Domain Decomposition Research Articles

A Rigorous Code Verification Process of the Domain Decomposition Method in a Finite Element Method for Electromagnetics

A Rigorous Code Verification Process of the Domain Decomposition Method in a Finite Element Method for Electromagnetics

A Parallel Domain Decomposition Method for the Fully-Mixed Stokes-Dual-Permeability Fluid Flow Model with Beavers-Joseph Interface Conditions

A Parallel Domain Decomposition Method for the Fully-Mixed Stokes-Dual-Permeability Fluid Flow Model with Beavers-Joseph Interface Conditions

Top-ii-vol: Massively Parallel Scalable Meshing for Seismic Risk Assessment of Nuclear Sites

High performance computing is widely used for conducting high-resolution geophysics Finite Element Method (FEM) simulations. These simulations are crucial for risk assessment at nuclear sites and help gain deeper insights into underlying physics. However, generating FEM-compatible meshes from point-cloud data – which often serves as input for mesh generation from geomodelling tools – poses significant challenges due to the lack of associated CAD data and extremely large-scale nature. This article introduces a workflow for automatically converting Digital Elevation Model (DEM) point-cloud data into three-dimensional unstructured volumetric meshes. Leveraging domaindecomposition method via the parallel MPI I/O programming, our meshing algorithm efficiently constructs meshes, accommodating an arbitrary number of CPUs and enabling either single or distributed mesh generation. Demonstrating parallel efficiency and scalability, we produced a 68 billion element tetrahedral mesh from real DEM point-cloud data of the Cadarache region in France in approximately 1 second using over 24000 processing units. Meshes produced by this technique are utilized for seismic hazard FEM simulations, one of which is presented in this study. Scalability tests on massively parallel computers show high scalability, with quasi-linear strong scaling characteristics up to 24000 processing units.

Enhanced LSTM-based robotic agent for load forecasting in low-voltage distributed photovoltaic power distribution network.

To ensure the safe operation and dispatching control of a low-voltage distributed photovoltaic (PV) power distribution network (PDN), the load forecasting problem of the PDN is studied in this study. Based on deep learning technology, this paper proposes a robot-assisted load forecasting method for low-voltage distributed photovoltaic power distribution networks using enhanced long short-term memory (LSTM). This method employs the frequency domain decomposition (FDD) to obtain boundary points and incorporates a dense layer following the LSTM layer to better extract data features. The LSTM is used to predict low-frequency and high-frequency components separately, enabling the model to precisely capture the voltage variation patterns across different frequency components, thereby achieving high-precision voltage prediction. By verifying the historical operation data set of a low-voltage distributed PV-PDN in Guangdong Province, experimental results demonstrate that the proposed "FDD+LSTM" model outperforms both recurrent neural network and support vector machine models in terms of prediction accuracy on both time scales of 1 h and 4 h. Precisely forecast the voltage in different seasons and time scales, which has a certain value in promoting the development of the PDN and related technology industry chain.

A modified domain decomposition spectral collocation method for parabolic partial differential equations

<p>In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.</p>

Численное моделирование пьезопроводных процессов в двумерной постановке для коллектора трещиновато-порового типа

The process of two-phase filtration in a carbonate formation of fractured-pore type is considered. A mathematical model in a spatially two-dimensional formulation is proposed, a numerical method for solution and a parallel algorithm for its implementation are developed. The mathematical model is based on the Buckley-Leverett approach. The reservoir takes into account the exchange of fluids between low-permeability pores and natural fracturing, specified within the framework of the dual porosity model. The numerical algorithm is based on the use of the finite difference method and the splitting scheme by physical processes. To speed up calculations, a parallel algorithm based on two-dimensional domain decomposition is used. Numerical experiments were carried out, which showed that the developed algorithm is highly efficient and allows one to calculate the necessary characteristics of the modeled physical process.

A Hard Constraint and Domain Decomposition Based Physics-Informed Neural Network Framework for Nonhomogeneous Transient Thermal Analysis

A Hard Constraint and Domain Decomposition Based Physics-Informed Neural Network Framework for Nonhomogeneous Transient Thermal Analysis

A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition, an accelerated Schwarz framework, and two-layer neural networks to approximate the boundary-to-boundary map for the subdomains, which is the key step in the Schwarz procedure. Conventionally, the boundary-to-boundary map requires solution of boundary-value elliptic problems on each subdomain. By leveraging the compressibility of multiscale problems, our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary map. Our method is applied to a multiscale semilinear elliptic equation and a multiscale $p$-Laplace equation. In both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

Domain Decomposition Framework for Maxwell Finite Element Solvers and Application to PIC

Domain Decomposition Framework for Maxwell Finite Element Solvers and Application to PIC

A DOMAIN-DECOMPOSED VAE METHOD FOR BAYESIAN INVERSE PROBLEMS

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and highdimensional parameterization of priors. This paper proposes a domain-decomposed variational autoencoder Markov chain Monte Carlo (DD-VAE-MCMC) method to tackle these challenges simultaneously. Through partitioning the global physical domain into small subdomains, the proposed method first constructs local deterministic generative models based on local historical data, which provide efficient local prior representations. Gaussian process models with active learning address the domain decomposition interface conditions. Then inversions are conducted on each subdomain independently in parallel and in low-dimensional latent parameter spaces. The local inference solutions are postprocessed through the Poisson image blending procedure to result in an efficient global inference result. Numerical examples are provided to demonstrate the performance of the proposed method.

Temperature effect on the modal frequencies of a steel railway bridge

This paper presents the dynamic identification of the Ostiglia-Revere railway bridge, a steel truss girder bridge located in Northern Italy. The bridge is 6.6 m wide, about 940 m long and composed of 12 spans. The accelerations of a bridge span caused by both ambient excitation and train passages have been continuously measured from August to November. The monitoring system consists of 4 temperature sensors and 4 biaxial MEMS accelerometers, acquiring accelerations with a sampling frequency of 80 Hz. Modal properties are estimated adopting two different identification approaches, namely the Enhanced Frequency Domain Decomposition and the Stochastic Subspace Identification. Particular attention is paid to two crucial issues for vibration-based structural health monitoring: the recognition of the same structural mode from results identified during different time windows (i.e., mode clustering), and the temperature effect on estimated modal properties. As the latter is concerned, two regressive models, namely a linear regression model and an ARX model, are fitted to the frequency-temperature data, strongly reducing the eventuality of false vibration-based damage detections in the future.

Dynamic Validation and Assessment of a Historical Bell Tower

The work investigates the dynamic validation and seismic assessment of a bell tower located in Caserta Vecchia, emphasizing its relevance in structural engineering. Given the tower historical significance and possible vulnerability, understanding its structural behaviour under seismic loading is vital for preservation efforts. To capture the bell tower structural intricacies, advanced photogrammetric surveying techniques were utilized. This produced a detailed 3D model of the bell tower, which was subsequently integrated into the Abaqus software for finite element analysis. This approach facilitated a comprehensive examination of the tower structural dynamics and vibrational characteristics. The robustness of the study has been further enhanced through a validation process. Frequency analysis outcomes from Abaqus were cross-referenced with real-world seismic data collected using structural health monitoring (SHM) systems. This seismic data was analyzed using the Frequency Domain Decomposition (FDD) technique. This method ensured that the analytical model results were consistent with observed seismic responses, thereby validating the model’s accuracy and reliability. Further dynamic analyses were conducted to evaluate the bell tower potential vulnerabilities during high-intensity seismic events. These analyses are essential for predicting the structural response and potential damage patterns during earthquakes, facilitating better preparedness and mitigation strategies. The applicability of the methodologies used in similar contexts offers opportunities for advancing heritage preservation and optimizing the seismic safety of such complex structures.

Experimental modal and FEM analysis of a historical building

The CEDRAV building in Cerreto di Spoleto, originally a monastery, was built in the 14th century on the top of a rock ridge. The two seismic events that occurred on September 26th, 1997, with magnitude Ms=5.4 and Ms=6, respectively, caused some damages to it, but the event occurred on 14 October 1997 caused the main damages. This study includes analyses mainly related to the part of the data acquired corresponding to tests and configurations using temporary deployments. The building is very complex and rigid. In fact, translational and torsional frequencies are close to one another, coupling occurs and damping ratio is low. Coupling of the frequencies and the low damping are two factors that cause beating effect when shaking is strong enough. For example, the approximate beating period is computed for the June 28th 2000 earthquake as (taking T1 = 1/9.7 = 0.104 s, and T2 = 1/10.4 = 0.096 s) Tb = 2.5 s, observable in the time history plots. On the basis of the experimental results obtained by means of temporary arrays, a permanent network was designed and installed, which recorded several seismic events. A preliminary analysis in frequency domain, based on the determination of auto and cross power spectral density, has been first performed; subsequently the modal structure identification by means of the Ibrahim time domain technique and the Frequency Domain Decomposition technique in the frequency domain, have been carried out. A frequency domain analysis of the structure has also been performed by means of the Frequency Response Function (FRF) analysis. The experimental results have been finally compared with those obtained from a FEM.

Elzaki projected differential transform method for multi-dimensional aggregation and combined aggregation-breakage equations

Numerous real-world fields, including planetary science, bio-pharmaceutical, chemical study, food processing industry, and many more are profoundly impacted by population balance equations. Model complexity limits the analytical investigations to a few aggregation-breakage parameters, although various numerical and semi-analytical schemes are available. This article proposes a new semi-analytical approach, the Elzaki integral transform as a pre-treatment to reinforce domain decomposition for better accuracy and convergence, in conjunction with the projected differential transform method for finding the closed form or approximated series solutions for non-linear aggregation, aggregation-breakage, and multi-dimensional aggregation equations. The technique’s key benefit over traditional numerical methods is its ability to solve linear or non-linear differential equations directly without discretization or linearization. Theoretical convergence analysis and error estimates of series solutions for both one and two dimensional aggregation models are of particular interest. Finally, several numerical examples of aggregation, aggregation-breakage, and two dimensional aggregation equations are taken to validate the accuracy of the proposed method by comparing numerical simulations with exact solutions. Interestingly, we have obtained closed form solutions for the pure aggregation equation when considering constant and product aggregation kernels. Additionally, error tables and graphs help to highlight the method’s innovative nature.

Nondestructive Estimation of Neutral Temperature in Rails: A Comparative Study of Machine Learning Strategies

This paper presents the latest findings of a nondestructive evaluation technique currently under development at the University of Pittsburgh to determine the rail neutral temperature (RNT) in continuous welded rails. The technique is based on the extraction of relevant features from rail vibrations and the use of machine learning (ML) to associate these features to the longitudinal stress of the rail of interest. The features contain the spectral information of the vibrations and are pooled together by frequency domain decomposition for input to ML algorithms. Minimum redundancy–maximum relevance and neighboring component analysis are used to identify relevant features to reduce the size of the input vector. In addition, seven algorithms were considered to identify the most accurate model for neutral temperature with respect to the ground truth RNT measured with a strain-gage rosette. The data used in this study were collected from a 5° curved rail on concrete ties. The vibrations were triggered with a hammer and recorded with a few wireless and wired accelerometers attached on the railhead. The results showed that the Gaussian process regressor performs best, and as few as 20 frequencies can be used to predict the RNT with sufficient accuracy.

Fully algebraic domain decomposition preconditioners with adaptive spectral bounds

Fully algebraic domain decomposition preconditioners with adaptive spectral bounds

Multi-Methodological Geophysical Approach for Rapid and Non-invasive Structural Characterization of Infrastructures

In the context of health monitoring of structures/infrastructure, we propose a combination of different rapid and non-invasive experimental methods that allows the determination of the main structural parameters of an infrastructure. It is based on simultaneous acquisition of 20 minutes of seismic ambient noise with seismic arrays placed at different points of the infrastructure without diverting or blocking the traffic flow or interrupting the operation of a road infrastructure. The signals are analyzed using different analysis techniques such as standard spectral analysis (Fourier Amplitude Spectra, FAS), Frequency Domain Decomposition (FDD), Ambient Noise Deconvolution Interferometry (ANDI), and Non Parametric Damping analysis (NonPaDAn). These combined techniques were applied to two different types of viaducts: the Gravina bridge, located on the SS.655-Bradanica, and the Monticello viaduct on the SS.407-Basentana (Albano di Lucania), both located in the Basilicata region (Italy). The Gravina bridge is a newly constructed arch bridge whose structural parameters, evaluated using this approach, represent the zero-time reference point for further investigations on the temporal evolution of the structural parameters. The Monticello bridge is a multi-span viaduct built in the 1970s whose estimated structural parameters were compared to the various degrees of degradation observed on the girders. The application of different methods has facilitated and improved the interpretation of the results obtained, proving very promising for the estimation of the main vibrational modes, the associated mode shapes, the equivalent damping and the wave propagation velocities.

Modular geodesics and wedge domains in non-compactly causal symmetric spaces

We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory. We adopt the perspective that the geometric implementation of the modular group is given by the flow generated by an Euler element of the Lie algebra (an element defining a 3-grading). Since any Euler element of a semisimple Lie algebra specifies a canonical non-compactly causal symmetric space M=G/H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M = G/H$$\\end{document}, we turn in this paper to the geometry of this flow. Our main results concern the positivity region W of the flow (the corresponding wedge region): If G has trivial center, then W is connected, it coincides with the so-called observer domain, specified by a trajectory of the modular flow which at the same time is a causal geodesic. It can also be characterized in terms of a geometric KMS condition, and it has a natural structure of an equivariant fiber bundle over a Riemannian symmetric space that exhibits it as a real form of the crown domain of G/K. Among the tools that we need for these results are two observations of independent interest: a polar decomposition of the positivity domain and a convexity theorem for G-translates of open H-orbits in the minimal flag manifold specified by the 3-grading.

A family of Nonoverlapping Spectral Additive Schwarz methods (NOSAS) and their economic versions

NOSAS (Nonoverlapping Spectral Additive Schwarz) methods are nonoverlapping iterative domain decomposition methods for efficiently solving large sparse linear systems arising from elliptic problems with heterogeneous coefficients. NOSAS methods are of additive Schwarz types with local Dirichlet solver on each nonoverlapping subdomain Ωi, plus a coarse problem on the interface of the subdomains. The coarse problem has global and local interaction components which are associated respectively to low-frequency and high-frequency modes obtained locally from a generalized eigenvalue problem defined on each subdomain’s interface. In this paper, we propose several variants of the NOSAS methods by selecting different generalized eigenvalue problems and different coarse space extensions. Additionally, we propose an economic variant to reduce the complexity of these generalized eigenvalue problems. The analysis of all the variants is established, and numerical tests are provided.

Generalized adaptive singular spectrum decomposition and its application in fault diagnosis of rotating machinery under varying speed

Rotating machinery fault signals often consist of multiple components with time varying frequencies under variable speed conditions. Spectral overlap exists among these components, making it difficult to independently separate the features of the components. Singular spectrum decomposition (SSD), a singular spectrum analysis-based signal decomposition method, has shown its great potential in suppressing background noise and extracting fault-related components in complex background noise environments. However, SSD is a frequency domain decomposition method with equivalent filtering characteristics, and it is susceptible to the mode mixing when processing signals with spectral overlap. Moreover, the choice of a key parameter in the iteration decomposition process of SSD, the embedding dimension, is determined using an empirical formula, which might cause suboptimal decomposition outcomes. To address these issues, this paper proposes a generalized adaptive singular spectrum decomposition (GASSD) method, which combines generalized demodulation with improved embedding dimension selection for SSD. GASSD incorporates SSD into the framework of adaptive generalized demodulation to separate specific frequency domain features. Firstly, for an effective generalized demodulation analysis, a region block synchronous ridge extraction method is proposed to accurately estimate the instantaneous frequency ridges from the time-frequency plane, which helps construct proper demodulation phase functions. Secondly, to achieve optimal analysis of SSD, a Gini moderation decomposition index is designed to improve the construction of the trajectory matrix by determining an appropriate embedding dimension. Finally, the reliability of the proposed method is demonstrated by analyzing wind turbine generator bearing fault signals and rotor rubbing fault signals.