Refinement Algorithm Research Articles

A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems

We propose a quadratically convergent algorithm for inverse symmetric eigenvalue problems based on matrix equations. The basic idea is seen in a recent study by Ogita and Aishima, while they derive an efficient iterative refinement algorithm for symmetric eigenvalue problems using special matrix equations. In other words, this study is interpreted as a unified view on quadratically convergent algorithms for eigenvalue problems and inverse eigenvalue problems based on matrix equations. To the best of our knowledge, such a unified development of algorithms is provided for the first time. Since the proposed algorithm for the inverse eigenvalue problems can be regarded as the Newton's method for the matrix equations, the quadratic convergence is naturally proved. Our algorithm is interpreted as an improved version of the Cayley transform method for the inverse eigenvalue problems. Although the Cayley transform method is one of the effective iterative methods, the Cayley transform takes O(n3) arithmetic operations to produce an orthogonal matrix using a skew-symmetric matrix in each iteration. Our algorithm can refine orthogonality without the Cayley transform, which reduces the operations in each iteration. It is worth noting that our approach overcomes the limitation of the Cayley transform method to the inverse standard eigenvalue problems, resulting in an extension to inverse generalized eigenvalue problems.

High accuracy mantle convection simulation through modern numerical methods – II: realistic models and problems

Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and adaptively refined meshes, sophisticated and efficient solvers, and parallelization to large clusters of computers. At the same time, many of these methods -- discussed in detail in a previous paper in this series -- were developed and tested primarily using model problems that lack many of the complexities that are common to the realistic models our community wants to solve today. With several years of experience solving complex and realistic models, we here revisit some of the algorithm designs of the earlier paper and discuss the incorporation of more complex physics. In particular, we re-consider time stepping and mesh refinement algorithms, evaluate approaches to incorporate compressibility, and discuss dealing with strongly varying material coefficients, latent heat, and how to track chemical compositions and heterogeneities. Taken together and implemented in a high-performance, massively parallel code, the techniques discussed in this paper then allow for high resolution, 3d, compressible, global mantle convection simulations with phase transitions, strongly temperature dependent viscosity and realistic material properties based on mineral physics data.

Marbling-based creative modelling

Most mathematical marbling simulations generate patterns for texture mapping and surface decoration. We explore the application of three-dimensional deformations inspired by mathematical marbling as a suite of tools to enable creative shape design. Our tools are expressed as analytical functions of space and are volume-preserving vector fields, meaning that the modelling process preserves volumes and avoids self-intersections. Complicated deformations are easily combined to create complex objects from simple ones. To achieve smooth and high-quality shapes, we also present a mesh refinement and simplification algorithm adapted to our deformations. We show a number of examples of shapes created with our technique in order to demonstrate its power and expressiveness.

Numerical Simulation of cracked orthotropic materials using extended isogeometric analysis

In the present study, extended isogeometric analysis (XIGA) is used to analyse cracks in orthotropic media. NURBS and T-splines geometric technologies are used to define the geometry and the solution. Knot insertion and order elevation are used in NURBS models, while a new local refinement algorithm is applied to T-spline models. In XIGA, the basic idea of the extended finite element method (X-FEM) is used along with isogeometric analysis for modelling discontinuities by including enrichment functions. Special orthotropic crack tip enrichments are used to reproduce the singular fields near a crack tip, and fracture properties of the models are defined by the mixed mode stress intensity factors (SIFs), which are obtained by means of the interaction integral (M-integral). Results of the proposed method are compared with other available results.

Self-Adaptive Numerical Methods for Computationally Challenging Problems

Self-adaptive numerical methods provide a powerful and automatic approach in scientific computing. In particular, Adaptive Mesh Refinement (AMR) algorithms have been widely used in computational science and engineering and have become a necessary tool in computer simulations of complex natural and engineering problems. The key ingredient for success of self-adaptive numerical methods is a posteriori error estimates that are able to accurately locate sources of global and local error in the current approximation. The workshop creates a forum for junior and senior researchers in numerical analysis and computational science and engineering to discuss recent advances, initiates future research projects, and establishes new collaborations on convergence theory of adaptive numerical methods and on the construction and analysis of efficient, reliable, and robust a posteriori error estimators for computationally challenging problems.

Learning Theory and Approximation

The main goal of this workshop – the third one of this type at the MFO – has been to blend mathematical results from statistical learning theory and approximation theory to strengthen both disciplines and use synergistic effects to work on current research questions. Learning theory aims at modeling unknown function relations and data structures from samples in an automatic manner. Approximation theory is naturally used for the advancement and closely connected to the further development of learning theory, in particular for the exploration of new useful algorithms, and for the theoretical understanding of existing methods. Conversely, the study of learning theory also gives rise to interesting theoretical problems for approximation theory such as the approximation and sparse representation of functions or the construction of rich kernel reproducing Hilbert spaces on general metric spaces. This workshop has concentrated on the following recent topics: Pitchfork bifurcation of dynamical systems arising from mathematical foundations of cell development; regularized kernel based learning in the Big Data situation; deep learning; convergence rates of learning and online learning algorithms; numerical refinement algorithms to learning; statistical robustness of regularized kernel based learning.

A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT–LBM–AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid–liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

A PCI planning algorithm for jointly reducing reference signal collisions in LTE uplink and downlink

In this paper, a novel automatic planning method is proposed for allocating Physical Cell Identifiers (PCI) to cells in a Long Term Evolution (LTE) system based on handover and cell load measurements. The method aims at avoiding PCI collision and confusion problems, while reducing Reference Signal (RS) collisions between neighbor cells. For this purpose, the problem is formulated to consider RS collisions both in DownLink (DL) and UpLink (UL). Then, a classical graph partitioning algorithm is adapted to solve the graph coloring problem behind PCI planning. The considered algorithm is the multi-level version of the Fiduccia and Mattheyses local refinement algorithm. Performance assessment is carried out on graphs constructed from data collected in live LTE network. Results show that the proposed algorithms can avoid PCI collision and confusion problems, while reducing DL RS collisions and almost eliminating UL RS collisions compared to a random plan.

Extended isogeometric analysis using analysis-suitable T-splines for plane crack problems

This study is dedicated to modeling cracks in plane problems by applying the recent technique analysis-suitable T-splines in the extended isogeometric analysis. A new local refinement algorithm is integrated for increasing the solution accuracy and reducing the excessive propagation of control points. However the singular fields near a crack tip are reproduced by the crack tip enrichment functions, and the Heaviside function is used to represent crack discontinuity. The results accuracy is tested by evaluation the mixed mode stress intensity factors which are computed by means of the interaction integral approach (M -integral). The obtained results are compared with the analytical methods.DOI: http://dx.doi.org/10.5755/j01.mech.23.1.13475

Automated Quantification of the Impact of Defects on the Mechanical Behavior of Deoxyribonucleic acid Origami Nanoplates.

Deoxyribonucleic acid (DNA) origami is a method for the bottom-up self-assembly of complex nanostructures for applications, such as biosensing, drug delivery, nanopore technologies, and nanomechanical devices. Effective design of such nanostructures requires a good understanding of their mechanical behavior. While a number of studies have focused on the mechanical properties of DNA origami structures, considering defects arising from molecular self-assembly is largely unexplored. In this paper, we present an automated computational framework to analyze the impact of such defects on the structural integrity of a model DNA origami nanoplate. The proposed computational approach relies on a noniterative conforming to interface-structured adaptive mesh refinement (CISAMR) algorithm, which enables the automated transformation of a binary image of the nanoplate into a high fidelity finite element model. We implement this technique to quantify the impact of defects on the mechanical behavior of the nanoplate by performing multiple simulations taking into account varying numbers and spatial arrangements of missing DNA strands. The analyses are carried out for two types of loading: uniform tensile displacement applied on all the DNA strands and asymmetric tensile displacement applied to strands at diagonal corners of the nanoplate.

스테레오 비전 후처리 알고리즘의 시차 개선 성능 평가

스테레오 비전 후처리 알고리즘의 시차 개선 성능 평가

Finite Element Modeling and Experimental Verification of Nitriding Process in S30C Steel

A mathematical model has been developed to simulate the nitriding process of plain carbon steel, considering the simultaneous diffusion of nitrogen in different iron-nitrogen (Fe-N) phases and the precipitation dynamics of γ’e and iron-nitride. The model can predict the distribution of nitrogen concentration, volume fraction of Fe-N phases and hardness. Furthermore, a finite element method (FEM) post-process technology is presented to avoid the limit of FEM mesh improvement and time-saving. The uniform-sum-division algorithm is adopted as local refinement algorithm (LRA) of meshes. The modified inverse distance weighting (IDW) method is used to interpolate the FEM simulated results. Then, the nitriding model and post-process technology are incorporated within the framework of the developed FEM code COSMAP (COmputer Simulation of MAnufacturing Process) based on metallo-thermo-mechanical theory. In order to validate the nitriding model and FEM post-process technology, the nitriding process of S30C steel is modeled by COSMAP software. The simulated distributions of nitrogen content and hardness are consistent with the measured ones. In addition, the simulated results at different mesh size are compared for two-dimensional model. It is indicated that the interpolated results agree well with the simulated results of fine mesh model and the experimental ones.Keywords: finite element, nitriding, S30C, iron nitride, inverse distance weighting

An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (S[formula omitted]) angular discretisation

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements.

Crack analysis in bimaterial interfaces using T-spline based XIGA

Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.

T-spline local refinement as a belief revision system: a rule-based implementation

As originally conceived, T-splines generalize both NURBS and Subdivision surfaces. Central to T-splines is the knot refinement algorithm, which seems to successfully import the local characteristic...

New additions to the ClusPro server motivated by CAPRI.

The heavily used protein-protein docking server ClusPro performs three computational steps as follows: (1) rigid body docking, (2) RMSD based clustering of the 1000 lowest energy structures, and (3) the removal of steric clashes by energy minimization. In response to challenges encountered in recent CAPRI targets, we added three new options to ClusPro. These are (1) accounting for small angle X-ray scattering data in docking; (2) considering pairwise interaction data as restraints; and (3) enabling discrimination between biological and crystallographic dimers. In addition, we have developed an extremely fast docking algorithm based on 5D rotational manifold FFT, and an algorithm for docking flexible peptides that include known sequence motifs. We feel that these developments will further improve the utility of ClusPro. However, CAPRI emphasized several shortcomings of the current server, including the problem of selecting the right energy parameters among the five options provided, and the problem of selecting the best models among the 10 generated for each parameter set. In addition, results convinced us that further development is needed for docking homology models. Finally, we discuss the difficulties we have encountered when attempting to develop a refinement algorithm that would be computationally efficient enough for inclusion in a heavily used server. Proteins 2017; 85:435-444. © 2016 Wiley Periodicals, Inc.

Hybrid Metaheuristic for Designing an End Effector as a Constrained Optimization Problem

Hybrid metaheuristics, explored in recent literature, are optimization methods that combine a global search metaheuristic with algorithms for refinement that in turn can be stochastic or deterministic. Although initially they were applied to combinatorial optimization, nowadays there are hybrid algorithms for a wide range of numerical problems: static or dynamic, mono or multi-objective, unconstrained or constrained, among others. In this paper a novel application of a hybrid method, MemMABC, is applied as a tool in a case study for the synthesis of an end effector presented as a constrained optimization problem, using a model for a two-finger gripper. The objective is to show the ability of hybrid metaheuristics as an alternative method for solving hard problems, specifically of numerical optimization. MemMABC is a memetic algorithm, that uses the modified artificial bee colony algorithm(MABC) for global searching and a version of random walk as local searcher, adapted to handle design constraints with an $\epsilon $ -constraint scheme. Grippers are end effectors used in a wide variety of robots, and are a good example of hard optimization problems. The simulation of results shows an accurate control of the gripping force along the opening range of the calculated mechanisms, suggesting that MemMABC can produce quality solutions for real-world engineering cases.

Refining Automatically Extracted Knowledge Bases Using Crowdsourcing.

Machine-constructed knowledge bases often contain noisy and inaccurate facts. There exists significant work in developing automated algorithms for knowledge base refinement. Automated approaches improve the quality of knowledge bases but are far from perfect. In this paper, we leverage crowdsourcing to improve the quality of automatically extracted knowledge bases. As human labelling is costly, an important research challenge is how we can use limited human resources to maximize the quality improvement for a knowledge base. To address this problem, we first introduce a concept of semantic constraints that can be used to detect potential errors and do inference among candidate facts. Then, based on semantic constraints, we propose rank-based and graph-based algorithms for crowdsourced knowledge refining, which judiciously select the most beneficial candidate facts to conduct crowdsourcing and prune unnecessary questions. Our experiments show that our method improves the quality of knowledge bases significantly and outperforms state-of-the-art automatic methods under a reasonable crowdsourcing cost.

Refficientlib: An Efficient Load-Rebalanced Adaptive Mesh Refinement Algorithm for High-Performance Computational Physics Meshes

In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. Some of the main features of the algorithm presented in this paper are its capability of handling multiple types of elements in two and three dimensions (triangular, quadrilateral, tetrahedral, and hexahedral), the small amount of memory required per processor, and the parallel scalability up to thousands of processors. The presented algorithm is also capable of dealing with nonbalanced hierarchical refinement, where multirefinement level jumps are possible between neighbor elements. An algorithm for dealing with load rebalancing is also presented, which allows us to move the hierarchical data structure between processors so that load unbalancing is kept below an acceptable level at all times during the simulation. A particular feature of the proposed algorithm is that arbitrary renumbering algorithms can be used in the load rebalancing step, including both graph partitioning and space-filling renumbering algorithms. The presented algorithm is packed in the Fortran 2003 object oriented library \textttRefficientLib, whose interface calls which allow it to be used from any computational physics code are summarized. Finally, numerical experiments illustrating the performance and scalability of the algorithm are presented.

$hp$-Adaptive Discontinuous Galerkin Methods for Neutron Transport Criticality Problems

In this article we consider the application of high-order/$hp$-version adaptive discontinuous Galerkin finite element methods (DGFEMs) for the discretization of the $k_{eff}$-eigenvalue problem associated with the neutron transport equation. To this end, we exploit the dual weighted residual approach to derive a reliable and efficient a posteriori error estimate for the computed critical value of $k_{eff}$. Moreover, by exploiting the underlying block structure of the $hp$-version DGFEM, we propose and implement an efficient numerical solver based on exploiting Tarjan's strongly connected components algorithm to compute the inverse of the underlying transport operator; this is then utilized as an efficient preconditioner for the $k_{eff}$-eigenvalue problem. Finally, on the basis of the derived a posteriori error estimator we propose an $hp$-adaptive refinement algorithm which automatically refines both the angular and spatial domains. The performance of this adaptive strategy is demonstrated on a series ...