Local Subdomains Research Articles

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

The Method of Fundamental Solutions is applied to the Laplace equation. Instead of using the traditional approach with external source points and boundary collocation points, the original domain decomposed into a lot of smaller, overlapping subdomains, and the Method of Fundamental Solutions is used to the individual local subdomains. After eliminating the local source points, local schemes are obtained. Instead of constructing a global scheme, the local subproblems are solved sequentially, in an iterative way. This mimics a multiplicative Schwarz method with overlapping subdomains, which assures the convergence of the method. Combining the iteration with a simple Seidel-type method, the resulting iteration is used as a smoothing procedure of a multi-level method. The points belonging to the coarse and fine levels are defined by a quadtree-generated cell system controlled by the boundary of the original domain. The multi-level character of the obtained method makes it possible to reduce the necessary number of iterations, that is, the overall computational cost can be significantly reduced. Moreover, the solution of large and ill-conditioned systems is completely avoided. The method is illustrated through several numerical test examples.

Capturing the Dynamic Conformational Changes of Human Isocitrate Dehydrogenase 1 (IDH1) upon Ligand and Metal Binding Using Hydrogen-Deuterium Exchange Mass Spectrometry.

Human isocitrate dehydrogenase 1 (IDH1) is a highly conserved metabolic enzyme that catalyzes the interconversion of isocitrate and α-ketoglutarate. Kinetic and structural studies with IDH1 have revealed evidence of striking conformational changes that occur upon binding of its substrates, isocitrate and NADP+, and its catalytic metal cation. Here, we used hydrogen-deuterium exchange mass spectrometry (HDX-MS) to build a comprehensive map of the dynamic conformational changes experienced by IDH1 upon ligand binding. IDH1 proved well-suited for HDX-MS analysis, allowing us to capture profound changes in solvent accessibility at substrate binding sites and at a known regulatory region, as well as at more distant local subdomains that appear to support closure of this protein into its active conformation. HDX-MS analysis suggested that IDH1 is primarily purified with NADP(H) bound in the absence of its metal cation. Subsequent metal cation binding, even in the absence of isocitrate, was critical for driving large conformational changes. WT IDH1 folded into its fully closed conformation only when the full complement of substrates and metal was present. Finally, we show evidence supporting a previously hypothesized partially open conformation that forms prior to the catalytically active state, and we propose this conformation is driven by isocitrate binding in the absence of metal.

A new deep transfer learning method for intelligent bridge damage diagnosis based on muti-channel sub-domain adaptation

Deep learning has been successfully and widely used in the field of intelligent diagnosis to accurately identify damage. These successes are based on the assumption that the training and test data are independent and identically distributed. They ignore that there is a distribution discrepancy between training (source domain) and test data (target domain) obtained under different working environments, loads, or bridges. This distribution discrepancy leads to severe performance degradation of the diagnostic model. To address these problems, a novel intelligent diagnosis method is proposed for bridges, namely, the multi-channel subdomain adaptation based deep transfer learning network. In this network, a multi-scale-based parallel multi-channel feature extractor and a multi-kernel local maximum mean discrepancy-based multi-channel subdomain adaptation module are proposed to learn domain-invariant features. Data sets from three different bridges are used for transfer diagnosis experiments to verify the generality and superiority of the method. This study will further facilitate the intelligentisation of structural health monitoring systems in the field of bridges.

ADAPTIVE PHASE-FIELD CONCURRENT MULTISCALE METHOD FOR EFFICIENT SIMULATION OF QUASI-BRITTLE FRACTURE

An adaptive phase-field concurrent multiscale method for efficient simulation of quasi-brittle fracture is presented. In this method, the analysis model is first subjected to coarse mesh discretization and the corresponding damage phase field calculation analysis. Then, adaptive dynamic local mesh refinement is performed for the coarse scale elements exceeding the given damage threshold during the iterative process. The locally refined mesh is defined as the local subdomain, the outermost coarse elements of the refined mesh, and the coarse elements without refinement are defined as the global subdomain. The variant s-version method is used to realize the direct coupling connection of mismatched meshes in different subdomains and the application of the continuity condition of field variables on the global-local subdomain interface. The division of the local subdomain, the global subdomain, and their overlapping domain are dynamically updated with the crack propagation path in the proposed method. The generation of the global-local computing mesh has great flexibility without the need for scale separation, which provides a more concise and flexible implementation for multiscale phase field adaptive simulation. The proposed method overcomes the extra burden and complexity of field variable conversion between coarse and fine scales, imposition of continuity conditions, and program implementation in existing phase field multiscale methods, which can be easily applied to the analysis on damage-fracture behavior of quasi-brittle structures. Typical examples verify the correctness, robustness, and advantages of the method.

Improving the estimation of thermospheric neutral density via two-step assimilation of in situ neutral density into a numerical model

AbstractNeutral thermospheric density is an essential quantity required for precise orbit determination of satellites, collision avoidance of satellites, re-entry prediction of satellites or space debris, and satellite lifetime assessments. Empirical models of the thermosphere fail to provide sufficient estimates of neutral thermospheric density along the orbits of satellites by reason of approximations, assumptions and a limited temporal resolution. At high solar activity these estimates can be off by 70% when comparing to observations at 12-hourly averages. In recent decades, neutral density is regularly observed with satellite accelerometers on board of low Earth orbiting satellites like CHAMP, GOCE, GRACE, GRACE-FO, or Swarm. When assimilating such along-track information into global models of thermosphere–ionosphere dynamics, it has been often observed that only a very local sub-domain of the model grid around the satellite’s position is updated. To extend the impact to the entire model domain we suggest a new two-step approach: we use accelerometer-derived neutral densities from the CHAMP mission in a first step to calibrate an empirical thermosphere density model (NRLMSIS 2.0). In a second step, we assimilate—for the first time—densities predicted for a regular three-dimensional grid into the TIE-GCM (Thermosphere Ionosphere Electrodynamics General Circulation Model). Data assimilation is performed using the Local Error-Subspace Transform Kalman Filter provided by the Parallel Data Assimilation Framework (PDAF). We test the new approach using a 2-week-long period containing the 5 April 2010 Geomagnetic storm. Accelerometer-derived neutral densities from the GRACE mission are used for additional evaluation. We demonstrate that the two-step approach globally improves the simulation of thermospheric density. We could significantly improve the density prediction for CHAMP and GRACE. In fact, the offset between the accelerometer-derived densities and the model prediction is reduced by 45% for CHAMP and 20% for GRACE when applying the two-step approach. The implication is that our approach allows one to much better ’transplant’ the precise CHAMP thermospheric density measurements to satellites flying at a similar altitude. Graphical Abstract

A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs) based on overlapping subdomains. Our approach reads as a constrained optimization statement that penalizes the jump at the components’ interfaces subject to the approximate satisfaction of the PDE in each local subdomain. Furthermore, the approach relies on the decomposition of the local states into a port component – associated with the solution on interior boundaries – and a bubble component that vanishes at ports: since the bubble components are uniquely determined by the solution value at the corresponding port, we can recast the constrained optimization statement into an unconstrained statement, which reads as a nonlinear least-squares problem and can be solved using the Gauss–Newton method. We present thorough numerical investigations for a two-dimensional neo-Hookean nonlinear mechanics problem to validate our method; we further discuss the well-posedness of the mathematical formulation and the a priori error analysis for linear coercive problems.

Dynamic Domain Adaptation for Class-Aware Cross-Subject and Cross-Session EEG Emotion Recognition.

It is vital to develop general models that can be shared across subjects and sessions in the real-world deployment of electroencephalogram (EEG) emotion recognition systems. Many prior studies have exploited domain adaptation algorithms to alleviate the inter-subject and inter-session discrepancies of EEG distributions. However, these methods only aligned the global domain divergence, but overlooked the local domain divergence with respect to each emotion category. This degenerates the emotion-discriminating ability of the domain invariant features. In this paper, we argue that aligning the EEG data within the same emotion categories is important for generalizable and discriminative features. Hence, we propose the dynamic domain adaptation (DDA) algorithm where the global and local divergences are disposed by minimizing the global domain discrepancy and local subdomain discrepancy, respectively. To tackle the absence of emotion labels in the target domain, we introduce a dynamic training strategy where the model focuses on optimizing the global domain discrepancy in the early training steps, and then gradually switches to the local subdomain discrepancy. The DDA algorithm is formally implemented as an unsupervised version and a semi-supervised version for different experimental settings. Based on the coarse-to-fine alignment, our model achieves the average peak accuracy of 91.08%, 92.89% on SEED, and 81.58%, 80.82% on SEED-IV in the cross-subject and cross-session scenarios, respectively.

A deep domain decomposition method based on Fourier features

In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency can degenerate for problems with high frequency modes. In this new F-D3M strategy, overlapping domain decomposition is conducted for the spatial domain, such that high frequency modes can be reduced to relatively low frequency ones. In each local subdomain, multi Fourier feature networks (MFFNets) are constructed, where efficient boundary and interface treatments are applied for the corresponding loss functions. We present a general mathematical framework of F-D3M, validate its accuracy and demonstrate its efficiency with numerical experiments.

An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows

This paper focusses on the numerical technique based on a localized meshless collocation method for approximating the Burgers-type equation in two dimensions. The method uses two main stages to approximate the unknown solution. First, the time derivative is discretized by the backward Euler method and a semi-discrete approach is obtained. Meanwhile, the unconditional stability and convergence of the semi-discrete scheme are proved by virtue of the discrete energy method in an appropriate Sobolev space. Second, a local radial basis function partition of unity (LRBF-PU) method is applied to approximate the spatial direction and a fully-discrete scheme is established. The LRBF-PU is based on subdividing the original domain to several subdomains and uses the radial basis function interpolation on each local subdomain. Compared with the global collocation technique, the main advantages of this technique are that it can reduce the computational cost and obtain a well linear system. Three illustrative examples are presented to demonstrate the accuracy and efficiency of the proposed method.

A convolutional plane wave model for sound field reconstruction

Spatial sound field interpolation relies on suitable models to conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest is large compared to the wavelength or when spherical and planar wavefronts are present or the sound field is complex, as in the near-field. To span such complex sound fields, the global reconstruction task can be partitioned into local subdomain problems. Previous studies have shown that partitioning approaches rely on sufficient measurements within each domain due to the higher number of model coefficients. This study proposes a joint analysis of all of the local subdomains while enforcing self-similarity between neighbouring partitions. More specifically, the coefficients of local plane wave representations are sought to have spatially smooth magnitudes. A convolutional model of the sound field in terms of plane wave filters is formulated and the inverse reconstruction problem is solved via the alternating direction method of multipliers. The experiments on simulated and measured sound fields suggest that the proposed method retains the flexibility of local models to conform to complex sound fields and also preserves the global structure to reconstruct from fewer measurements.

Development of Three-Dimensional LES Based Meshless Model of Continuous Casting of Steel

A large-eddy simulation (LES) based meshless model is developed for the three-dimensional (3D) problem of continuous casting (CC) of steel billet. The local collocation meshless method based on radial basis functions (RBF) is applied in 3D. The method applies scaled multiquadric (MQ) RBF with a shape parameter on seven nodded local sub-domains. The incompressible turbulent fluid flow is described using mass, energy, and momentum conservation equations and the LES turbulence model. The solidification system is solved with the mixture continuum model. The Boussinesq approximation for buoyancy and the Darcy approximation for porous media are used. Chorin’s fractional step method is used to couple velocity and pressure. The microscopic model is closed with the lever rule model. The LES model is compared to the two-equation Low Re k−ε turbulence Reynolds Averaged Navier–Stokes (RANS) model in terms of temperature, velocity and computational times. The LES model resolves transient character of vortices which RANS-type turbulence models are unable to tackle. The computational cost of LES models is considerably higher than in RANS. On the other hand, it results in a much lower computational cost than the direct numerical simulation (DNS). The paper demonstrates the ability of the method to solve realistic industrial 3D examples. Trivial adjustment of nodal densities, high accuracy, and low numerical diffusivity are the main advantages of this meshless method.

A multi-resolution approach to hydraulic fracture simulation

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

A meshless solution of the compressible viscous flow in axisymmetric tubes with varying cross-sections

The meshless Diffuse Approximate Method (DAM) is for the first time formulated and applied to simulate the compressible Newtonian flow of an ideal gas in an axisymmetric tube with varying cross-sections. The problem is structured by coupled partial differential equations for conservation of mass, momentum and energy, and the equation of state closure. These equations are solved in primitive variables and strong form. DAM is formulated on irregular node arrangement by using the second and third-order polynomial shape functions and Gaussian weights, leading to weighted least squares approximation on overlapping local subdomains. Pressure-velocity coupling is performed by the Pressure Implicit with Splitting of Operators (PISO) scheme. The solution of the represented novel application of DAM is verified by matching the meshless results with the fine-mesh finite-volume method results. The characteristics of meshless DAM for this kind of problem are systematically assessed by a detailed investigation of the varying node density, shape function order, Gaussian weight's shape, and the number of nodes in a local subdomain. The sensitivity study of DAM parameters shows that for the tested problems, the most suitable values of the Gaussian weight function and the number of nodes in a local subdomain are 5.0 and 13, respectively. Third-order convergence rate with better results is observed while using third-order polynomial shape functions.

A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations

This paper introduces a novel localized radial Trefftz collocation method (LRTCM) for steady-state heat conduction analysis in 2D and 3D functionally graded materials (FGMs) with exponential variations. The LRTCM is constructed by combining the traditional radial Trefftz collocation method (RTCM) and the localized collocation scheme. In the proposed LRTCM, the radial Trefftz basis of the heat conduction equation in FGMs is derived by the variable transformation and domain mapping method, and the approximation solution at each node is expressed as a linear combination of a radial Trefftz basis in each local subdomain, thus the resulting sparse linear system naturally satisfies governing equation at interior nodes and boundary conditions at boundary nodes. The LRTCM not only inherits the advantages of the RTCM (meshlessness, no fictitious boundary and high accuracy), but also works well in large-scale structures or with more complicated boundary conditions when compared to the RTCM. Finally, the feasibility, accuracy, efficiency and stability of the proposed method are investigated by three examples.

Local euchromatin enrichment in lamina-associated domains anticipates their repositioning in the adipogenic lineage

BackgroundInteractions of chromatin with the nuclear lamina via lamina-associated domains (LADs) confer structural stability to the genome. The dynamics of positioning of LADs during differentiation, and how LADs impinge on developmental gene expression, remains, however, elusive.ResultsWe examined changes in the association of lamin B1 with the genome in the first 72 h of differentiation of adipose stem cells into adipocytes. We demonstrate a repositioning of entire stand-alone LADs and of LAD edges as a prominent nuclear structural feature of early adipogenesis. Whereas adipogenic genes are released from LADs, LADs sequester downregulated or repressed genes irrelevant for the adipose lineage. However, LAD repositioning only partly concurs with gene expression changes. Differentially expressed genes in LADs, including LADs conserved throughout differentiation, reside in local euchromatic and lamin-depleted sub-domains. In these sub-domains, pre-differentiation histone modification profiles correlate with the LAD versus inter-LAD outcome of these genes during adipogenic commitment. Lastly, we link differentially expressed genes in LADs to short-range enhancers which overall co-partition with these genes in LADs versus inter-LADs during differentiation.ConclusionsWe conclude that LADs are predictable structural features of adipose nuclear architecture that restrain non-adipogenic genes in a repressive environment.

A localized spatiotemporal particle collocation method for long-time transient homogeneous diffusion analysis

This short communication proposes a novel localized spatiotemporal particle collocation method (LSPCM) to analyze long-time transient homogeneous diffusion problems. A time-dependent general solution of diffusion equation without singularity or near singularity at origin is developed. The LSPCM bypasses Laplace transformation or finite difference method to treat the time derivative of the diffusion equation, and can directly approximate the transient homogeneous diffusion problems. Each discrete node in computational domain is only supported by its nearby nodes covered by the local spatiotemporal subdomain. The physical variable of each discrete node is approximated by the linear combination of the physical variable of its nearby nodes and the time-dependent general solutions. Through satisfying boundary conditions and continuity conditions, the LSPCM eventually results in a large-scale sparse linear system which is easy to store and solve. Numerical experiments show that the LSPCM can accurately simulate long-time transient homogeneous diffusion problems by using a very long-time interval.

A multiscale domain decomposition approach for parabolic equations using expanded mixed method

We study the multiscale mortar expanded mixed method for second order parabolic partial differential equations. This technique involves non-overlapping domain decomposition which restrict a large problem into smaller pieces. Each block in the domain decomposition is discretized by expanded mixed method. The flux continuity is ensured by constructing a finite element space on the interface between subdomains. A pressure variable is introduced on the interfaces which play the role of Dirichlet boundary condition for each subdomain internal boundary. We demonstrate the unique solvability of discrete problem. We considered both continuous time and discrete time formulation and established a priori error estimates for local subdomain approximations. We derived the optimal order convergence for the appropriate choice of mortar space. An error estimate for mortar pressure variable is also provided. The numerical experiments are performed to show the accuracy and effectiveness of method.

Domain decomposition and expanded mixed method for parabolic partial differential equations

We developed and analyzed the multiblock mortar expanded mixed method for second order parabolic partial differential equations. This is a domain decomposition method in which the computational domain is expressed as the union of non-overlapping subdomains separated by interfaces. An auxiliary variable is introduced on the interface which represents the pressure and serves as Dirichlet boundary condition for local subdomain problems. The interface variable also plays the part of Lagrange multiplier to enforce flux matching condition on the interfaces. We explored the expanded mixed method to discretize each subdomain. We propose the semi-discrete formulation and address the solvability of the discrete problem. The optimal order convergence is provided for the continuous time case. We also investigate the fully discrete formulation and derived corresponding error estimates. The numerical experiments are conducted to demonstrate the theory developed in the paper.

A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains. For purely diffusion problems, we already proved that this scheme converges under minimal regularity assumptions (Abdulle and Rosilho de Souza, 2019) [1]. In this paper, we provide an algorithm for the automatic identification of the local elliptic problems' subdomains employing a flux reconstruction strategy. Reliable error estimators are derived for the local adaptive method. Numerical comparisons with a classical nonlocal adaptive algorithm illustrate the efficiency of the method.

Distinct small non-coding RNA landscape in the axons and released extracellular vesicles of developing primary cortical neurons and the axoplasm of adult nerves

ABSTRACT Neurons have highlighted the needs for decentralized gene expression and specific RNA function in somato-dendritic and axonal compartments, as well as in intercellular communication via extracellular vesicles (EVs). Despite advances in miRNA biology, the identity and regulatory capacity of other small non-coding RNAs (sncRNAs) in neuronal models and local subdomains has been largely unexplored. We identified a highly complex and differentially localized content of sncRNAs in axons and EVs during early neuronal development of cortical primary neurons and in adult axons in vivo. This content goes far beyond miRNAs and includes most known sncRNAs and precisely processed fragments from tRNAs, sno/snRNAs, Y RNAs and vtRNAs. Although miRNAs are the major sncRNA biotype in whole-cell samples, their relative abundance is significantly decreased in axons and neuronal EVs, where specific tRNA fragments (tRFs and tRHs/tiRNAs) mainly derived from tRNAs Gly-GCC, Val-CAC and Val-AAC predominate. Notably, although 5ʹ-tRHs compose the great majority of tRNA-derived fragments observed in vitro, a shift to 3ʹ-tRNAs is observed in mature axons in vivo. The existence of these complex sncRNA populations that are specific to distinct neuronal subdomains and selectively incorporated into EVs, equip neurons with key molecular tools for spatiotemporal functional control and cell-to-cell communication.