Mesh Alignment Research Articles

Extended ALE Method for fluid–structure interaction problems with large structural displacements

Standard Arbitrary Lagrangian–Eulerian (ALE) methods for the simulation of fluid–structure interaction (FSI) problems fail due to excessive mesh deformations when the structural displacement is large. We propose a method that successfully deals with this problem, keeping the same mesh connectivity while enforcing mesh alignment with the structure. The proposed Extended ALE Method relies on a variational mesh optimization technique, where mesh alignment with the structure is achieved via a constraint. This gives rise to a constrained optimization problem for mesh optimization, which is solved whenever the mesh quality deteriorates. The performance of the proposed Extended ALE Method is demonstrated on a series of numerical examples involving 2D FSI problems with large displacements. Two-way coupling between the fluid and structure is considered in all the examples. The FSI problems are solved using either a Dirichlet–Neumann algorithm, or a Robin–Neumann algorithm. The Dirichlet–Neumann algorithm is enhanced by an adaptive relaxation procedure based on Aitken's acceleration. We show that the proposed method has excellent performance in problems with large displacements, and that it agrees well with a standard ALE method in problems with mild displacement.

A virtual reality training program for improvement of robotic surgical skills.

The purpose of this study was to use a simulated virtual reality environment for training of surgical skills and then to identify if the learning that occurred was transferable to a real world surgical task. The virtual surgical tasks consisted of bimanual carrying, needle passing and mesh alignment. In this ongoing study, the experimental group (n = 5) was trained by performing four blocks of the virtual surgical tasks using the da Vinci surgical robot. Pre and post training, all subjects were tested by performing a suturing task on a "life-like" suture pad. The control group (n = 5) performed only the suturing task. Significantly larger pre and post differences were revealed in time to task completion (p < 0.05) and total distance travelled by the dominant side instrument tip (p < 0.01) in the experimental group as compared to the control group. These differences were specific to the suture running aspect of the surgical task. In conclusion, virtual reality surgical skills training may produce a significant learning effect that can transfer to actual robot-assisted laparoscopic procedures.

The geometry of r-adaptive meshes generated using optimal transport methods

The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor and mesh metric are useful theoretical tools for understanding a method's level of mesh alignment, or anisotropy. We consider a mesh redistribution method based on the Monge–Ampère equation which combines equidistribution of a given scalar density function with optimal transport. It does not involve explicit use of a metric tensor, although such a tensor must exist for the method, and an interesting question to ask is whether or not the alignment produced by the metric gives an anisotropic mesh. For model problems with a linear feature and with a radially symmetric feature, we derive the exact form of the metric, which involves expressions for its eigenvalues and eigenvectors. The eigenvectors are shown to be orthogonal and tangential to the feature, and the ratio of the eigenvalues (corresponding to the level of anisotropy) is shown to depend, both locally and globally, on the value of the density function and the amount of curvature. We thereby demonstrate how the optimal transport method produces an anisotropic mesh along a given feature while equidistributing a suitably chosen scalar density function. Numerical results are given to verify these results and to demonstrate how the analysis is useful for problems involving more complex features, including for a non-trivial time dependant nonlinear PDE which evolves narrow and curved reaction fronts.

Using the medial axis to represent flow features for feature-aligned unstructured quad-dominant mesh generation

A method to represent complex flow structures as geometric entities, using the medial axis for the purpose of generating flow feature-aligned meshes, is presented. The medial curves representing the flow features are embedded in the domain to guide mesh alignment and location of background sources, which influence element spacing and orientation when the mesh is regenerated. The resulting meshes possess regions of high-quality anisotropic quadrilateral elements locally aligned with the flow features. To further optimise the mesh based on the solution, a nodal movement adaptation scheme is applied which allows full alignment of the cell interfaces with the flow features, making the mesh more suitable for the one-dimensional approximate Riemann solvers and higher-order reconstruction schemes. The technique and its potential for improving the numerical simulation is presented for a range of test cases for the solution of the Euler and Navier–Stokes equations for compressible flows, which include shock waves, boundary layers and steady trailing wakes as the dominant flow features.

Computer assisted detection of abnormal airway variation in CT scans related to paediatric tuberculosis.

Airway deformation and stenosis can be key signs of pathology such as lymphadenopathy. This study presents a local airway point distribution model (LA-PDM) to automatically analyse regions of the airway tree in CT scans and identify abnormal airway deformation. In our method, the airway tree is segmented and the centreline identified from each chest CT scan. Thin-plate splines, along with a local mesh alignment method for tubular meshes, are used to register the airways and develop point distribution models (PDM). Each PDM is then used to analyse and classify local regions of the airway. This LA-PDM method was developed using 89 training cases and evaluated on a 90 CT test set, where each set includes paediatric tuberculosis (TB) cases (with airway involvement) and non-TB cases (without airway involvement). The LA-PDM was able to accurately distinguish cases with airway involvement with an AUC of the ROC classification (and 95% confidence interval) of 0.87 (0.77-0.94) for the Trachea-LMB-RMB region and 0.81 (0.68-0.90) for the RMB-RUL-BI region - outperforming a comparison method based on airway cross-sectional features. This has the potential to assist and improve airway analysis from CT scans by detecting involved airways and visualising affected airway regions.

A hybrid level set–front tracking finite element approach for fluid–structure interaction and two-phase flow applications

We present a hybrid level set–front tracking approach suitable for fluid–structure interaction and two-phase flow applications. Our approach aims at extending geometrical flexibility of standard mesh moving/front tracking methods by introducing an additional implicit level set representation of the geometry under consideration. The computational mesh is automatically aligned to the implicitly described geometry by minimizing a nonlinear, constrained functional. Resulting triangulations approximate the geometry accurately while being optimal in a certain sense. Due to the mesh alignment, finite element spaces defined on these triangulations may be easily adjusted to account for special solution properties such as discontinuities across interfaces. In order to demonstrate the flexibility of the proposed approach, we apply it to a simplified one-way coupled fluid–structure interaction problem inspired by the flow induced by a moving cardiac valve. Furthermore we evaluate the approach by solving a two-phase flow benchmark problem.

Refined Tetrahedral Meshes with Mach Cone Aligned Prisms for Sonic Boom Analysis

A tetrahedral mesh generation method for acquiring accurate sonic boom pressure signatures several body lengths from an aircraft model has been developed. The method serves as a tool for aerodynamicists to efficiently create useful meshes for sonic boom analysis. The procedure includes generating a refined near-field grid with a cylindrically shaped boundary that encompasses the model just beyond its surface and a prismatic mesh from the cylindrical boundary to the far field. Projecting the boundary in the radial direction and forming prisms between neighboring layer faces creates the prism mesh. Each prism is subdivided into three tetrahedra resulting in a mesh comprised entirely of tetrahedral cells. The prism structure permits radial stretching and mesh alignment with the Mach cone around the aircraft model for accurate on- and offtrack signatures. Computational results for four models compared with experimental data validate this methodology.

A stabilized Fractional Step, Runge–Kutta Taylor SPH algorithm for coupled problems in geomechanics

Failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering. Many finite element formulations for coupled problems present difficulties such as overestimating failure loads, or mesh alignment dependence resulting on spurious failure mechanisms. Moreover, the spaces where field variables are approximated have to fulfill additional requirements ensuring stability. Stress-velocity-pore pressure formulations in FE analysis provide accurate results for wave propagation and failure analysis. However, finite elements present important limitations when deformations are large. The purpose of this paper is to present a stabilized Fractional Step, SPH algorithm which combines the advantages of the SPH method for large deformation problems with those of the Taylor Galerkin algorithm used within the finite element framework.

A COMBINED EXTENDED AND EDGE-BASED SMOOTHED FINITE ELEMENT METHOD (ES-XFEM) FOR FRACTURE ANALYSIS OF 2D ELASTICITY

This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.

Sequentially linear analysis of shear critical reinforced concrete beams without shear reinforcement

Analyzing brittle structures with nonlinear finite element analysis is frequently attended with numerical problems. As an alternative method sequentially linear analysis could be utilized, resulting in the avoidance of convergence and bifurcation problems. To demonstrate its attractiveness, sequentially linear analyses are performed on a tested shear critical reinforced concrete beam without shear reinforcement. These beams are generally known to behave extremely brittle and therefore difficult to analyze with standard nonlinear finite element analysis. The results of the alternative method are presented in this study and compared with the results of corresponding nonlinear analyses using an incremental-iterative solution procedure. Sensitivity studies have been performed with respect to the adopted amount of material fracture energy, the number of damage increments in the discretized stress – strain curve, the shear retention after cracking, mesh refinement and mesh alignment, and the possibility of non-symmetric failure modes. The comparisons between numerical and experimental results show that the alternative method is able to simulate the brittle failure behavior of the beam properly.

Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth

This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.

A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method

The extended finite element method is applied on the two-dimensional (2-D) finite piezoelectric media weakened by a crack. The fourfold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors. Four sequence of analysis, namely crack–mesh alignment, aspect ratio, mesh with local refinement and domain independency is done on the center and edge crack problems. These four analyses when combined together give an optimum result to study the finite specimen. It is observed that for smaller values of strip width to crack length ratio the finiteness of the specimen size affects the intensity factors.

Electromyographic correlates of learning during robotic surgical training in virtual reality.

The purpose of this study was to investigate the muscle activation and the muscle frequency response of the dominant arm muscles (flexor carpi radialis and extensor digitorum) and hand muscles (abductor pollicis and first dorsal interosseous) during robotic surgical skills training in a virtual environment. The virtual surgical training tasks consisted of bimanual carrying, needle passing and mesh alignment. The experimental group (n=5) was trained by performing four blocks of the virtual surgical tasks using the da Vinci™ surgical robot. During the pre- and post-training tests, all subjects were tested by performing a suturing task on a "life-like" suture pad. The control group (n=5) performed only the suturing task without any virtual task training. Differences between pre- and post-training tests were significantly greater in the virtual reality group, as compared to the control group in the muscle activation of the hand muscle (abductor pollicis) for both the suture tying and the suture running (p<0.05). In conclusion, changes in electrographic activity shows that training in virtual reality leads to specific changes in neuromotor control of robotic surgical tasks.

Towards SPH modelling of failure problems in geomechanics

ABSTRACT Failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering. Many Finite Element (FE) formulations for coupled problems present difficulties such as overestimating failure loads, or mesh alignment dependence resulting on spurious failure mechanisms. Moreover, the spaces where field variables are approximated have to fulfill additional requirements ensuring stability. Stress-velocity-pore pressure formulations in FE analysis provide accurate results for wave propagation and failure analysis. However, FE present important limitations when deformations are large. The purpose of this paper is to present a stabilized Fractional Step, SPH algorithm which combines the advantages of the SPH method for large deformation problems with those of the Taylor-Galerkin algorithm used within the FE framework.

Regular versus irregular meshing for complicated models and their effect on synthetic seismograms

SUMMARY We present a detailed study on the numerical effects due to staircase approximations of non-planar material interfaces and the importance of mesh alignment to such material boundaries using the discontinuous Galerkin finite element method. Our aim is to define clear rules that have to be adhered to guarantee acceptable synthetic data in seismic forward modelling for the cases where material contrasts occurring along curved interfaces are discretized with regular meshes. To this end, we compare results of structured staircase approximations with reference results obtained by unstructured triangular meshes that can be aligned to non-planar interfaces. We investigate different mesh spacings, wave frequencies, and material contrasts to cover various parameter ranges that allow us to measure their influence on the accuracy of the resulting waveforms. Our results show that acceptable synthetic results strongly depend on the material contrast and we give a quantitative estimate of the required mesh resolution in the sense of numbers of elements per shortest dominant wavelength to obtain satisfying seismograms even if the material interfaces are not respected by the mesh. We apply our rules to two different test cases including a multilayered model and a basin structure, both with non-planar interfaces of small and large material contrasts to confirm the validity of our study. We finally conclude that for moderate material contrasts regular meshing can be beneficial due to its simple mesh generation process and typically superior computational efficiency compared to unstructured meshes, however, the correct frequency- and material-dependent mesh resolution has to be chosen.

The Effect of Music on Robot-Assisted Laparoscopic Surgical Performance

Music is often played in the operating room to increase the surgeon's concentration and to mask noise. It could have a beneficial effect on surgical performance. Ten participants with limited experience with the da Vinci robotic surgical system were recruited to perform two surgical tasks: suture tying and mesh alignment when classical, jazz, hip-hop, and Jamaican music were presented. Kinematics of the instrument tips of the surgical robot and surface electromyography of the subjects were recorded. Results revealed that a significant music effect was found for both tasks with decreased time to task completion (P = .005) and total travel distance (P = .021) as well as reduced muscle activations ( P = .016) and increased median muscle frequency (P = .034). Subjects improved their performance significantly when they listened to either hip-hop or Jamaican music. In conclusion, music with high rhythmicity has a beneficial effect on robotic surgical performance. Musical environment may benefit surgical training and make acquisition of surgical skills more efficient.

The impact of environmental noise on robot-assisted laparoscopic surgical performance

An operating room is a noisy environment. How noise affects performance during robotic surgery remains unknown. We investigated whether noise during training with the da Vinci surgical robot (Intuitive Surgical, Inc., Sunnyvale, CA) would affect the performance of simple operative tasks by the surgeon. Twelve medical students performed 3 inanimate operative tasks (bimanual carrying, suture tying, and mesh alignment) on the da Vinci Surgical System with or without the presence of noise. Prerecorded noise from an actual operating room was used. The kinematics of the robotic surgical instrument tips and the muscle activation patterns of the subjects were evaluated. We found noise effects for all 3 tasks with increases in the time to task completion (23%; P=.046), the total distance traveled (8%; P=.011) of the surgical instrument tips, and the muscle activation volume (87%; P=.015) with the presence of noise. We confirmed that the mesh alignment task was the most difficult task with the greatest time to task completion and the greatest muscle activation volume, whereas the suture tying task and the bimanual carrying could be considered the intermediate and the least difficult task, respectively. The noise effects were significantly greater while performing more difficult tasks. Our findings demonstrated that noise degraded robotic surgical performance; however, the impact of noise on robotic surgery will depend on the level of difficulty of the task. Subsequent research is required to identify how different types of noise, such as random or rhythmic sounds, affect the performance of operative tasks using robots such as the da Vinci.

On the Convergence of DGFEM Applied to the Discrete Ordinates Transport Equation for Structured and Unstructured Triangular Meshes

The convergence properties of the discontinuous Galerkin finite element method (DGFEM) applied to the transport equation are presented for variants of Larsen’s test case. The analysis is performed for two-dimensional structured and unstructured triangular meshes, with DGFEM approximations up to order 4. Pure absorber media and scattering media are considered. The influence of the mesh alignment with the singularities of the transport solution is described. The numerically observed convergence rates are related to theoretical results.

복잡한 지반층을 고려한 지반-말뚝-구조물의 상호작용 동해석

The precise analysis of soil-pile-structure interaction requires a proper description of soil layer, pile, and structure. In commonly used finite element simulations, mesh boundaries should match the material discontinuity line. However, in practice, the geometry of soil profiles and piles may be so complex that mesh alignment becomes a wasteful and difficult task. To overcome these difficulties, a different integration method is adopted in this paper, which enables easy integration over a regular element with material discontinuity regardless of the location of the discontinuity line. By applying this integration method, the mesh can be generated rapidly and in a highly structured manner, leading to a very regular stiffness matrix. The influence of the shape of the soil profile and piles on the response is examined, and the validity of the proposed soil-pile structure interaction analysis method is demonstrated through several examples. It is seen that the proposed analysis method can be easily used on soil-pile-structure interaction problems with complex interfaces between materials to produce reliable results regardless of the material discontinuity line.

Adaptive anisotropic meshing for steady convection-dominated problems

Obtaining accurate solutions for convection–diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov–Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.