Local Basis Research Articles

NGLSFusion: Non-Use GPU Lightweight Indoor Semantic SLAM

Perception of the indoor environment is the basis of mobile robot localization, navigation, and path planning, and it is particularly important to construct semantic maps in real time using minimal resources. The existing methods are too dependent on the graphics processing unit (GPU) for acquiring semantic information about the indoor environment, and cannot build the semantic map in real time on the central processing unit (CPU). To address the above problems, this paper proposes a non-use GPU for lightweight indoor semantic map construction algorithm, named NGLSFusion. In the VO method, ORB features are used for the initialization of the first frame, new keyframes are created by optical flow method, and feature points are extracted by direct method, which speeds up the tracking speed. In the semantic map construction method, a pretrained model of the lightweight network LinkNet is optimized to provide semantic information in real time on devices with limited computing power, and a semantic point cloud is fused using OctoMap and Voxblox. Experimental results show that the algorithm in this paper ensures the accuracy of camera pose while speeding up the tracking speed, and obtains a reconstructed semantic map with complete structure without using GPU.

Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations

AbstractIn this paper, a hybrid numerical scheme based on combining exponential time differencing (ETD) and local radial basis function collocation method was constructed. Model problems with different boundary conditions were considered, and the resulting linear system was carefully analyzed. The relation between the number of points employed in the local radial basis function collocation method and the condition number of the coefficient matrix was given. For application, three typical differential equations were investigated, that is, the Allen–Cahn equation for checking the maximum‐preserving property, the combustion equation for checking the monotonicity‐preserving property, and the Gray–Scott system for checking the robustness of the proposed scheme. Numerical examples show the effectiveness of the proposed method.

Local N-electron valence state perturbation theory using pair-natural orbitals based on localized virtual molecular orbitals.

Second-order N-electron valence state perturbation theory (NEVPT2) is an exactly size-consistent and intruder-state-free multi-reference theory. To accelerate the NEVPT2 computation, Guo and Neese combined it with the local pair-natural orbital (PNO) method using the projected atomic orbitals (PAOs) as the underlying local basis [Guo et al., J. Chem. Phys. 144, 094111 (2016)]. In this paper, we report the further development of the PNO-NEVPT2 method using the orthonormal and non-redundant localized virtual molecular orbitals (LVMOs) instead of PAOs. The LVMOs were previously considered to perform relatively poor compared to PAOs because the resulting orbital domains were unacceptably large. Our prior work, however, showed that this drawback can be remedied by re-forming the domain construction scheme using differential overlap integrals [Saitow et al., J. Chem. Phys. 157, 084101 (2022)]. In this work, we develop further refinements to enhance the feasibility of using LVMOs. We first developed a two-level semi-local approach for screening out so-called weak-pairs to select or truncate the pairs for PNO constructions more flexibly. As a refinement specific to the Pipek-Mezey localization for LVMOs, we introduced an iterative scheme to truncate the Givens rotations using varying thresholds. We assessed the LVMO-based PNO-NEVPT2 method through benchmark calculations for linear phenyl alkanes, which demonstrate that it performs comparably well relative to the PAO-based approach. In addition, we evaluated the Co-C bond dissociation energies for the cobalamin derivatives composed of 200 or more atoms, which confirms that the LVMO-based method can recover more than 99.85% of the canonical NEVPT2 correlation energy.

Localized RBF methods for modeling infiltration using the Kirchhoff-transformed Richards equation

We develop a new approach to solve the nonlinear Richards equation based on the Kirchhoff transformation and localized radial basis function (LRBF) techniques. Our aim is to reduce the nonlinearity of the governing equation and apply LRBF methods for modeling unsaturated flow through heterogeneous soils. In our methodology, we propose special techniques which deal with the heterogeneity of the medium in order to apply the Kirchhoff transformation where we used the Brooks and Corey model for the capillary pressure function and a power-law relation in saturation for the relative permeability function. The new approach allows us to avoid the technical issues encountered in the Kirchhoff transformation due to soil heterogeneity in order to reduce the nonlinearity of the model equation. The resulting Kirchhoff-transformed Richards equation is solved using LRBF methods which have advantages in terms of computational cost since they do not require mesh generation. Furthermore, LRBF techniques lead to a system with a sparse matrix which allows us to avoid ill-conditioned issues. To validate the developed approach for predicting the dynamics of unsaturated flow in porous media, numerical experiments are performed in one, two, and three-dimensional soils. The numerical results demonstrate the efficiency and accuracy of the proposed techniques for modeling infiltration through heterogeneous soils.

Wave packet enriched finite elements for thermo-electro-elastic wave propagation problems with discontinuous wavefronts

In this article, we study the numerical properties of the recently developed local (element-domain) harmonic basis function enriched finite element (FE) for wave propagation problems. The study includes the effect of the enrichment harmonics on the conditioning of system matrices and how the diagonal scaling mass lumping technique influences the possible ill-conditioning and the solution accuracy. Subsequently, a wave packet enriched thermoelectromechanical FE formulation is presented for axisymmetric and planar wave propagation problems in piezoelastic media. The conventional Lagrange interpolations for the displacement, temperature, and electric potential fields are enriched with the element-domain sinusoidal functions which satisfy the partition of unity condition. The extended Hamilton’s principle and constitutive relations of the Lord–Shulman and Green–Lindsay generalized piezothermoelasticity are employed to derive the coupled system of equations of motion which is solved using Newmark- direct time integration scheme. The performance of the proposed elements is assessed and wave characteristics are studied for the problems of thermoelastic shock waves in an elastic annular disk and thermoelectric shock waves in a piezoelectric hollow cylinder. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for these problems involving sharp discontinuities in the fields at the wavefronts.

Research on the modified surrogate model based on local RBF for concrete dam static and dynamic response analysis

In recent years, as AI technology has advanced, online monitoring of dams has garnered increasing interest. In addition, surrogate model technology is a crucial component of online monitoring. As a result, developing a high-quality surrogate model has become one of the pillars of dam online monitoring. This work proposes a local radial basis function based on sensitivity modification to address the deficiencies of the current radial basis function. In addition, a benchmark function is utilized to validate the method’s viability. Comparisons with BP neural network and RBF demonstrate the usefulness of the proposed strategy. The analysis demonstrates that the proposed strategy for constructing a surrogate model of the dam’s structural behavior is possible and accurate. This paper aims to establish a high-quality surrogate model to provide technical support for dam online monitoring.

Symmetrization of Localized Molecular Orbitals.

We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The vast potential of our algorithm to compress a full set of molecular orbitals into only a minimal set of symmetry-unique orbitals is demonstrated, starting from localized bases of either Pipek-Mezey or Foster-Boys orbitals. Comparisons of results based on either of these two localization procedures indicate that Foster-Boys molecular orbitals can be spanned by a smaller number of symmetry-unique orbitals on average, making these outstanding candidates for the exploitation of general, (non-)Abelian point-group symmetries in a range of local correlation methods. As an illustration of said compressibility, our algorithm is capable of identifying a mere 14 symmetry-unique orbitals for the buckminsterfullerene in the highly symmetric Ih molecular point group, corresponding to only 1.7% of its total 840 molecular orbitals in a standard double-ζ basis set. The present work thus marks an important advancement in the exploitation of point-group symmetry within local correlation methods, for which the appropriate adaption of symmetry uniqueness among orbitals has the potential to yield unprecedented speed-ups.

Adaptive multiscale extended finite element method (MS-XFEM) for the simulation of multiple fractures propagation in geological formations

In fractured geological formations, as a result of the in-situ stress changes, fractures can propagate or slide. This phenomenon can be efficiently modeled by the extended finite element method (XFEM) when there are only a few fractures present. However, geological reservoirs contain many fractures which can also cross and are densely populated. Therefore, the classical XFEM is too expensive to be applied for the simulation of propagating fractures in geological formations. To reduce the costs, typically, homogenization or upscaling is used. However, they result in inaccurate solutions, since no separation of scales exists in this process. To resolve this challenge, in this work, a multiscale XFEM (MS-XFEM) for propagating fractures is developed and presented. In each time step, given the current geometries of the fractures, local XFEM-based basis functions are constructed or adaptively updated. The adaptive update takes place in certain regions where fracture geometries are changed due to propagation. Using these basis functions, a very efficient FEM-based coarse-scale system is developed since it has no extra degrees of freedom (DOFs). Once the coarse-scale system is solved, its solution is prolonged to the fine-scale original resolution using the basis functions. This approximate fine-scale solution is then used to estimate the group of growing fractures tips and their growing angles. This allows for exploiting the locality of the propagation process fully while solving a global system. To control the error, an iterative procedure is also developed. Proof-of-concept test cases are presented to study the developed MS-XFEM algorithm. It is shown that MS-XFEM results are capable of predicting the propagating paths for complicated fracture patterns. As such, MS-XFEM casts a promising method for field-scale applications.

Improving strong scalability of electronic structure simulations with reduced overhead of communications

Physically realizable semiconductor electronic devices easily include more than several million atoms even though they are in nanoscale, so electronic structure simulations of huge atomic systems are the key to predict performance characteristics of such devices. The empirical tight-binding (TB) model, which uses a finite set of localized bases for descriptions of a single atom with assumption of nearest-neighbor coupling, has been extensively adopted to solve electronic structures of large-scale atomic systems, and the size-capability of TB simulations has been continuously improved with aids of parallel computing. Recently, we have demonstrated a strong scalability of TB simulations up to 2,500 computing nodes for a model problem consisting of 400 million atoms, where the scalability is limited due to the overhead of collective communications that the core numerical method must involve to get a partial eigenspectrum of the sparse Hamiltonian system matrix. To reduce the cost of Message Passing Interface (MPI) communications and its effect on the end-to-end simulation time, here we design an equivalent transformation of the sparse matrix eigensolver, and employ a core dedicated to MPI communications with dynamic scheduling of threads. Through rigorous benchmark tests against model problems of various sizes, it is confirmed that our method improves the strong scalability of TB simulations by more than 10% in a huge computing environment, by reducing the time-cost of both core computations and collective communications.

Numerical modeling of the ion‐acoustic solitary waves arising in nonlinear dispersive system

This paper proposes a numerical scheme for the (2 + 1)‐dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK‐BBME). The ZK‐BBME represents a long‐wave model with large wavelength that explains the water wave phenomena in nonlinear dispersive system. The solution of the ZK‐BBME is discretized by using hybridization of the finite difference and localized radial basis function based on partition of unity method. The association of this hybridization leads to a meshless method and it does not requires any linearization. In the initial step, the PDE is converted into a nonlinear ODE system by making use of radial kernels. In the next step, the obtained nonlinear ODE system is solved based on an ODE solver of high order. The global collocation technique imposes a large computational cost because a dense algebraic system must be calculated. This proposed strategy is based on decomposing the initial domain into a number of sub‐domains using kernel approximation on each sub‐domain. Three numerical examples are illustrated to clarify the efficiency and accuracy of the proposed strategy.

Karhunen-Loeve-based approach to tracking of rapidly fading wireless communication channels

When parameters of wireless communication channels vary at a fast rate, simple estimation algorithms, such as weighted least squares (WLS) or least mean squares (LMS) algorithms, cannot estimate them with accuracy needed to secure reliable operation of the underlying communication systems. In cases like this, the local basis function (LBF) estimation technique can be used instead, significantly increasing the achievable tracking accuracy. We show that when some prior knowledge of statistical properties of parameter changes is available, such as the bandwidth of their variation, both the type and the number of basis functions, used in the LBF approach to approximate time-varying channel parameters, can be optimized using the Karhunen-Loève (KL) decomposition based technique.

Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method

The free vibration of two-directional functionally graded (2D-FG) thick curved nanobeam with concentrated mass is investigated for various boundary conditions. Hamilton’s principle is employed to develop the governing equations of the 2D-FG curved nanobeam using the first-order shear deformation theory (FSDT). The small scale effect is captured by the nonlocal elasticity theory of Eringen. The nanobeam is functionally graded in the transverse and circumferential directions of the curved nanobeam. The governing equations of the system are obtained as three coupled partial differential equations with non-constant coefficients. An appropriate meshless formulation is developed to discretize the governing equations based on local weak formulation and radial basis function. The presented meshless method is employed to study the free vibration of the one-directional and two-directional functional graded curved nanobeams. Simple-simple, free-free, clamped-clamped, and clamped-free edge conditions are investigated. Moreover, an analytical solution is developed for simple-simple transversely 1D-FG curved nanobeam. In the numerical results, the natural frequencies and mode shapes of shadow and deep curved nanobeam are studied and the influence of effective parameters such as nonlocal parameter, FG power indexes, opening angle, edge conditions, and concentrated mass are investigated. It is seen that shear locking effect is eliminated in present meshless formulation.

A pore-level multiscale method for the elastic deformation of fractured porous media

Pore-scale models are useful for understanding and upscaling the mechanical deformation of fractured porous media. The highest fidelity solutions are obtained by direct numerical simulation (DNS), in which the governing equations are discretized and solved with a fine-grid solver (e.g., finite elements) over a 3D image (e.g., X-ray) of a porous sample. However, the downside of DNS is its high computational cost. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy in modeling the linear elastic response of porous solids with arbitrary microstructure and crack pattern. PLMM decomposes the solid into subdomains, over which local basis and correction functions are built. These functions are then coupled with a global problem to yield an approximate solution, whose errors can be iteratively corrected. A key feature of PLMM is that the decomposition need not conform to the cracks, unlike a previous formulation by the authors. This paves the way towards solving crack nucleation and growth problems in the future without the need to dynamically update the decomposition. We represent cracks diffusely using a phase-field variable and explore three strategies for capturing them through either the basis or correction functions. The implications of each strategy on the convergence rate and computational cost are analyzed.

Distribution and accumulation of heavy metals in the catchment catenary complex and bottom sediments of the water body in an urban environment

Problem Statement. The pollutant intake into water bodies is one of the issues of urban areas. The pollutant input from the residential area of the city with surface runoff can many times exceed the input of pollutants from industrial and recreational areas, as well as from point pollutant sources. The objective of the study is 1) assess the distribution of chemical elements in catchments of water bodies in an urbanised area, 2) accumulation of chemical elements in solid matter of bottom sediments of surface water bodies with catchments in the functional areas of the city, 3) identify the main mechanisms of transfer of elements in solid matter from catchments to water bodies. The study was conducted on the example of Ekaterinburg (Russia). The material for the study consisted of the results of a landscape environmental and geochemical survey carried out in the city area in 2019–2021. Results. The distributions of element concentrations between functional landscape zones in the catenaries of the Kharitonovsky Garden and Chemodanchik reservoir catchments in Ekaterinburg were obtained. The distributions of metal concentrations in the catchment components show a tendency for the transfer of substance of different origin from the landscape components by lateral migration flows to the local basis of denudation (a drainless surface water body). At the same time in the bottom sediments of the reservoir there is a multiple accumulation of both pollutants and elements of typomorphic association. Dust fractions are the main carrier of contaminants in catchments.

A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model

This work deals with the finite element approximation of a prestressed shell model in the case of isometrically deformed shell. Using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirm the efficiency of our residual a posteriori estimator.

Reinforcement learning control with function approximation via multivariate simplex splines

SummaryIn the field of optimal control for continuous nonlinear systems, function approximation methods are often employed to overcome the curse of dimensionality. Compared to other global function approximators like neural networks, multivariate splines can be easily evaluated and adapted on a local basis with linearity in the parameters. In this work, a multivariate spline based reinforcement learning (RL) strategy is proposed for solving the continuous‐time nonlinear control problem. Based on the classic value iteration method, multivariate splines are integrated into RL algorithms to approximate continuous value functions and policy functions from discrete action and value samples. Hence, the determined splines with updated coefficients can be utilized in continuous control of nonlinear systems. In the simulation experiment, the performance of the spline‐based RL control is evaluated in controlling an under‐actuated inverted pendulum. The proposed method is compared with the value iteration based discrete control strategy and the neural network based continuous control strategy. The simulation results indicate that the proposed method based on multivariate splines has better control performance with less state oscillations, energy consumption and convergence time in comparison with discrete value iteration and neural network based RL, and the adoption of simplex splines improves the function approximation efficiency with less computation time than neural network optimization.

Stability of 𝚤canonical bases of irreducible finite type of real rank one

It has been known since their birth in Bao and Wang’s work that the ı \imath canonical bases of ı \imath quantum groups are not stable in general. In the author’s previous work, the stability of ı \imath canonical bases of certain quasi-split types turned out to be closely related to the theory of ı \imath crystals. In this paper, we prove the stability of ı \imath canonical bases of irreducible finite type of real rank 1 1 , for which the theory of ı \imath crystals has not been developed, by means of global and local crystal bases.

Building Children's Awareness with Local Knowledge-Based Mangrove Literacy Models in Coastal Areas

Degradation of coastal environment that occurs in parts of Indonesia's coastal areas is generally caused by erosion, climate change, development, and loss of mangrove forests. This degradation also has an impact on the reduction of the land area inhabited by the community. Bedono Village in Sayung District, Demak Regency, Central Java is one of the areas with the worst conditions, where a third of its area was lost due to tidal floods. One alternative solution that can be done is to restore the function of mangroves in a sustainable manner which is carried out on a local basis and inclusive awareness. This paper aims to discuss the concept of conscientization from Paulo Freire which emphasizes the presence of consistency and inclusiveness as the fruit of full self-awareness to solve the problem of the decrease of the quality of the coastal environment and the reduce of Indonesia's coastal areas. The research approach used is qualitative and Participatory Rural Appraisal (PRA). PRA is used to map the problems and potentials of coastal communities and children's groups, including the local wisdom values of the community. The data collection technique uses interviews, observation, documentation, and group discussions from August to November 2021. Through a socio-cultural approach, and collaboration with formal and informal educational institutions, the result of this study can be a repressive and preventive model in alleviating environmental problems, especially coastal problems. By formulating and applying the Paulo Freire consientizacio model based on local potential, it was found that the reconstruction of mangrove conservation education was able to build children's critical and transformative awareness that would be able to solve problems in coastal areas. Based on an inclusive mangrove literacy approach, the application of education is targeted at the children of this generation as conservation agents capable of caring for and innovating to improve the environment with awareness that has been formed through mangrove literacy education from an early age.

The local radial basis function collocation method for elastic wave propagation analysis in 2D composite plate

In this paper, the local radial basis function collocation method (LRBFCM) is applied to simulate the in-plane elastic wave propagation in composite plate. In order to reduce the influence caused by large aspect ratio, an improved LRBFCM based on direct method is developed so that the governing equations can be numerically decoupled by using bilinear nodes in different directions. Several numerical examples are given to demonstrate the accuracy and efficiency of the proposed technique in simulating the elastic wave propagation with large aspect ratio.

A Study on the Language-Related Adjustment Problems of Pupil-Teachers

Adjustment is an age-old concept that helps in maintaining wellbeing of the individual and the society. Pre-service teacher education prepares students towards making a competent individual that can effectively manage the society, hence the pre-service teachers must be a well-adjusted individual. Language often plays a key role in determining the adjustment pattern of any individual. The present study made an attempt to explore the adjustment problems of pupil-teachers with specific focus on the local and official language related issues. The objectives included identification of language-related adjustment levels of pupil-teachers and the difference of adjustment level on the basis of certain demographic variables like gender, locality, area, and age group. The sample of this descriptive survey study comprised of 165 pupil-teachers of Western Odisha region selected through simple random sampling. The data was collected using a self-standardized tool named LBAS (Language Barrier and Adjustment Scale). The findings revealed that there was a significant level of adjustment issues among the pupil-teachers. However, there were no significant differences amongst the pupil-teachers on the basis of gender, locality, area, and age group.