Refinement Algorithm Research Articles

Goal-oriented mesh adaptivity for inverse problems in linear micromorphic elasticity

In this work, we extend goal-oriented mesh adaptivity to parameter identification for a class of linear micromorphic elasticity problems. Starting from a compact formulation in our previous work (Ju and Mahnkhen, 2017), we propose a two-level optimization framework based on goal-oriented error estimation. By means of a sensitivity analysis of the generalized constitutive relations, we establish a gradient-based solver for the inverse problem, where parameters are optimized within an inner optimization loop for a given mesh. Exact error representations are derived from a Lagrange method, aiming at a quantity of interest as a user-defined functional of the parameters. By using a patch recovery technique for enhanced solutions, a computable error estimator is presented and used to drive an adaptive refinement algorithm, which forms an outer optimization loop. For a numerical study, we investigate the performance of the resulting adaptive procedure in case of perfect, incomplete and perturbed data. The results confirm the effectiveness of the proposed adaptive procedure.

Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach

The present study proposes an accurate lattice Boltzmann direct coupling algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. Consequently, any interfering noise that may pollute the acoustic predictions must be reduced.The proposed grid refinement algorithm differs from conventionally used ones, in which an overlapping mesh layer is considered. Instead, it provides a direct connection allowing a tighter link between fine and coarse grids, especially with the use of a coherent equilibrium function shared by both grids. Moreover, the direct coupling makes the algorithm more local and prevents the duplication of points, which might be detrimental for massive parallelization. This work follows our first study (Astoul et al. 2020 [1]) on the deleterious effect of non-hydrodynamic modes crossing mesh transitions, which can be addressed using an appropriate collision model: the hybrid recursive regularization. The grid coupling algorithm is assessed in the context of computational aeroacoustics and compared to a widely-used cell-vertex algorithm. The validation benchmark includes the simulation of (1) an acoustic pulse, (2) a vortex transport by a mean flow, and finally, (3) a turbulent circular cylinder wake flow at high Reynolds number. In the end, the proposed approach is proven to drastically reduced the spurious noise generated at grid interfaces, hence, paving the way for accurate and efficient aeroacoustic simulations based on lattice Boltzmann methods.

Atomization of misaligned impinging liquid jets

This study numerically investigated the atomization characteristics of misaligned impinging jets, with the misalignment ratio ê ranging between 0 and 0.2, by employing the volume of fluid method with an adaptive mesh refinement algorithm. The results show that the droplet Sauter mean diameter varies non-monotonically with ê and reaches the minimum value, which implies the best atomization performance, at ê=0.1 under operating conditions concerned in the present work. Meanwhile, the moderately misaligned impingement also leads to a more uniform spatial dispersion of the atomized fragments and droplets. These unique spray behaviors can be attributed to the instability and disintegration of the liquid sheet formed upon jet impingement, as evident from the non-monotonic dependence of the breakup length of the liquid sheet on the misalignment ratio ê. Analyses on the velocity fluctuation and vorticity distribution further suggest that the misalignment alters the intrinsic instability mode of the liquid sheet by introducing a lateral stretch effect, which diverts the peak streamwise momentum away from the centerline. The current finding indicates that misalignment tuning could be a promising optimization and control technique in propellant mixing and atomization.

P-wave picking for earthquake early warning: refinement of aTpdmethod

SUMMARYDetecting P-wave onsets for online processing is an important component for real-time seismology. As earthquake early warning systems around the world come into operation, the importance of reliable P-wave detection has increased, since the accuracy of the earthquake information depends primarily on the quality of the detection. In addition to the accuracy of arrival time determination, the robustness in the presence of noise and the speed of detection are important factors in the methods used for the earthquake early warning. In this paper, we tried to improve the P-wave detection method designed for real-time processing of continuous waveforms. We used the new Tpd method, and proposed a refinement algorithm to determine the P-wave arrival time. Applying the refinement process substantially decreases the errors of the P-wave arrival time. Using 606 strong motion records of the 2011 Tohoku earthquake sequence to test the refinement methods, the median of the error was decreased from 0.15 to 0.04 s. Only three P-wave arrivals were missed by the best threshold. Our results show that the Tpd method provides better accuracy for estimating the P-wave arrival time compared to the STA/LTA method. The Tpd method also shows better performance in detecting the P-wave arrivals of the target earthquakes in the presence of noise and coda of previous earthquakes. The Tpd method can be computed quickly, so it would be suitable for the implementation in earthquake early warning systems.

Constrained multi-objective optimization of compact microwave circuits by design triangulation and pareto front interpolation

Development of microwave components is an inherently multi-objective task. This is especially pertinent to the design closure stage, i.e., final adjustment of geometry and/or material parameters carried out to improve the electrical performance of the system. The design goals are often conflicting so that the improvement of one normally leads to a degradation of others. Compact microwave passives constitute a representative case: reduction of the circuit footprint area is detrimental to electrical figures of merit (e.g., the operating bandwidth). Identification of the best available trade-off designs requires multi-objective optimization (MO). This is a computationally expensive task, especially when executed at the level of full-wave electromagnetic (EM) simulation. The computational complexity issue can be mitigated through the employment of surrogate modeling methods, yet their application is limited by a typically high nonlinearity of system responses, and the curse of dimensionality. In this paper, a novel technique for fast MO of compact microwave components is proposed, which allows for sequential rendition of the trade-off designs using triangulation of the already available Pareto front as well as rapid refinement algorithms. Our methodology is purely deterministic; in particular, it does not rely on population-based nature-inspired procedures. The three major benefits are low computational cost, possibility of handling explicit design constraints, and a capability of producing a visually uniform representation of the Pareto front. The algorithm is demonstrated using a compact branch-line coupler and a three-section impedance matching transformer. In both cases, considerable savings are obtained over the benchmark, here, the state-of-the-art surrogate-assisted MO technique.

DYNAMIC ANALYSIS OF VARIABLE MESH ISOGEOMETRIC THIN PLATE BASED ON T-SPLINE

The local strain of a thin plate with large displacement and large deformation will change dramatically under contact and collision working conditions. In order to ensure the accuracy and computational efficiency of flexible thin plate system’s dynamic analysis, this investigation integrates computer aided design (CAD) and computer aided engineering (CAE) systems, and proposes an isogeometric analysis (IGA) method for variable mesh flexible multibody system based on T-spline surface elements. Firstly, the kinematic description of a Kirchhoff thin plate based on T-spline surface elements is modeled, and the elastic model of a thin plate discretized by T-spline surface elements is established according to the nonlinear Green−Lagrange strain. Secondly, the goal of updating mesh of T-spline surface locally is achieved by inserting knots into the local region of the corresponding T-mesh. The transformation matrix, which is used to calculate the new generalized coordinates, generalized velocities and generalized accelerations of the refined system, is obtained by using the T-spline blending function refinement algorithm. The calculating solution algorithm for the dynamic equation of the system with variable degrees of freedom is created by combining the generalized α method with geometry update routine, and thus the local mesh refinement algorithm for the surface which is modeled by T-spline is formed. Finally, statics examples and flexible pendulum model verify the correctness for the elastic model of Kirchhoff thin plate based on T-spline surface, as well as computation precision and convergence for the proposed method in the dynamics analysis respectively. The dynamic analysis of the impacted flexible thin plate shows that the T-spline element and local refinement algorithm proposed in this paper can realize local mesh update only in the area where the strain changes violently, such as contact and collision, so as to control the degree of freedom of the system and improve the computational efficiency.

A High-Precision and Wideband Fundamental Frequency Measurement Method for Synchronous Sampling Used in the Power Analyzer

In the dedicated high-precision power quality analyzer, synchronous sampling is required to reduce the effect of spectrum leakage produced by the discrete Fourier transform process. Thus, accurate fundamental frequency measurement is urgently needed. However, due to the harmonics and noise in the power signal, it is difficult to achieve the accurate fundamental frequency measurement. Moreover, with the wide application of high-frequency programmable power supply, the fundamental frequency is gradually increasing, which requires power analyzers to have the abilities of both high precision and a wide range of the fundamental frequency measurement. To solve these issues, a new fundamental frequency measurement architecture used in synchronous sampling is proposed. This architecture consists of a small-point fast Fourier transform module, spectrum refinement algorithm, and a multimodal optimization method to calculate the accurate fundamental frequency under large harmonic conditions. In the practical hardware platform results, this architecture has a large fundamental frequency measurement range from 20 Hz to 200 kHz with a relative error which is <0.004%. The wideband fundamental frequency measurement structure proposed in this article achieves high measurement accuracy.

Modeling Fracture in Rate-Dependent Polymer Networks: A Quasicontinuum Approach

Abstract Soft materials, such as rubber and gels, exhibit rate-dependent response where the stiffness, strength, and fracture patterns depend largely on loading rates. Thus, accurate modeling of the mechanical behavior requires accounting for different sources of rate dependence such as the intrinsic viscoelastic behavior of the polymer chains and the dynamic bond breakage and formation mechanism. In this chapter, we extend the QC approach presented in Ghareeb and Elbanna (2020, An Adaptive Quasi-Continuum Approach for Modeling Fracture in Networked Materials: Application to Modeling of Polymer Networks, J. Mech. Phys. Solids, 137, p. 103819) to include rate-dependent behavior of polymer networks. We propose a homogenization rule for the viscous forces in the polymer chains and update the adaptive mesh refinement algorithm to account for dynamic bond breakage. Then, we use nonlinear finite element framework with predictor–corrector scheme to solve for the nodal displacements and velocities. We demonstrate the accuracy of the method by verifying it against fully discrete simulations for different examples of network structures and loading conditions. We further use the method to investigate the effects of the loading rates on the fracture characteristics of networks with different rate-dependent parameters. Finally, We discuss the implications of the extended method for multiscale analysis of fracture in rate-dependent polymer networks.

Phase-field simulation of ductile fracture in shell structures

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff–Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, displacement and rotational continuity and C0 and C1 continuity of the phase-field, the latter required if a higher-order phase-field formulation is adopted. We study the mesh dependency of the numerical model and we show that mesh refinement allows for capturing important features of ductile fracture such as cracking along shear bands. Therefore, we investigate the effectiveness of a predictor–corrector algorithm for adaptive mesh refinement based on LR NURBS. Thanks to the adoption of time- and space-adaptivity strategies, it is possible to simulate the failure of complex structures with a reasonable computational effort. Finally, we compare the predictions of the numerical model with experimental results.

H 1-stability of the L2-projection onto finite element spaces on adaptively refined quadrilateral meshes

Abstract The $L^2$-orthogonal projection $ {\varPi }_h:L^2(\varOmega )\rightarrow {\mathbb{V}}_h$ onto a finite element (FE) space $ {\mathbb{V}}_h$ is called $H^1$-stable iff $ \|{ {\varPi }_h u}\|_{H^{1}}(\varOmega )\leq C\|{u}\|_{H^{1}}(\varOmega ) $ for any $u\in H^1(\varOmega )$ with a positive constant $C\neq C(h)$ independent of the mesh size $h>0$. Stability of this projection in the $H^1$-norm is an important component in the numerical analysis of FE methods, and it has been extensively studied before for triangular meshes in two dimensions and tetrahedral meshes in three dimensions. In this work, we analyse $H^1$-stability of adaptively refined quadrilateral meshes in two dimensions. We show that the refinement strategies Q-RG and Q-RB, introduced originally in Bank et al. (1983, Some refinement algorithms and data structures for regular local mesh refinement. Sci. Comput., 1, 3–17) and Kobbelt (1996, Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Comput. Graph Forum, 15, 409–420), are $H^1$-stable for FE spaces of polynomial degree $p=2,\ldots ,9$.

АЛГОРИТМЫ КИНЕМАТИЧЕСКОГО УПРАВЛЕНИЯ МНОГОЗВЕННЫМИ МАНИПУЛЯЦИОННЫМИ РОБОТАМИ НА ОСНОВЕ НЕЧЁТКОЙ НЕЙРОННОЙ СЕТИ

The paper considers the possibility of constructing a kinematic control algorithm for manipulating robots with a serial-connected links. The construction of a control system based on a fuzzy neural network is proposed. The results of experimental studies on the selection of parameters of a fuzzy neural network in accordance with the set optimality criterion (in terms of speed), taking into account the subsequent iterative refinement by the Newton-Raphson method, are presented. The following network parameters are considered: the number and type of node membership functions, the size of the training sample with a different number of training approaches. An algorithm for forming a training sample for fuzzy neural networks is proposed in order to reduce the positioning error of the working body of the manipulating mechanism near the outer boundary of the workspace. The possibility of adapting the kinematic control algorithms by adjusting the parameters of the membership functions in the network nodes when performing the same type of tasks, based on the data of the Newton-Raphson refinement algorithm, is demonstrated. In the framework of this work, a comparative analysis of the developed kinematic control algorithm with algorithms based on iterative and neural network methods for solving the inverse kinematics problem of a manipulative robot is carried out. The conclusion is made about the increase in the speed for calculations of kinematic control algorithms while maintaining the required accuracy

АЛГОРИТМЫ КИНЕМАТИЧЕСКОГО УПРАВЛЕНИЯ МНОГОЗВЕННЫМИ МАНИПУЛЯЦИОННЫМИ РОБОТАМИ НА ОСНОВЕ НЕЧЁТКОЙ НЕЙРОННОЙ СЕТИ

The paper considers the possibility of constructing a kinematic control algorithm for manipulating robots with a serial-connected links. The construction of a control system based on a fuzzy neural network is proposed. The results of experimental studies on the selection of parameters of a fuzzy neural network in accordance with the set optimality criterion (in terms of speed), taking into account the subsequent iterative refinement by the Newton-Raphson method, are presented. The following network parameters are considered: the number and type of node membership functions, the size of the training sample with a different number of training approaches. An algorithm for forming a training sample for fuzzy neural networks is proposed in order to reduce the positioning error of the working body of the manipulating mechanism near the outer boundary of the workspace. The possibility of adapting the kinematic control algorithms by adjusting the parameters of the membership functions in the network nodes when performing the same type of tasks, based on the data of the Newton-Raphson refinement algorithm, is demonstrated. In the framework of this work, a comparative analysis of the developed kinematic control algorithm with algorithms based on iterative and neural network methods for solving the inverse kinematics problem of a manipulative robot is carried out. The conclusion is made about the increase in the speed for calculations of kinematic control algorithms while maintaining the required accuracy

Development and Evaluation of GlycanDock: A Protein-Glycoligand Docking Refinement Algorithm in Rosetta.

Carbohydrate chains are ubiquitous in the complex molecular processes of life. These highly diverse chains are recognized by a variety of protein receptors, enabling glycans to regulate many biological functions. High-resolution structures of protein-glycoligand complexes reveal the atomic details necessary to understand this level of molecular recognition and inform application-focused scientific and engineering pursuits. When experimental challenges hinder high-throughput determination of quality structures, computational tools can, in principle, fill the gap. In this work, we introduce GlycanDock, a residue-centric protein-glycoligand docking refinement algorithm developed within the Rosetta macromolecular modeling and design software suite. We performed a benchmark docking assessment using a set of 109 experimentally determined protein-glycoligand complexes as well as 62 unbound protein structures. The GlycanDock algorithm can sample and discriminate among protein-glycoligand models of native-like structural accuracy with statistical reliability from starting structures of up to 7 Å root-mean-square deviation in the glycoligand ring atoms. We show that GlycanDock-refined models qualitatively replicated the known binding specificity of a bacterial carbohydrate-binding module. Finally, we present a protein-glycoligand docking pipeline for generating putative protein-glycoligand complexes when only the glycoligand sequence and unbound protein structure are known. In combination with other carbohydrate modeling tools, the GlycanDock docking refinement algorithm will accelerate research in the glycosciences.

Application of the finite volume method for geomechanics calculation and analysis on temperature dependent poromechanical stress and displacement fields in enhanced geothermal system

The hot dry rock (HDR) development is a hot research field in recent years. Numerical simulation based on thermal-hydraulic-mechanical coupling model is a key technique for the HDR development evaluation. The calculation of geomechanics is an important part of the coupling thermal-hydraulic-mechanical simulation, and it is usually implemented by finite element method. However, meshing methods of geological modeling software are designed to serve seepage simulation, and grid quality cannot meet the requirements of finite element method. In this paper, finite volume method has been proposed to calculate the distribution of underground stress field, in order to solve the problem of discontinuous grid vertexes and calculation failure caused by finite element method. In addition, the mesh of geological modeling software is for finite difference method or finite volume method, which cannot be used directly by finite element method. In this paper, spatial discretization pattern of quasi static stress balance equation based on the finite volume method is obtained, the local grid refinement algorithm is proposed, the solution workflow of thermal-hydraulic-mechanical (THM) coupling model is presented, and the solution of displacement discretization equations and THM one way coupling model are implemented by C++ programming language. Finally, the feasibility and accuracy of the finite volume method of stress field calculation are verified through a series of numerical test examples compared with commercial finite element software. Several THM coupling simulation cases of enhanced geothermal system are presented by finite volume method. Numerical test results show that the calculation error between finite volume method and finite element method is less than 1%. Moreover, the variation of principal stress, induced by pore pressure and thermal stress, can reach 8 to 20 MPa. The finite volume method provides a unified technical framework for geomechanics and thermal-hydraulic calculation. Moreover, the method can be directly combined with geological modeling software without using two sets of grids. The results prove that the finite volume method would be a promising approach for thermal-hydraulic-mechanical simulation.

Recurrent neural networks as optimal mesh refinement strategies

We show that optimal mesh refinement algorithms for a large class of PDEs can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input size, i.e., number of elements of the mesh. This includes problems for which no optimal adaptive strategy is known yet. The proposed algorithm is problem independent in the sense that it only requires the current numerical approximation in order to optimally refine the mesh. Thus, the method is a provably optimal black-box mesh refinement tool for a wide variety of PDE problems.

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

A Sequential Least Squares Method for Elliptic Equations in Non-Divergence Form

We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation to the gradient in a piecewisely irrotational polynomial space. Then together with the numerical gradient, we seek a numerical solution of the primitive variable in continuous finite element space. The variational setting naturally provides a posteriori error which could be used in an adaptive refinement algorithm. The error estimates in $L^2$ norm and energy norms for both two unknowns are derived. By a series of numerical experiments, we verify the convergence rates and show the efficiency of the adaptive algorithm.

Applications of a central ENO and AUSM schemes based compressible N-S solver with reconstructed conservative variables

In this study we couple a family of AUSM-flux splitting schemes with the CENO high-order scheme and evaluate the overall performance of the developed in-house solver in terms of modeling the flow physics accurately for a wide range of benchmark problems. The solver uses reconstructed conservative variables. The problems include inviscid and viscous flows that cover low subsonic through transonic and hypersonic regimes. We test the order of accuracy of the implemented CENO scheme by interpolating a smooth spherical cosine function and then calculating the L-norms. The obtained results confirm the consistency between the spatial accuracy and the order of reconstruction up to 5th order. We are able to reach 4th order of accuracy in time by using a Runge-Kutta scheme and thereby we obtain a perfect match with the WENO results available in the literature for the unsteady problem of interaction of a moving vortex with a stationary normal shock. In order to reduce the computational cost of the developed solver and to be able to model more challenging problems, we utilize the advantageous adaptive mesh refinement that allows us to resolve the discontinuities near shocks and slip lines. Our adaptive mesh refinement algorithm is based on a smoothness indicator factor, and allows us to reach the same level of accuracy as the WENO schemes do for the inviscid double Mach reflection problem by using considerably less amount of cells.

A structured study on the dynamic bifurcation behavior of a continuous ethanol fermentor

The oscillatory behavior of a continuous ethanol fermentor, in the high feed sugar concentration region (200 g/L), is analyzed using the bifurcation theory. The mathematical model was solved using the arc-length continuation method including a refinement algorithm based on the Heaviside step function technique. Experimental data for ethanol production using Zymomonas mobillis were fitted to a phenomenological model based on the concept of dynamic specific growth rate and inhibition. Thus, a through connection is defined between model parameters and oscillatory behavior. Our approach shows the rich static and dynamic bifurcation topology of the continuous fermentation reactor, which includes Fold, Hopf, Bautin, and Cusp bifurcations. The four-dimensional model shows that intricate oscillations can occur and that the periodic attractors of the system can have thoughtful consequences on reactor performance. In fact, it is evidenced that, in some conditions, periodic/bifurcation behavior presents higher ethanol productivity than the corresponding steady-state. Bifurcation analysis provides insight into the possible operation conditions and their impact on conversion and productivity of the fermentation process.

A Strategy to Couple Thickened Flame Model and Adaptive Mesh Refinement for the LES of Turbulent Premixed Combustion

A trend towards the increasing use of Adaptive Mesh Refinement (AMR) algorithms to simulate combustion processes is observed in the recent literature. AMR is attractive as it enables the physical phenomena of interest to be tracked by the numerical mesh, reducing the computational cost drastically. It is particularly efficient for combustion as small computational cells are needed very locally to resolve the flame structure. However, the questions arising from the coupling between AMR and the turbulent flame propagation have rarely been investigated so far. Indeed, the incomplete cascading of turbulent structures from a relatively coarse mesh used to solve the flow to a finer mesh solving the flame has implications on the turbulent combustion model which must be considered. In the present paper, a strategy for coupling AMR with the Thickened Flame Model (TFM) is proposed. It is shown that, under conditions relevant to industrial cases, the standard TFM model strongly under-estimates the turbulent flame propagation when the effects of AMR is not taken into account. A new model, AMR-E, is introduced to take this effect into account. The behavior of the model is first analyzed on an a priori 1D-study and is consequently validated on a 3-D turbulent flame propagation in Homogeneous Isotropic Turbulence (HIT). In particular, it is shown that the presented model has a similar behavior for different AMR refinement levels in the flame front.