Complicated Domains Research Articles

MultiShape: a spectral element method, with applications to Dynamic Density Functional Theory and PDE-constrained optimization

Abstract A new numerical framework is developed to solve general nonlinear and nonlocal PDEs on complicated two-dimensional domains. This enables the solution of a wide range of both steady and time-dependent problems on nonstandard geometries, as well as providing the ability to impose nonlinear and nonlocal boundary conditions (typical of those arising in the modelling of physical phenomena) in a flexible and automated way. This spectral element methodology, which we called MultiShape, is compatible with other state-of-the-art numerical methods, such as differential–algebraic equation solvers and optimization algorithms. MultiShape is an open-source Matlab library, in which the numerical implementation is designed to be user-friendly: the problem set-up and computations are done automatically through intuitive operator definitions and notation. Validation tests are presented, before we showcase the power and versatility of MultiShape with three motivating examples in Dynamic Density Functional Theory and PDE-constrained optimization.

Global Inference and Test for Eigensystems of Imaging Data Over Complicated Domains

A nonparametric approach for analyzing eigensystems of image data over a complex domain is novelly developed. The proposed estimators, which are based on bivariate splines, have both oracle efficiency of O p ( n − 1 / 2 ) , meaning they are asymptotically indistinguishable from estimators computed with true trajectories, and computational efficiency with more convenient spectrum decomposition forms. Under mild conditions, we derive consistency and weak convergence of our proposed estimators, which can be used to construct confidence intervals and simultaneous confidence corridors for any individual eigenvalue and eigenfunction, as well as design uniform inference procedures for eigensystems with a diverging number of components. In addition, we extend our method to two-sample test problems. Extensive simulation results provide strong support for the asymptotic theory, and the procedures are applied to two potential seawater temperature data sets to demonstrate its validity.

Statistical Inference for Mean Function of Longitudinal Imaging Data over Complicated Domains

Statistical Inference for Mean Function of Longitudinal Imaging Data over Complicated Domains

Constructing an AI-driven teacher training model for vocational education: teachers’ information literacy and teaching competence at the same time

Abstract With the integration of various emerging technologies represented by artificial intelligence into the field of education, the education sector has set off a research boom in wisdom education, forming a series of new forms of education such as wisdom classrooms and wisdom teaching. This paper takes education informatics as the connecting point to sort out the logical connection between teachers’ information literacy and smart education. The intelligent system, various subjects, and complicated knowledge domains are united to form a specific objective relationship and multivariate correlation network to construct a specific field of AI-enabled teacher training. Embedding the training process of vocational education teachers in each stage of the AI-assisted teacher training system, we examined their learning mood, concentration, and the impact on their information literacy ability under AI-driven. AI-driven interactions at all stages could greatly awaken learners’ emotions, which could enable teachers to focus more on training, as shown in the results. In addition, the composite mean value of teachers’ information literacy under AI-driven was 4.10, which was significantly higher than that of 3.42 before use (p<0.001). AI technology-enabled vocational teacher training can be a significant direction for teacher training reform.

A hybrid approach for expressive numeric and temporal planning with control parameters

Since the release of PDDL 2.1, many planners accepted the challenge of addressing more complicated domains and problems, including both temporal and numeric features for scheduling and resources management. However, very few planners can handle a significant subset of the features that the language allows for modeling. To handle a level of expressiveness sufficient to work with more realistic problems, we have designed NextFLAP (Numeric EXpressions in TFLAP). The planner follows a hybrid approach, which combines a forward partial-order planner with a numeric constraint solver/optimizer. Additionally, we include a new feature, the control parameters, which are relevant for direct modeling numerical quantities and physical properties of objects in the actions, such as ‘partially charging of a battery’ or ‘obtaining a certain amount of resources’. This feature overcomes a limitation of the PDDL language, which is that the parameters of the actions must be objects (finite domain values) and, in no case, numeric variables. In this paper we illustrate the advantages of using these temporal and numeric modeling features and then describe our planning system, NextFLAP, that can handle these domains. We show that NextFLAP is competitive with other state-of-the-art planners and that it generates good-quality plans.

Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations

Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems.

Modelling of many real-world processes, such as drug delivery, wastewater treatment, and pharmaceutical production, requires accurate descriptions of the dynamics of hard particles confined in complicated domains. In particular, when modelling sedimentation processes or systems with driven flows, it is important to accurately capture volume exclusion effects. This work applies Dynamic Density Functional Theory to the evolution of a particle density under diffusion, external forces, particle-particle interaction, and volume exclusion. Using a spectral element framework, for the first time it is possible to include all of these effects in dynamic simulations on complex domains. Moreover, this allows one to apply complicated no-flux, and other non-local, non-linear, boundary conditions. The methodology is also extended to control problems, addressing questions of how to enhance production set-up in industrially-motivated processes. In this work the relevant models are introduced, numerical methods are discussed, and several example problems are solved to demonstrate the methods' versatility. It is shown that incorporating volume exclusion is crucial for simulation accuracy and we illustrate that the choice of boundary conditions significantly impacts the dynamics.

Three dimensional meshfree analysis for time-Caputo and space-Laplacian fractional diffusion equation

Numerical exploration of spatial fractional differential equations in three dimensions is not trivial due to their complexity, especially for complicated problem domains. In this work, the time-Caputo and space-Laplacian fractional diffusion equations in three dimensions are analyzed using a meshfree technique. In the temporal dimension, the classical L1 finite difference scheme is used to approach the Caputo fractional derivative. The spatial discretization is realized by a three dimensional reproducing kernel particle method (RKPM), which can eliminate the dependence of shape functions on certain meshes. Therefore RKPM is very suitable to approximate the field variable in complicated three dimensional domains compared with other mesh-dependent methods. For the purpose of increasing the computational efficiency, the stabilized conforming nodal integration (SCNI) and lumped mass matrix techniques are adopted in the Galerkin meshfree formulation. In the proposed method, the tedious derivatives computing for meshfree shape functions, numerical integration for Galerkin weak form and time-consuming inverse calculating for the large size mass matrix are all realized by more efficient approaches comparing with the conventional Galerkin RKPM. Several numerical examples in various domains with structured and unstructured discretization are studied to demonstrate the proposed methodology, and the results show very favorable performance of the proposed method regarding the accuracy and effectiveness.

SRL-assisted AFM: Generating planar unstructured quadrilateral meshes with supervised and reinforcement learning-assisted advancing front method

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named “SRL-assisted AFM” for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using “policy networks”. These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers.

A State-of-the-Art Review on Recent Load Frequency Control Architectures of Various Power System Configurations

Load frequency management (LFM) work has become more difficult due to hybrid power systems. These power systems are responsible for increased power quality issues, exacerbating control problems. Frequency changes and power quality issues are the central concerns caused by these modern power systems. Frequency deviations occur mainly due to variations in generation, consumption, or both, and one of the critical reasons is the low inertia of the modern renewable penetrated hybrid power systems. So, to handle all these issues related to frequency and many more, the need for the best controller arises, which can easily handle any nonlinearities. This article comprehensively analyzes various load frequency control (LFC) architectures in various power system configurations. It focuses on the frequency management features of various power systems, including microgrids that use renewable energy and electric vehicles, with a complete understanding of current development states. Different controllers and tactics underwent comparative investigations. The detailed tabular analysis of frequency control architectures provides a deep insight into the LFC assessment of various power system configurations. The importance of better controllers for LFC planning in complicated power system domains is also emphasized in this work.

Efficient numerical method for Stokes flows in unbounded domains with informative boundary condition using axial Green function method

SummaryFlow calculations in an unbounded domain have limitations and challenges due to its infiniteness. A common approach is to impose a far‐field asymptotic condition to determine a unique flow. The leading behavior of the flow is identified at the far field, and then an unknown coefficient is assumed for the second behavior. This allows us to propose an efficient numerical method to solve two‐dimensional steady Stokes and potential flows in a truncated domain along with the coefficients. The second term provides crucial hydrodynamic information for the flow and is referred to as the informative boundary condition. The truncation creates artificial boundaries requiring boundary conditions for the approximate solution. The axial Green function method (AGM), combined with a specific one‐dimensional Green function over a semi‐infinite axis‐parallel line extended to infinity, allows us to implement the informative boundary condition in the truncated domain. AGMs, designed for complicated domains, are now applied to infinite domain cases because AGMs' versatility enables implementing the informative boundary condition by changing only the axial Green function. This approach's efficiency, accuracy, and consistency are investigated through several appealing Stokes flow problems including potential ones in infinite domains.

An optimized deep learning model for optical character recognition applications

The convolutional neural networks (CNN) are among the most utilized neural networks in various applications, including deep learning. In recent years, the continuing extension of CNN into increasingly complicated domains has made its training process more difficult. Thus, researchers adopted optimized hybrid algorithms to address this problem. In this work, a novel chaotic black hole algorithm-based approach was created for the training of CNN to optimize its performance via avoidance of entrapment in the local minima. The logistic chaotic map was used to initialize the population instead of using the uniform distribution. The proposed training algorithm was developed based on a specific benchmark problem for optical character recognition applications; the proposed method was evaluated for performance in terms of computational accuracy, convergence analysis, and cost.

Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation

Abstract In this paper, we construct stochastic simulation algorithms for solving an elastostatics problem governed by the Lamé equation. Two different stochastic simulation methods are suggested: (1) a method based on a random walk on spheres, which is iteratively applied to anisotropic diffusion equations that are related through the mixed second-order derivatives (this method is meshless and can be applied to boundary value problems for complicated domains); (2) a randomized algorithm for solving large systems of linear algebraic equations that is the core of this method. It needs a mesh formation, but even for very fine grids, the algorithm shows a high efficiency. Both methods are scalable and can be easily parallelized.

Analyzing data in complicated 3D domains: Smoothing, semiparametric regression, and functional principal component analysis.

In this work, we introduce a family of methods for the analysis of data observed at locations scattered in three-dimensional (3D) domains, with possibly complicated shapes. The proposed family of methods includes smoothing, regression, and functional principal component analysis for functional signals defined over (possibly nonconvex) 3D domains, appropriately complying with the nontrivial shape of the domain. This constitutes an important advance with respect to the literature, because the available methods to analyze data observed in 3D domains rely on Euclidean distances, which are inappropriate when the shape of the domain influences the phenomenon under study. The common building block of the proposed methods is a nonparametric regression model with differential regularization. We derive the asymptotic properties of the methods and show, through simulation studies, that they are superior to the available alternatives for the analysis of data in 3D domains, even when considering domains with simple shapes. We finally illustrate an application to a neurosciences study, with neuroimaging signals from functional magnetic resonance imaging, measuring neural activity in the gray matter, a nonconvex volume with a highly complicatedstructure.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two- and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

Meshfree methods for two-dimensional three-temperature radiation diffusion equations

Two-dimensional three-temperature radiation diffusion equations coupled with the temperatures of photon, electron and ion are widely used in the numerical research of laser-driven implosion in inertial confinement fusion experiments. The equations describe the radiation evolution of electron, ion and photon among various materials. So they have strong nonlinearity and are built on complicated computational domains. Traditional numerical methods such as finite difference method and finite element method rely on meshes for discretization. In this paper, two types of meshfree methods based on radial basis function are proposed to solve two-dimensional three-temperature radiation diffusion equations. The first is using direct linearization of the diffusion term on each time layer and using non-symmetric collocation method combined with the compactly supported radial basis function on space. The second is using non-symmetric collocation method on space but constructing a successive permutation iteration algorithm with fully implicit scheme on each time layer. By comparing different linearization methods, we can find that successive permutation iteration algorithm is more effective. Accurate performance of the proposed methods are confirmed by a large number of numerical experiments.

Generic workflow of groundwater flow simulations in geologically complicated domains with millions of unstructured grids

Numerical groundwater flow simulation involves manual and tedious pre-processing and post-processing procedures. Hence, this study developed a systematic and efficient workflow to alleviate model buildup and data-processing burdens, allowing researchers to focus on the application aspects of simulation results. This highly automatic workflow allows researchers to execute three-dimensional groundwater flow simulations in sites with complex hydrogeological conditions. Processes in the workflow are formed as a trilogy: building a hydrogeological conceptual model, generating a site-specific unstructured mesh and specifying simulation conditions, and executing the simulation and post-processing results. The workflow feasibility has been demonstrated by simulating the three-component (water, brine, and air) fluid flow in Huayu Islet, the only andesitic island of the basaltic Penghu archipelago, using TOUGH3 (Transport of Unsaturated Groundwater and Heat version 3) and its EOS7 (Equation of State #7) fluid module. Our self-developed mesh generator can produce a locally refined unstructured mesh with millions of grid cells that can capture the essential geological features of Huayu. It was found that, of the three scenarios considered, only the one using a fine mesh coupled with a two-phase Dirichlet boundary condition at the top surface could obtain a physically meaningful bowl-shaped fresh water and brine interface and reasonable transport pathway characteristics. In summary, the developed workflow serves as a practical methodology to authentically characterize the hydrogeologic mechanisms of a site with complicated geology.

An augmented interface approach in fictitious domain methods

We introduce a new type of fictitious domain method to solve elliptic problems defined over curved complicated domains. In fictitious domain methods with a penalty approach, given domain Ω is embedded into a rectangular domain R and a penalty is applied over the whole fictitious part R ﹨ Ω . We apply the L 2 penalty over a small strip Ω δ around ∂Ω in R ﹨ Ω and present a priori estimates with the sharp convergence of the penalized problem's solution to the original problem's solution. We use the linear finite element method to solve the penalized problem and attain the desired error estimates. Numerical experiments ensure the theoretical estimations and forecast the optimal convergence irrespective of the shape and convexity of the domain.

Implementation of Web-Based Psychosocial Interventions for Adults With Acquired Brain Injury and Their Caregivers: Systematic Review.

BackgroundMore than 135 million people worldwide live with acquired brain injury (ABI) and its many psychosocial sequelae. This growing global burden necessitates scalable rehabilitation services. Despite demonstrated potential to increase the accessibility and scalability of psychosocial supports, digital health interventions are challenging to implement and sustain. The Nonadoption, Abandonment, Scale-Up, Spread, and Sustainability (NASSS) framework can offer developers and researchers a comprehensive overview of considerations to implement, scale, and sustain digital health interventions.ObjectiveThis systematic review identified published, peer-reviewed primary evidence of implementation outcomes, strategies, and factors for web-based psychosocial interventions targeting either adults with ABI or their formal or informal caregivers; evaluated and summarized this evidence; synthesized qualitative and quantitative implementation data according to the NASSS framework; and provided recommendations for future implementation. Results were compared with 3 hypotheses which state that complexity (dynamic, unpredictable, and poorly characterized factors) in most or all NASSS domains increases likelihood of implementation failure; success is achievable, but difficult with many complicated domains (containing multiple interacting factors); and simplicity (straightforward, predictable, and few factors) in most or all domains increases the likelihood of success.MethodsFrom a comprehensive search of MEDLINE, EMBASE, PsycINFO, CINAHL, Scopus, speechBITE, and neuroBITE, we reviewed primary implementation evidence from January 2008 to June 2020. For web-based psychosocial interventions delivered via standard desktop computer, mobile phone, tablet, television, and virtual reality devices to adults with ABI or their formal or informal caregivers, we extracted intervention characteristics, stakeholder involvement, implementation scope and outcomes, study design and quality, and implementation data. Implementation data were both narratively synthesized and descriptively quantified across all 7 domains (condition, technology, value proposition, adopters, organization, wider system, and their interaction over time) and all subdomains of the NASSS framework. Study quality and risk of bias were assessed using the 2018 Mixed Methods Appraisal Tool.ResultsWe identified 60 peer-reviewed studies from 12 countries, including 5723 adults with ABI, 1920 carers, and 50 health care staff. The findings aligned with all 3 hypotheses.ConclusionsAlthough studies were of low methodological quality and insufficient number to statistically test relationships, the results appeared consistent with recommendations to reduce complexity as much as possible to facilitate implementation. Although studies excluded individuals with a range of comorbidities and sociocultural challenges, such simplification of NASSS domain 1 may have been necessary to advance intervention value propositions (domain 3). However, to create equitable digital health solutions that can be successfully implemented in real-world settings, it is recommended that developers involve people with ABI, their close others, and health care staff in addressing complexities in domains 2 to 7 from the earliest intervention design stages.Trial RegistrationPROSPERO International Prospective Register of Systematic Reviews CRD42020186387; https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42020186387International Registered Report Identifier (IRRID)RR2-10.1177/20552076211035988

Resolving Boundary Layers with Harmonic Extension Finite Elements

In recent years, the standard numerical methods for partial differential equations have been extended with variants that address the issue of domain discretisation in complicated domains. Sometimes similar requirements are induced by local parameter-dependent features of the solutions, for instance, boundary or internal layers. The adaptive reference elements are one way with which harmonic extension elements, an extension of the p-version of the finite element method, can be implemented. In combination with simple replacement rule-based mesh generation, the performance of the method is shown to be equivalent to that of the standard p-version in problems where the boundary layers dominate the solution. The performance over a parameter range is demonstrated in an application of computational asymptotic analysis, where known estimates are recovered via computational means only.