Initial Mesh Research Articles

Fast and Reliable Limit Analysis Approach for the Structural Assessment of FRP-Reinforced Masonry Arches

This contribution is devoted to assess the capability of a new upper-bound approach for the limit analysis of FRP-reinforced masonry arches by comparing it to both experimental tests and a number of existing numerical procedures. The approach is based on an idea previously presented by the Authors and relies on the representation of the geometry of both the arch and of FRP reinforcement through Non Uniform Rational B-Spline (NURBS) functions. This allows generating a rigid body assembly starting from the assigned geometry composed by very few elements which still provide an exact representation of the original shape. A homogenized kinematic formulation for the limit analysis of the obtained rigid blocks assembly is derived, which accounts for the main properties of masonry material. FRP material is included exploiting the Italian CNR Recommendations for the design of FRP based reinforcing interventions. The approach is capable of accurately predicting the load bearing capacity of masonry arches of arbitrary geometry, provided that the initial mesh is adjusted by means of a suitably devised Genetic Algorithm (GA) until the active interfaces among blocks (e.g. hinges) closely approximate the actual failure mechanism.

An ultraweak DPG method for viscoelastic fluids

We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1,2]. In our analysis, we develop an intrinsic a posteriori error indicator which we use for adaptive mesh generation. The DPG method is useful for the problem we consider because the method is inherently stable—requiring no stabilization of the linearized discretization in order to handle the advective terms in the model. Because stabilization is a pressing issue in these models, this happens to become a very useful property of the method which simplifies our analysis. This built-in stability at all length scales and the a posteriori error indicator additionally allows for the generation of parameter-specific meshes starting from a common coarse initial mesh. A DPG discretization always produces a symmetric positive definite stiffness matrix. This feature allows us to use the most efficient direct solvers for all of our computations. We use the Camellia finite element software package [3,4] for all of our analysis.

A parallel log barrier-based mesh warping algorithm for distributed memory machines

Parallel dynamic meshes are essential for computational simulations of large-scale scientific applications involving motion. To address this need, we propose parallel LBWARP, a parallel log barrier-based tetrahedral mesh warping algorithm for distributed memory machines. Our algorithm is a general-purpose, geometric mesh warping algorithm that parallelizes the sequential LBWARP algorithm proposed by Shontz and Vavasis. The first step of the algorithm involves computation of a set of local weights for each interior node which describe the relative distances of the node to each of its neighbors. The weight computation step is the most time consuming in the parallel algorithm. Based on our choice of the mesh partition and the corresponding distribution of data and assignment of tasks to processors, communication among processors is avoided in an embarrassingly parallel computation of the weights. Once this representation of the initial mesh is determined, a target deformation of the boundary is applied, also in an embarrassingly parallel manner. Finally, new coordinates of the interior nodes are obtained by solving a system of linear equations with multiple right-hand sides that is based on the weights and boundary deformation. This linear system can be solved using one of three parallel sparse linear solvers, i.e., the distributed block BiCG, block GMRES, or LU algorithm, all of which support the solution of linear systems with multiple right-hand side vectors. Our numerical results demonstrate good efficiency and strong scalability of parallel LBWARP on up to 64 processors, as the experiments show close to linear speedup in all cases. Weak scalability is also demonstrated. The performance of the parallel sparse linear solvers is dependent on factors such as the mesh size, the amount of available memory, and the number of processors. For example, the distributed LU algorithm gives better performance on small meshes, whereas the distributed block BiCG and distributed block GMRES algorithms yield better performance when the amount of available memory is limited. Finally, we demonstrate the parallel LBWARP performance for a sequence of mesh deformations which can significantly reduce the runtime of the overall algorithm. When applied to k deformations, parallel LBWARP reuses the weight matrix, that was computed during the first deformation, when the distributed LU linear solver is employed. This gives close to k-time performance for sufficiently many deformations.

General optimal shape of plasmonic nano particles based absorption coefficient using a linearization approach

In this paper, the problem of determining the shape of plasmonic nano particle for maximum absorption coefficient in the visible part of light spectrum is considered. In order to determine a general optimal shape, a new linearization solution method in spherical coordinates is presented. Indeed, by using this approach which is based on an embedding process, the solution is determined via an appropriate finite linear programming problem by an iterative method based on particle swarm optimization (PSO) algorithm. This approach in comparison to the other methods has some advantages: the optimization is global and does not need any initial shape and mesh designing. This approach can be useful also in optical applications such as plasmonic nano antenna, plasmonic solar cell and plasmonic sensor. The numerical simulation results also show the efficiency of the proposed method especially in comparison.

A multilevel decoupling method for the Navier–Stokes/Darcy model

This paper considers a multilevel decoupling method for the coupled Navier–Stokes/Darcy model describing a free flowing fluid over a porous medium. The method utilizes a sequence of meshes on which a low dimensional fully coupled nonlinear problem is solved only on a very coarse initial mesh. On subsequent finer meshes, the approximate solution in each flow region is obtained by solving a linear decoupled problem and performing a correction step. The correction step in each domain is achieved by solving a linear system that differs from the original decoupled system only in the right hand side. We prove optimal error estimates and demonstrate that for a sequence of meshes with spacing hj=hj−12, the decoupling method is computationally efficient and achieves the same order of approximation as the fully coupled method.

Algoritmo de remallado automático de elementos triangulares durante los análisis con elemento finito

In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.

Analysis of Complications of Pelvic Mesh Excision Surgery Using the Clavien-Dindo Classification System

We describe and categorize complications using the Clavien-Dindo classification system in patients who underwent vaginal mesh excision surgery. With institutional review board approval we retrospectively reviewed the records of 277 patients who underwent vaginal mesh extraction between 2007 and 2015 at a single institution. Surgical complications were stratified using the Clavien-Dindo classification system. Complications were perioperative (prior to discharge) or postoperative (within 90 days). Indications for initial mesh placement, mesh revision procedure, time to resolution and medical comorbidities were assessed. Of the 277 patients 47.3% had at least 1 surgical complication, including multiple complications in 7.2%. A total of 155 complications were identified, which were grade II in 49.0% of cases, grade I in 25.8%, grade IIIb in 18.7%, grade IIIa in 5.2% and grade IVa in 1.3%. No grade IVb or V complications were identified. The indication for initial mesh placement did not significantly affect complication frequency. Patients who underwent combined stress urinary incontinence and pelvic organ prolapse mesh revision surgeries had an increased frequency of complications compared to those treated with mesh revision surgery for pelvic organ prolapse or stress urinary incontinence alone (p = 0.045). Most complications occurred postoperatively and resolved by 90 days. Age, body mass index, smoking status and diabetes were not associated with increased complications. Despite the complexity of mesh revision surgery most complications are minor. Serious complications may develop, emphasizing the need for proper patient counseling and surgical experience when performing these procedures.

Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision

In this paper, we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended Loop surface subdivision approach. The exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure, which is thought of as the initial control mesh of Loop subdivision. By performing extended Loop subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of quartic box-spline while maintaining its original exactness. The limit function representation of extended Loop subdivision forms our finite element space, which possesses C1 smoothness and the flexibility of mesh topology. We establish its inverse inequalities which resemble the ones of general finite element spaces. We develop the approximation estimate with the aid of H1 convergence property of the corresponding linear models. It enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models. Numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results.

Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme

Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

Convergence of natural adaptive least squares finite element methods

The first-order div least squares finite element methods provide inherent a posteriori error estimator by the elementwise evaluation of the functional. In this paper we prove Q-linear convergence of the associated adaptive mesh-refining strategy for a sufficiently fine initial mesh with some sufficiently large bulk parameter for piecewise constant right-hand sides in a Poisson model problem. The proof relies on some modification of known supercloseness results to non-convex polygonal domains plus the flux representation formula. The analysis is carried out for the lowest-order case in two-dimensions for the simplicity of the presentation.

Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the “exact” adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

Multi-view Performance Capture of Surface Details

This paper presents a novel approach to recover true fine surface detail of deforming meshes reconstructed from multi-view video. Template-based methods for performance capture usually produce a coarse-to-medium scale detail 4D surface reconstruction which does not contain the real high-frequency geometric detail present in the original video footage. Fine scale deformation is often incorporated in a second pass by using stereo constraints, features, or shading-based refinement. In this paper, we propose an alternative solution to this second stage by formulating dense dynamic surface reconstruction as a global optimization problem of the densely deforming surface. Our main contribution is an implicit representation of a deformable mesh that uses a set of Gaussian functions on the surface to represent the initial coarse mesh, and a set of Gaussians for the images to represent the original captured multi-view images. We effectively find the fine scale deformations for all mesh vertices, which maximize photo-temporal-consistency, by densely optimizing our model-to-image consistency energy on all vertex positions. Our formulation yields a smooth closed form energy with implicit occlusion handling and analytic derivatives. Furthermore, it does not require error-prone correspondence finding or discrete sampling of surface displacement values. We demonstrate our approach on a variety of datasets of human subjects wearing loose clothing and performing different motions. We qualitatively and quantitatively demonstrate that our technique successfully reproduces finer detail than the input baseline geometry.

Convergence and quasi-optimality of adaptive finite element methods for harmonic forms

Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies extensively on accurate computation of harmonic forms. In this work we study the convergence properties of adaptive finite element methods (AFEM) for computing harmonic forms. We show that a properly defined AFEM is contractive and achieves optimal convergence rate beginning from any initial conforming mesh. This result is contrasted with related AFEM convergence results for elliptic eigenvalue problems, where the initial mesh must be sufficiently fine in order for AFEM to achieve any provable convergence rate.

A high-order log barrier-based mesh generation and warping method

The ability to generate high-order meshes that conform to the boundary of curved geometries is a hurdle in the adoption of high-order computational methods for the numerical solution of partial differential equations. In this paper, we propose a method for generating and warping second-order Lagrange triangular and tetrahedral meshes based on a log barrier method. In the case of generation, the approach consists of modifying an initial linear mesh by first, adding nodes at the midpoint of each edge; second, displacing the newly added boundary midpoints to the curved boundary, and third, solving for the final positions of the interior nodes based on the boundary deformation. By allowing all of the boundary nodes to move, the approach can also be used to warp second-order triangular and tetrahedral meshes. We present several numerical examples in both two and three dimensions which demonstrate the capabilities of our method in generating and warping second-order curvilinear meshes.

Feature moving operation of hexahedral mesh

In the product design process, the finite element mesh regeneration is an inevitable step, but it is time consuming. The mesh editing is a kind of an effective mesh regeneration technique. In this paper, a method for widely moving features of hexahedral mesh is proposed to satisfy application requirement. After the feature moving operation is applied to CAD model, the mesh deformation based on the mean value coordinates is carried out in the corresponding deformed region of the hex mesh to decrease the possible inverted elements caused by a wide range deformation. Then, the parameters of generating the density field are extracted from the initial hexahedral mesh, and used to calculate the local target density field by considering the geometric and topological information on the deformed region. Finally, based on difference between current density field and target density field of deformed region, the local refining and coarsening operations are devised and conducted to make the deformed region compatible with the target density field. Experimental results for the mechanical parts verify the effectiveness of proposed method.

Convergence of Adaptive Mixed Finite Element Methods for the Hodge Laplacian Equation: Without Harmonic Forms

Finite element exterior calculus (FEEC) has been developed as a systematic framework for constructing and analyzing stable and accurate numerical methods for partial differential equations by employing differential complexes. This paper is devoted to analyzing the convergence of adaptive mixed finite element methods for the Hodge Laplacian equations based on FEEC without considering harmonic forms. A residual type a posteriori error estimate is obtained by using the Hodge decomposition, the regular decomposition, and bounded commuting quasi-interpolants. An additional marking strategy is added to ensure the quasi-orthogonality, based on which the convergence of adaptive mixed finite element methods is obtained without assuming the initial mesh size is small enough.

A Genetic Algorithm NURBS-based new approach for fast kinematic limit analysis of masonry vaults

The present paper proposes a new Genetic Algorithm NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. A given masonry vault geometry can be represented by a NURBS (Non-Uniform Rational B-Spline) parametric surface and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material is deduced, with internal dissipation allowed exclusively along element edges. The approach is capable of well predicting the load bearing capacity of any masonry vault of generic shape. It is proved that, even by using a mesh constituted by very few elements, a good estimate of the collapse load multiplier is obtained provided that the initial mesh is adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism. The proposed method turns out to be both accurate and much less computationally expensive than existing methods for the limit analysis of masonry vaults.

Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Gårding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.

Association Between the Amount of Vaginal Mesh Used With Mesh Erosions and Repeated Surgery After Repairing Pelvic Organ Prolapse and Stress Urinary Incontinence

Mesh, a synthetic graft, has been used in pelvic organ prolapse (POP) repair and stress urinary incontinence (SUI) to augment and strengthen weakened tissue. Polypropylene mesh has come under scrutiny by the US Food and Drug Administration. To examine the rates of mesh complications and invasive reintervention after the placement of vaginal mesh for POP repair or SUI surgery. This investigation was an observational cohort study at inpatient and ambulatory surgery settings in New York State. Participants were women who underwent transvaginal repair for POP or SUI with mesh between January 1, 2008, and December 31, 2012, and were followed up through December 31, 2013. They were divided into the following 4 groups based on the amount of mesh exposure: transvaginal POP repair surgery with mesh and concurrent sling use (vaginal mesh plus sling group), transvaginal POP repair with mesh and no concurrent sling use (vaginal mesh group), transvaginal POP repair without mesh but concurrent sling use for SUI (POP sling group), and sling for SUI alone (SUI sling group). The primary outcome was the occurrence of mesh complications and repeated invasive intervention within 1 year after the initial mesh implantation. A time-to-event analysis was performed to examine the occurrence of mesh erosions and subsequent reintervention. Secondary analyses of an age association (<65 vs ≥65 years) were conducted. The study identified 41 604 women who underwent 1 of the 4 procedures. The mean (SD) age of women at their initial mesh implantation was 56.2 (13.0) years. The highest risk of erosions was found in the vaginal mesh plus sling group (2.72%; 95% CI, 2.31%-3.21%) and the lowest in the SUI sling group (1.57%; 95% CI, 1.41%-1.74%). The risk of repeated surgery with concomitant erosion diagnosis was also the highest in the vaginal mesh plus sling group (2.13%; 95% CI, 1.76%-2.56%) and the lowest in the SUI sling group (1.16%; 95% CI, 1.03%-1.31%). The combined use of POP mesh and SUI mesh sling was associated with the highest erosion and repeated intervention risk, while mesh sling alone had the lowest erosion and repeated intervention risk. There is evidence for a dose-response relationship between the amount of mesh used and subsequent mesh erosions, complications, and invasive repeated intervention.

Error sensitivity to refinement: a criterion for optimal grid adaptation

Most indicators used for automatic grid refinement are suboptimal, in the sense that they do not really minimize the global solution error. This paper concerns with a new indicator, related to the sensitivity map of global stability problems, suitable for an optimal grid refinement that minimizes the global solution error. The new criterion is derived from the properties of the adjoint operator and provides a map of the sensitivity of the global error (or its estimate) to a local mesh refinement. Examples are presented for both a scalar partial differential equation and for the system of Navier–Stokes equations. In the last case, we also present a grid-adaptation algorithm based on the new estimator and on the \(FreeFem++\) software that improves the accuracy of the solution of almost two order of magnitude by redistributing the nodes of the initial computational mesh.