mesh refinements in such a region, we propose an interface problem based on the natural domain decomposition suggested by the physical device. Two different interface continuity conditions are discussed. Then, we write the corresponding variational formulations adapting the so called three-fields formulation for domain decomposition and we approximate them using a proper finite element method. Finally, numerical experiments are performed to illustrate some specific features of this interface approach. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive space-time algorithm based on domain decomposition for the large-scale simulation of a recently developed thermodynamically consistent reservoir problem. In the approach, the bound constraints are represented by means of a minimum-type complementarity function to enforce the positivity of the reservoir model, and a space-time mixed finite element method is applied for the parallel-in-time monolithic discretization. In particular, we propose a time-adaptive strategy using the improved backward differencing formula of second order, to take full advantage of the high degree of space-time parallelism. Moreover, the complicated dynamics with higher nonlinearity of space-time discretization require some innovative nonlinear and linear solution strategies. Therefore, we present a class of modified semismooth Newton algorithms to enhance the convergence rate of nonlinear iterations. Multilevel space-time restricted additive Schwarz algorithms, whose subdomains cover both space and time variables, are also studied for domain decomposition-based preconditioning. Numerical experiments demonstrate the robustness and parallel scalability of the proposed adaptive space-time algorithm on a supercomputer with tens of thousands of processor cores. [ABSTRACT FROM AUTHOR]

We investigate additive Schwarz methods for semilinear elliptic problems with convex energy functionals, which have wide scientific applications. A key observation is that the convergence rates of both one- and two-level additive Schwarz methods have bounds independent of the nonlinear term in the problem. That is, the convergence rates do not deteriorate by the presence of nonlinearity, so that solving a semilinear problem requires no more iterations than a linear problem. Moreover, the two-level method is scalable in the sense that the convergence rate of the method depends on H/h and H/δ only, where h and H are the typical diameters of an element and a subdomain, respectively, and δ measures the overlap among the subdomains. Numerical results are provided to support our theoretical findings. [ABSTRACT FROM AUTHOR]

Practical acoustic propagation modeling is significantly affected by ocean dynamics, and then can be exploited in numerous oceanic applications, where "practical" refers to modeling acoustic propagation in simulations that mimic real-world ocean environments. Physics-based numerical models provide approximate solutions of wave equation and rely on accurate prior environmental knowledge while the environment of practical scenarios is largely unknown. In contrast, data-driven machine learning offers a promising avenue to estimate practical acoustic propagation by learning from dataset. However, collecting such a high-quality, noise-free, and dense dataset remains challenging. Under the practical hurdle posed by the above approaches, the emergence of physics-informed neural network (PINN) presents an alternative to integrate physics and data but with limited representation capacity. In this work, a framework, termed spatial domain decomposition-based physics-informed neural networks (SPINNs), is proposed to enhance the representation capacity in spatially dependent oceanic scenarios and effectively learn from incomplete and biased prior physics and noisy dataset. Experiments demonstrate SPINNs' advantages over PINN in practical acoustic propagation estimation. The learning capacity of SPINNs toward physics and dataset during training is further analyzed. This work holds promise for practical applications and future expansion. [ABSTRACT FROM AUTHOR]

The Schwarz domain decomposition (SDD) method is known for its high efficacy in solving large-scale systems of partial differential equations, primarily due to its parallelizability. However, the method's reliance on iteration introduces substantial computational expenses. In this study, we propose a reduced-order Schwarz domain decomposition (ROSDD) method tailored specifically for the convection-diffusion equation. Utilizing the proper orthogonal decomposition (POD) technique, the ROSDD method significantly reduces computational costs by considering only a small number of unknowns. Since the equation typically exhibits convection-dominated behavior, we employ the characteristic finite element discretization scheme. Consequently, we derive optimal a priori error estimates to assess the accuracy of our approach. Finally, we conduct some numerical experiments to validate the superiority of the ROSDD method. [ABSTRACT FROM AUTHOR]

Background: Deep learning-based digital image correlation (DL-based DIC) has gained increasing attention in the last two years. However, existing DL-based DIC algorithms are impractical because their application scenarios are mostly limited to small deformations. Objective: To enable the use of DL-based DIC in real-world general experimental mechanics scenarios that would involve large deformations and rotations, we propose to improve DL-based DIC with the domain decomposition method (DDM). Methods: In the improved method, the region of interest is divided into subimages, and subimages are pre-aligned using the preregistered control points to effectively eliminate the large deformation components. The residual deformations in each subimage are small and limited, which can be well extracted using existing DL-based DIC methods. Results: Through synthesized and real-world experiments, the improved DL-based DIC method can achieve high-accuracy pixelwise matching in practical applications with strong robustness and high computational efficiency. Conclusions: The improved DL-based DIC combines the advantages of traditional and DL-based DIC methods but overcomes the limitations, greatly improving the robustness and applicability of existing DL-based methods. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of a synchronous Structural Health Monitoring (SHM) framework utilizing wireless, low-cost, and off-the-shelf components. Vibration-based condition monitoring plays a crucial role in assessing the reliability of structural systems by detecting damage through changes in vibration parameters. The adoption of low-cost Micro-Electro-Mechanical Systems (MEMS) sensors in Wireless Sensor Networks (WSNs) has gained traction, emphasizing the need for precise time synchronization to schedule wake-up times of multiple sensor nodes for data collection. To address this challenge, our proposed method introduces a TCP/IP socket programming-based mimic broadcasting mechanism and a scalable sensing network controlled by a central gateway, leveraging the Raspberry Pi Python platform. The system operates using Internet of Things (IoT) concepts and adopts a star topology, where a packet is transmitted from the gateway to initiate measurements simultaneously on multiple sensor nodes. The sensor node comprises a MEMS accelerometer, a real time clock DS3231 module and Raspberry Pi Zero 2W (RPi0-2W), while the gateway employs a Raspberry Pi 4 (RPi4). To ensure accurate time synchronization, all Pi0-2W nodes were configured as Network Time Protocol (NTP) clients, synchronizing with an RPi4 server using chrony, the reliable implementation of the NTP. Through experimental evaluations, the system demonstrates its effectiveness and reliability in achieving initial time synchronization. This study addresses the challenge of achieving precise time alignment between sensor nodes through the utilization of the Dynamic Time Wrapping (DTW) method for Frequency Domain Decomposition (FDD) applications. The contribution of this research significantly enhances the field by improving the accuracy and reliability of time-aligned measurements, with a specific focus on utilizing low-cost sensors. By developing a practical and cost-effective SHM framework, this work advances the accessibility and scalability of structural health monitoring solutions, facilitating more widespread adoption and implementation in various engineering applications [ABSTRACT FROM AUTHOR]

A problem of mathematical simulation of a fuel element region, including many fuel pellets and a cladding fragment, is considered in an axisymmetric formulation. It is assumed that the cladding is a thermoelastic-plastic body and that the pellet is a thermoelastic body with account for cracking of the material. Different variants of the domain decomposition method are used to numerically simulate the thermal and mechanical contact of pellets with each other and with the cladding. Calculation results are presented, in which the region containing ten pellets reaches a nominal power and the effect of pellet cracking on the thermomechanical state of the fuel element is estimated. [ABSTRACT FROM AUTHOR]

Transient high-frequency spherical wave propagation in the porous medium is studied using the Biot-JKD theory. The porous media is considered to be a composed of deformable solid skeleton and viscous incompressible fluid inside the pores. In order to treat the fractional proportionality of the dynamic tortuosity to the frequency (or equivalently, to time) due to the viscous interaction between solid and fluid phases, the fractional calculus theory along with the Laplace and Fourier transforms are used to solve the coupled governing partial differential equations of the scaler and vector potential functions obtained from the Helmholtz's decomposition in the Laplace domain. Both the longitudinal and transverse waves, additionally the reflection and transmission kernels are determined in detail at the Laplace domain. For the Laplace-to-time inversion transform, Durbin's numerical formula is used and the independence of the results from the involved tuning and accuracy parameters is checked. The effects of the porosity, dynamic tortuosity, characteristics length, etc. on the reflected pressure and stress are investigated. The general pattern of the results is similar to our previous knowledge of wave propagation. Further works and experiments may be conducted in future works for various applications. [ABSTRACT FROM AUTHOR]

Electromagnetic metamaterials possess characteristics such as having large-scale, periodic, multi-media, and complex geometric structures, making them highly suitable for simulation using the finite element domain decomposition method (DDM). This work proposes a non-conformal DDM for simulating finite-period metamaterials, achieving simulation with a minimal number of domains while significantly reducing computational resource consumption. First, the computational domain of the periodic metamaterial is partitioned into several non-conformal hexahedral subdomains. Subsequently, a limited number of non-repetitive subdomain models with non-matching grids are constructed, leveraging the three-dimensional rotational and translational properties of these subdomains to facilitate simulation. By eliminating the necessity to construct models for every subdomain, a substantial reduction in memory consumption is achieved. Second, an iteration method for solving the matrix equations of subdomains is enhanced by introducing a multifrontal block incomplete Cholesky decomposition preconditioner, thereby enhancing the computational efficiency of matrix equations with a large number of unknowns. Meanwhile, parallel computing techniques are employed to accelerate the proposed method. Finally, we integrate the aforementioned method into a solver and leverage it to develop an electromagnetic simulation tool tailored for metamaterials. The tool is employed to simulate metamaterial structures of varying scales, resulting in notable reductions in both memory and time consumption while maintaining accuracy comparable to commercial software. [ABSTRACT FROM AUTHOR]

A rapidly converging domain decomposition algorithm is introduced for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers. Firstly, a space-time decomposition of the original problem is considered. Subsequently, an iterative process is proposed, wherein the exchange of information to neighboring subdomains is accomplished through the utilization of piecewise-linear interpolation. It is shown that the algorithm provides uniformly convergent numerical approximations to the solution. Our analysis utilizes some novel auxiliary problems, barrier functions, and a new maximum principle result. More importantly, we showed that only one iteration is needed for small values of the perturbation parameter. Some numerical results supporting the theory and demonstrating the effectiveness of the algorithm are presented. [ABSTRACT FROM AUTHOR]

The diffusive viscous (DV) model is a useful tool for interpreting low-frequency seismic attenuation and the influence of fluid saturation on frequency-dependent reflections. Among present methods for the numerical solution of the corresponding DV wave equation, the finite-difference frequency-domain (FDFD) method with complex-valued adaptive coefficients (CVAC) has the advantage of efficiently suppressing both numerical dispersion and numerical attenuation. In this research, the FDFD method with CVAC is first generalized to a 3D DV equation. In addition, the current calculation of CVAC involves the numerical integration of propagation angles, conjugate gradient (CG) iterative optimization, and the sequential selection of initial values, which is difficult and inefficient for implementation. An improved method is developed for calculating CVAC, in which a complex-valued least-squares problem is constructed by substituting the 3D complex-valued plane-wave solutions into the FDFD scheme. The QR-decomposition method is used to efficiently solve the least-squares problem. Numerical dispersion and attenuation analyses reveal that the FDFD method with CVAC requires ∼2.5 spatial points in a wavelength within a dispersion deviation of 1% and an attenuation deviation of 10% for the 3D DV equation. An analytic solution for 3D DV wave equation in homogeneous media is proposed to verify the effectiveness of the proposed method. Numerical examples also demonstrate that the FDFD method with CVAC can obtain accurate wavefield modelling results for 3D DV models with a limited number of spatial points in a wavelength, and the FDFD method with QR-based CVAC requires less computational time than the FDFD method with CG-based CVAC. [ABSTRACT FROM AUTHOR]

The phase field approach to fracture becomes popular for complicated fracture problems in recent years. However, its widespread application is hindered by its high computational cost. In this article, we propose an efficient parallel explicit‐implicit solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method, specifically, the dual‐primal finite element tearing and interconnecting (FETI‐DP) method. In this scheme, the displacement field is updated by an explicit algorithm in parallel, and the phase field is implicitly solved by the FETI‐DP method. In particular, Lagrange multipliers are introduced to ensure the interface continuity of the phase field. In the computational process, the information exchange among subdomains merely exists in a few substeps, which renders the cost for communication very small. Moreover, the size of equations to be solved is proportional to the total area of subdomain interfaces, which is significantly reduced compared with a typical single‐domain solution procedure. The solution scheme is able to perform phase field simulations with a million of degrees of freedom using only 0.034 core hours per load step, and has flexible extensibility for existing phase field codes. Several numerical examples demonstrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

Numerical simulation of blood flows in patient-specific arteries is becoming an important tool in understanding vascular diseases and surgery planning. Depending on the branching geometry and the patient parameters, the flow can be quite complicated with local vortex structures and rotations, but the principal component of the flow is always along the centerline of the artery. Based on this observation, we introduce a new two-level domain decomposition method for unsteady incompressible Navier–Stokes equations in three-dimensional complex patient-specific arteries, and the key component of the preconditioner is a parameterized one-dimensional unsteady Navier–Stokes or Stokes coarse problem defined along the centerline of the artery. The one-dimensional preconditioner and some overlapping three-dimensional subdomain preconditioners are combined additively to form the two-level method via interpolations using radial basis functions. The most important feature of the method is that the cost of solving the coarse problem is nearly negligible compared with the subdomain solver. The blood flow is modeled by the unsteady incompressible Navier–Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. Numerical experiments indicate that the proposed method is highly effective and robust for complex arteries with many branches, in other words, the number of linear and nonlinear iterations changes very little when the mesh is refined or the number of subdomains is increased or the number of arterial branches is increased. [ABSTRACT FROM AUTHOR]

We consider a non-overlapping domain decomposition method for optimal control problems of the tracking type governed by time-fractional diffusion equations in one space dimension, where the fractional time derivative is considered in the Caputo sense. We concentrate on a transmission problem defined on two adjacent intervals, where at the interface we introduce an iterative non-overlapping domain decomposition in the spirit of P.L. Lions for the corresponding first-order optimality system, such that the optimality system corresponding to the optimal control problem on the entire domain is iteratively decomposed into two systems on the respective sub-domains; this approach can be framed as first optimize, then decompose. We show that the iteration involving the states and adjoint states converges in the appropriate spaces. Moreover, we show that the decomposed systems on the sub-domain can in turn be interpreted as optimality systems of so-called virtual control problems on the sub-domains. Using this property, we are able to solve the original optimal control problem by an iterative solution of optimal control problems on the sub-domains. This approach can be framed as first decompose, then optimize. We provide a mathematical analysis of the problems as well as a numerical finite difference discretization using the L1-method with respect to the Caputo derivative, along with two examples in order to verify the method. [ABSTRACT FROM AUTHOR]

Multiphysics coupling simulations are of great importance and challenge in engineering and industrial applications. A new efficient full‐wave energy‐conservative projection method between two heterogeneous meshes is proposed in this article, for the analysis of electromagnetic‐thermal‐stress coupling in the printed circuit boards (PCBs) and antenna arrays. The projected variables are directly chosen as the electric fields instead of conventional thermal sources, and a scalable domain decomposition method is used to solve the projection problems. In addition, a bounding‐box algorithm and the spatial K‐dimensional Tree searching algorithm are developed for physical quantity projection between the two heterogeneous meshes. A series of numerical analysis of the electromagnetic‐thermal‐stress coupling process are conducted. In particular, a realistic PCB example is presented, where 144 CPU cores are used and two heterogeneous meshes of over 20 million grids are constructed. A realistic antenna array with 10 000 units is also presented, where 1200 CPU cores are used and two heterogeneous meshes of over 100 million grids are constructed. [ABSTRACT FROM AUTHOR]

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch‐dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation‐diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug‐induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed. [ABSTRACT FROM AUTHOR]

This study proposed an improved analytical method for electromagnetic field analysis of a wound rotor synchronous machine (WRSM) considering the permeability of soft magnetic materials. A simplified analytical model considering the magnetic permeability of each region is presented. The governing equations of each region are derived from Maxwell's equations and the electromagnetic field theory, and a general solution is derived by using mathematical techniques. The analytical solutions of all domains are derived by calculating the boundary conditions. To validate the proposed analytical method, the radial and circumferential magnetic flux densities are compared with finite element analysis (FEA) results. In addition, electromagnetic performance parameters such as flux linkage, back-electromotive force, and torque are determined using electromagnetic theories. In particular, the magnetic saturation of the soft magnetic material is due to field and armature current, and the superiority of the proposed method is demonstrated by comparing the improved analytical method considering the global saturation of each region with the nonlinear FEA result considering local saturation. The proposed analytical method can be widely used in the initial and optimal design of WRSM because it can consider saturation of the core due to changes in field and armature current. [ABSTRACT FROM AUTHOR]

In this paper, an electromagnetic analysis method is proposed to improve force characteristics by using spring permanent magnets (PMs) along the axial and circumferential directions of a linear oscillatory generator (LOG). For accurate electromagnetic analysis, a detailed analysis model of the LOG is developed, and the governing equations of each subdomain are derived based on Maxwell's equations and electromagnetic theory. Analytical solutions of the magnetic vector potential in each subdomain are derived using boundary conditions. The reliability of the proposed method is verified through a comparison with the results of a two-dimensional finite element analysis (FEA). In particular, the force characteristics depending on the spring PM is effectively derived by considering the three-dimensional (3D) circumferential and axial end effects. The proposed analysis method is used to determine the thickness of spring PM that transforms the detent force of the LOG with the spring PM into restoring force. The reliability of the proposed analysis method is verified through comparison with the results of a 3D FEA. [ABSTRACT FROM AUTHOR]