Two-level Method Research Articles

The Impact of Site Contexts in Increasing the Diversity of Architectural Concepts: Using an Interactive Architectural Approach

Recently, new alternatives have been applied to enhance the architectural design process through comprehensive interaction with all variables. This approach suggests a dynamic scheme to collect all factors comprehensively. This research introduces approaches to better cognition of architectural concepts based on the site context parameter. It investigates the role of site context in generating architectural ideas by formulating a model of analysis to find similarities and differences in senior architects’ strategies. This approach aims to adapt context to explore aspects that may create diversity in architectural products. The reality is that creating original architectural concepts has received progressively less attention in the professional practice of architecture in recent decades. The research applied a mixed methodology, checklist factors and graphical analysis. It used a two-level method with several steps to evaluate the twelve international cases related to deconstructive architects (Eisenman, Koolhaas, and Hadid). This study concludes that creating a site context that supports the surrounding context can enrich the design concept and create unexpected results.

Bridging the simulation-to-real gap of depth images for deep reinforcement learning

While deep reinforcement learning (DRL) models are effective at learning appropriate actions from high-dimensional data, they require large amounts of costly and time-consuming training data to be collected in real-world settings. For this reason, collecting data in simulations offers a promising alternative, but transferring policy networks from simulation to reality can be challenging due to differences in perception between the virtual and real worlds. This paper proposes a two-level method to bridge the simulation-to-reality (sim-to-real) gap for depth images, specifically for autonomous environmental navigation that uses DRL. Simulated depth images are first translated at a perception level through generative adversarial network (GAN) to make them look like real data from a depth sensor. Simulated and GAN-generated depth images are encoded into latent representations, and the encoder is trained in the latent space to make the two images paired. This encoder is trained simultaneously with a reinforcement learning network model to extract domain-invariant and task-relevant features from depth images and map the behavioral similarity of states to the latent space. Our experimental results demonstrate that our approach can effectively bridge the sim-to-real gap, enabling policies learned in simulation to maintain their control performance in the real world.

A two-level finite element method with grad-div stabilizations for the incompressible Navier–Stokes equations

This article presents and studies a two-level grad-div stabilized finite element discretization method for solving numerically the steady incompressible Navier–Stokes equations. The method consists of two steps. In the first step, we compute a rough solution by solving a nonlinear Navier–Stokes system on a coarse grid. And then, in the second step, we pass the coarse grid solution to a fine grid to linearize the nonlinear term, update the solution by solving a linearized problem based on Newton iterations. In both steps, a grad-div stabilization term is incorporated into the system to reduce the influence of pressure on the approximate velocity. We analyze stability and asymptotic convergence of the approximate solutions, derive explicit dependence of the solution errors on the grad-div stabilization parameter and viscosity. We perform also some numerical tests to validate the theoretical analysis and illustrate the efficiency of the proposed method. Compared with the standard two-level method without stabilizations, the grad-div stabilization term added in present method improves the accuracy of the approximate velocity, accelerates the convergence of the nonlinear iterations for the coarse mesh nonlinear system, and reduces the computational time.

Deep Ensemble Learning Model for Diagnosis of Lung Diseases from Chest X -Ray Images

Objectives: This study aims to develop a robust medical recognition system using deep learning for the identification of various lung diseases, including COVID-19, pneumonia, lung opacity, and normal states, from chest X-ray images. The focus is on implementing ensemble fixed features learning methods to enhance diagnostic capabilities, contributing to the development of a cost-effective and reliable diagnostic tool for combating the global epidemic of lung disorders. Methods: The study utilizes a Kaggle dataset containing COVID-19 chest radiography images. Raw X-ray images undergo preprocessing for contrast enhancement and noise removal while addressing dataset imbalance through near-miss resampling. Ensemble learning techniques, including two and three-level methods, are employed to harness the strengths of individual base learners—VGG16, InceptionV3, and MobileNetV2. The model's performance is evaluated using metrics such as accuracy, recall, precision, and F1-score. For remote access, a user interface and a shared web link are developed using Python Gradio. Findings: In two-level ensembles, features from base learners are concatenated and classified using a support vector machine. Three-level ensembles use concatenated features classified by three machine learning classifiers, employing a majority voting system for the final prediction. The two-level method achieved 93% accuracy, precision, recall, and F1 score. The three-level ensemble model demonstrates superior performance, achieving 94% accuracy in detecting four lung diseases, namely COVID-19, pneumonia, lung opacity, and normal states. Novelty: This research contributes to the field by showcasing the efficacy of deep learning technology, particularly ensemble learning, in enhancing the detection of lung diseases from raw chest X-ray images. The model employs three modified and efficient pretrained networks for automatic feature extraction, eliminating the need for manual feature engineering. The developed model stands as a promising decision-support tool for healthcare professionals, particularly in low-resource environments. Keywords: Convolutional Neural Network (CNN), Deep Learning (DL), Transfer Learning (TL), Ensemble learning (EL), Fixed feature extraction, Chest X­rays (CXR), Lung diseases

Combined mean-field and full-field homogenization of porous elasto-plastic materials and composites under arbitrary stress triaxialities

A predictive micromechanical approach is proposed for porous materials where the unreinforced or reinforced matrix phase is elasto-plastic with hardening. The cavities can be spheres, long or short cylinders. The approach is based on an alternative microstructure made of elasto-plastic inhomogeneities embedded in a homogenized porous matrix phase, and the volume fractions are determined from a maximum packing argument. The effective properties of single hollow solids are computed with an energy-based approach coupled with full-field finite element (FE) analyses. Next, the alternative microstructures are homogenized with mean-field (MF) models. For reinforced porous materials, a two-level method is adopted, where the proposed approach is used at the lower level to obtain a fictitious homogenized matrix, in which reinforcements are embedded at the upper level. The present work is restricted to monotonic and proportional loadings and to the secant formulation of isotropic or transversely isotropic elasto-plasticity. However, no constitutive models are supposed or identified. The predictions were verified against reference full-field FE results on the actual microstructures in 3D and 2D plane strain or stress, for arbitrary stress triaxialities, and good agreement was found in all cases.

Дворівневий метод моделювання руху рідини за допомогою решітчастої моделі Больцмана та згорткової нейронної мережі

A new two-level method for modeling fluid movement in closed surfaces is proposed. The metod simulates an unsteady hydrodynamic process and includes two levels of description of the modeling process. The first level supports the development of the process over time and is implemented based on the Boltzmann lattice model. At the second level, for each time layer, based on the obtained velocity field, the pressure distribution is refined by modeling the solution of the Poisson equation in the working area using a convolutional neural network, which is pre-trained on a training data set formed for a given set of typical problems. A method combi¬ning both technologies is proposed, taking into account the compensation of the compressibi¬lity characteristic. The structure and features of neural network training are described. Experiments were conducted on models simulating the human digestive tract in various states. The performance of the developed method is compared with the numerical way of solving the Poisson equation.

Fast energy transition as a best strategy for all? The nash equilibrium of long-term energy planning strategies in coupled power markets

The research links energy system development planning to day-ahead energy markets, market coupling, and renewable energy integration, with a novel approach based on game theory. A two-level method is suggested for long-term energy strategy decisions. In the first stage, four hypothetical zones are simulated using an energy system's operation optimization model, emphasizing electricity flows. Game theory is employed in the second stage to select the best market-coupled zone strategy. A game reflecting transition dynamic, renewables integration, and demand response is formulated in the second step of the approach, where each of the four zones have two possible strategies (fast or slow transition), resulting in 16 sets of strategies (scenarios). Results demonstrate the feasibility of determining a Nash equilibrium, enhancing decision-making compared to prior methods. For the observed hypothetical case, a pure Nash equilibrium is found, where all zones opt for a rapid energy transition.

Model of small-focal ischemic cerebral infarction as a basis for the development of new methods of stroke therapy

Background. Among the existing experimental models of cerebral stroke in large animals, there is no possibility to create a focal brain infarction of limited volume, which would provide an opportunity to evaluate both the endogenous potential of neuroregeneration and to establish the effectiveness of new drugs on postischemic brain remodeling.
 Aim. Development of a method for modeling small-focal ischemic infarction of the cerebral cortex in a mini-pig.
 Material and methods. The study used mature female mini-pigs of the Vietnamese fold-bellied breed. Two-level occlusion of the great vessels was performed by ligation of the right common carotid artery and subsequent cauterization of the distal branches of the middle cerebral artery. In the postoperative period, the survival rate of animals and neurological deficit were assessed. On the 7th day, the animals were taken out of the experiment, the brain was isolated from the cranial box. Macroscopic and microscopic examinations included analysis of the localization and area of cerebral infarction, as well as morphological changes in the infarcted and peri-infarcted areas of the cerebral cortex.
 Results. With a 100% survival rate of experimental animals on the 3rd day after the operation, a neurological examination revealed violations of skin sensitivity and muscle tone in the hind and fore limbs, which partially recovered a week after the onset of ischemic stroke. Macroscopic examination of the brain on the 7th day after the operation visually revealed a small-focal ischemic cerebral infarction in the parietal lobe of the left hemisphere. Histological analysis of the cerebral cortex revealed a wedge-shaped necrotic focus of ischemic injury. In the peri-infarction region of the brain, reactive tissue changes with preserved nerve cells, mostly without visible damage, were found.
 Conclusion. The developed two-level method of stroke modeling in a mini pig induces ischemic cerebral infarction of limited volume in the parietal lobe; non-critical histological changes in the peri-infarct area and a slight neurological deficit suggest the possibility of using this model to develop new methods of stroke therapy.

A spatiotemporal two-level method for high-fidelity thermal analysis of laser powder bed fusion

Numerical simulation of the laser powder bed fusion (LPBF) procedure for additive manufacturing (AM) is difficult due to the presence of multiple scales in both time and space, ranging from the part scale (order of centimeters/seconds) to the powder scale (order of microns/milliseconds). This difficulty is compounded by the fact that the regions of small-scale behavior are not fixed, but change in time as the geometry is produced. While much work in recent years has been focused on resolving the problem of multiple scales in space, there has been less work done on multiscale approaches for the temporal discretization of LPBF problems. In the present contribution, we extend on a previously introduced two-level method in space by combining it with a multiscale time integration method. The unique transfer of information through the transmission conditions allows for interaction between the space and time scales while reducing computational costs. At the same time, all of the advantages of the two-level method in space (namely its geometrical flexibility and the ease in which one may deploy structured, uniform meshes) remain intact. Adopting the proposed multiscale time integration scheme, we observe a computational speed-up by a factor × 2 . 44 compared to the same two-level approach with uniform time integration, when simulating a laser source traveling on a bare plate of nickel-based superalloy material following an alternating scan path of fifty laser tracks. • A Two-level method is extended to a spatiotemporal formulation without continuous mesh update. • The two-level formulation allows for full scale separation, such that different spatial and temporal approximations are used on each scale. • An overall speed-up factor of approximately 2.5 is observed while the temperature profile closely captures reference solutions.

A highly parallel fully implicit domain decomposition method for the simulation of the hemodynamics of a patient-specific artery at the full-body scale

The numerical simulation of blood flows in the human body with a certain level of clinical accuracy is important for the understanding of the human physiology. The success of the modeling relies on a robust numerical method with the corresponding software that can handle the complex geometry, the complex fluid flows and run efficiently on a supercomputer. In this work, we introduce a highly parallel domain decomposition method to solve the three-dimensional incompressible Navier-Stokes equations on a patient-specific artery at the full-body scale from neck to feet with 222 outlets and a minimum diameter around 1.0 mm. A locally refined, unstructured mesh is used to resolve the complex fluid flow. Moreover, a two-level method is introduced to determine the model parameters in the Windkessel outlet boundary condition to guarantee clinically correct flow distributions to 14 major regions. A fully implicit Newton-Krylov-Schwarz method is used to solve the nonlinear algebraic system at each time step and numerical experiments show that the proposed method is robust with respect to the complex geometry, the graph-based partition of the complex mesh, the ill-conditioned sparse systems with locally dense blocks, and different model parameters and is scalable with up to 15,360 processor cores. With the proposed method, one simulation of the blood flow in a full-body arterial network can be obtained in about 8 hours per cardiac cycle, which enables its potential use in a wide range of clinical scenarios.

Emergency Decision-Making for Middle Route of South-to-North Water Diversion Project Using Case-Based Reasoning and Prospect Theory

The middle route of the South-to-North Water Diversion Project is one of the crucial frameworks of China’s water network and an essential channel for water resource allocation in North China. The safe operation of the project has a huge impact on regional economic development, social stability and other aspects. The objectives of this research are to improve the disposal efficiency of all kinds of accidents during the operation of the Middle Route of the South-to-North Water Diversion Project, reduce people’s property losses and ensure the safety of water supply along the line. This paper will put forward a new emergency decision-making method based on case-based reasoning technology and prospect theory. The method is divided into two parts: (1) Collecting the historical case information and building the case library. The frame representation in the case-based reasoning technology is used to describe the characteristics of historical cases and adopt the two-level method of historical cases fast retrieval and similarity fuzzy matching retrieval to complete the preliminary selection of emergency plans; (2) The decision-making and optimization model of disposal plans based on prospect theory, namely, using the value function and probability weight classification to measure the prospect value of similar schemes and selecting the optimal disposal scheme, in order to improve the science and rationality of the decision-making results. Finally, examples are taken to verify the feasibility and effectiveness of the method.

Two-Level Finite Element Iterative Algorithm Based on Stabilized Method for the Stationary Incompressible Magnetohydrodynamics

In this paper, based on the stabilization technique, the Oseen iterative method and the two-level finite element algorithm are combined to numerically solve the stationary incompressible magnetohydrodynamic (MHD) equations. For the low regularity of the magnetic field, when dealing with the magnetic field sub-problem, the Lagrange multiplier technique is used. The stabilized method is applied to approximate the flow field sub-problem to circumvent the inf-sup condition restrictions. One- and two-level stabilized finite element algorithms are presented, and their stability and convergence analysis is given. The two-level method uses the Oseen iteration to solve the nonlinear MHD equations on a coarse grid of size H, and then employs the linearized correction on a fine grid with grid size h. The error analysis shows that when the grid sizes satisfy , the two-level stabilization method has the same convergence order as the one-level one. However, the former saves more computational cost than the latter one. Finally, through some numerical experiments, it has been verified that our proposed method is effective. The two-level stabilized method takes less than half the time of the one-level one when using the second class Nédélec element to approximate magnetic field, and even takes almost a third of the computing time of the one-level one when adopting the first class Nédélec element.

A two-level multiphysics finite element method for a nonlinear poroelasticity model

In this paper, we propose a two-level multiphysics finite element method for a nonlinear poroelasticity model. To clearly reveal the multiphysics processes and overcome the “locking phenomenon”, we reformulate the original fluid-solid coupled problem into a fluid-fluid coupled problem–a generalized nonlinear Stokes problem coupled with a diffusion problem. To reduce the cost of computation, we propose two fully discrete coupling and decoupling two-level multiphysics finite element methods and use the backward Euler method for time variable of the reformulated nonlinear poroelasticity model. In computation, the generalized nonlinear poroelasticity (Stokes in Algorithm 2) problem is solved by using the Newton iterative method on a coarse mesh, then a linearized poroelasticity problem is solved on a fine mesh by using the solution of the coarse mesh. Then, we give the stability analysis and error estimates of the proposed methods. Finally, we show some numerical examples to verify the theoretical results–overcoming “locking phenomenon” and reducing the computational cost. • It is the first time to propose a two-level multiphysics finite element method for the nonlinear poroelasticity model. • The optimal order error estimate of the proposed two-level method is given. • To reduce the cost of computation, a poroelasticity problem is solved by using the Newton method on a coarse mesh.

Upper German Dialects as a Linguo-Cultural Phenomenon

Introduction. The study attempts to reveal the role of the dialect as a linguo-cultural phenomenon through the prism of its semantics. The lack of studies on dialects from the linguo-cultural point of view – modern cultural linguistics is mostly focused on standard languages and national cultural codes – determines the novelty and relevance of this issue. Methodology and sources. The research content consists of more than 100 Bavarian and Swabian dialect words which reflect culture specifics of each region, selected from the 20th- 21st centuries fiction, regional media materials and local advertising by using the systematic sampling method. To identify the regional culture specifics, the study provides a two-level method, based on the analysis of lexicographic sources and results of the interview and questionnaire of 66 respondents. The updated range of denotative and connotative meanings of each lexeme is considered within 10 thematic groups. Results and discussion. It has been found out that the researched dialects clearly reflect the South German regional tradition and history which can be traced in the semantics of the dialect words. Despite the globalization, a partly similar historical development of the two regions, as well as the belonging of the Bavarian and Swabian dialects to the same dialect continuum, the analysis of the dialect semantic structures within thematic groups revealed some similarities and differences which lead to conclusions regarding the specifics of the South German linguo-cultural code. Conclusion. It has been concluded that the further study on linguistic variety from the interdisciplinary point of view, including cultural linguistics and pragmatics, allows to better understand the role of dialect in modern communication.

Two-level group convolution

Group convolution has been widely used in order to reduce the computation time of convolution, which takes most of the training time of convolutional neural networks. However, it is well known that a large number of groups significantly reduce the performance of group convolution. In this paper, we propose a new convolution methodology called “two-level” group convolution that is robust with respect to the increase of the number of groups and suitable for multi-GPU parallel computation. We first observe that the group convolution can be interpreted as a one-level block Jacobi approximation of the standard convolution, which is a popular notion in the field of numerical analysis. In numerical analysis, there have been numerous studies on the two-level method that introduces an intergroup structure that resolves the performance degradation issue without disturbing parallel computation. Motivated by these, we introduce a coarse-level structure which promotes intergroup communication without being a bottleneck in the group convolution. We show that all the additional work induced by the coarse-level structure can be efficiently processed in a distributed memory system. Numerical results that verify the robustness of the proposed method with respect to the number of groups are presented. Moreover, we compare the proposed method to various approaches for group convolution in order to highlight the superiority of the proposed method in terms of execution time, memory efficiency, and performance.

Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation

In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the second step, we use the finite difference method to solve the proposed problem. This two-level mesh scheme is obtained by combining the radial basis function with finite difference. We prove the stability and convergence of scheme and show that the convergence order is O τ 2 + h 2 , where τ and h are the time step size and space step size, respectively. The results of numerical examples are compared with analytical solutions to show the efficiency of proposed scheme. The numerical results are in good agreement with theoretical ones.

Heat Transfer under Magnetohydrodynamics Flow of Nanofluids Past an Inclined Plate with Non Uniform Boundary Conditions

This paper deals with natural thermal convection combined with the mass transfer of nanoparticles occurring in the boundary layers of a nanofluid subjected to magnetohydrodynamics. The wall consists of an inclined plate is considered according to a temperature as well as the volume fraction of the nanoparticles varying as the power of the axial coordinate. In addition, internal heat generation/absorption is taken into account in the mathematical formulation. The governing partial differential equations based on Buongiorno's approach are transformed into a set of ordinary differential equations. The two-level method of no-similarity equations is used to achieve higher accuracy. The whole calculation procedure is implemented using a limit value problem program written according to the Matlab computer language that applies the Lobbato IIIa finite difference method. The obtained results have revealed that small variations of the boundary conditions with the axial coordinate become very significant on the local Nusselt number and the local Sherwood number for nanoparticles. Moreover, a better heat transfer has been obtained with a larger S. However, a trade-off between desired heat transfer rate and level of reduced skin friction should be scheduled.

Two-level method part-scale thermal analysis of laser powder bed fusion additive manufacturing

Numerical simulations of a complete laser powder bed fusion (LPBF) additive manufacturing (AM) process are extremely challenging, or even impossible, to achieve without a radical model reduction of the complex physical phenomena occurring during the process. However, even when we adopt a reduced model with simplified physics, the complex geometries of parts usually produced by the LPBF AM processes make this kind of analysis computationally expensive. In fact, small geometrical features—which might be generated when the part is designed following the principle of the so-called design for AM, for instance, by means of topology optimization procedures—often require complex conformal meshes. Immersed boundary methods offer an alternative to deal with this kind of complexity, without requiring complicated meshing strategies. The two-level method lies within this family of numerical methods and presents a flexible tool to deal with multi-scale problems. In this contribution, we apply a modified version of the recently introduced two-level method to part-scale thermal analysis of LPBF manufactured components. We first validate the proposed part-scale model with respect to experimental measurements from the literature. Then, we apply the presented numerical framework to simulate a complete LPBF process of a topologically optimized structure, showing the capability of the method to easily deal with complex geometrical features.

Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?

Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications.

Properties of Fiber Bragg Grating in CYTOP Fiber Response to Temperature, Humidity, and Strain Using Factorial Design.

The characteristics of fiber Bragg grating (FBG) in cyclic transparent fluoropolymer (CYTOP) optical fiber have attracted more and more attention in recent years. However, different results of the FBG response to environmental parameters are reported. This work presents a three-variable two-level factorial experimental method to investigate the FBG response to temperature, humidity, and strain in CYTOP fiber. Two uniform FBGs are inscribed separately in CYTOP fiber with and without over-clad. With only eight measuring points, the interactions among three variable parameters are computed and the parameter sensitivities and cross-sensitivities are estimated. Similar temperature and strain sensitivities were found for both gratings, whereas significant cross-sensitivity between humidity and temperature was present only in FBG inscribed in CYTOP fiber with over-clad.