Meshfree methods are becoming an increasingly popular alternative to mesh-based methods of numerical simulation. The biggest stated advantage of meshfree methods is the avoidance of generating a mesh ...on the computational domain. However, even today a surprisingly large amount of meshfree literature ironically uses the nodes of a mesh as the point set that discretizes the domain. On the other hand, already existing efficient meshfree methods to generate point clouds are apparently not very well known among meshfree communities, which has led to recent work redeveloping existing algorithms. In this paper, we present a brief overview of point cloud generation methods for domains and surfaces and discuss their features and challenges, in particular in the context of applicability to industry-relevant complex geometries.
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these ...methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future benchmarking of new methods. We review traditional methods and recent ones which appeared in the last decade. We aim to help newcomers to the field understand the main characteristics of these methods and to provide sufficient information to both simplify implementation and benchmarking of new methods. Some of the examples are chosen within a subset of problems where collocation is traditionally known to perform sub-par, namely when the solution sought is non-smooth, i.e. contains discontinuities, singularities or sharp gradients. For such problems and other simpler ones with smooth solutions, we study in depth the influence of the weight function, correction function, and the number of nodes in a given support. We also propose new stabilization approaches to improve the accuracy of the numerical methods. In particular, we experiment with the use of a Voronoi diagram for weight computation, collocation method stabilization approaches, and support node selection for problems with singular solutions. With an appropriate selection of the above-mentioned parameters, the resulting collocation methods are compared to the moving least-squares method (and variations thereof), the radial basis function finite difference method and the finite element method. Extensive tests involving two and three dimensional problems indicate that the methods perform well in terms of efficiency (accuracy versus computational time), even for non-smooth solutions.
The detection of associations between protein complexes and human inherited diseases is of great importance in understanding mechanisms of diseases. Dysfunctions of a protein complex are usually ...defined by its member disturbance and consequently result in certain diseases. Although individual disease proteins have been widely predicted, computational methods are still absent for systematically investigating disease-related protein complexes.
We propose a method, MAXCOM, for the prioritization of candidate protein complexes. MAXCOM performs a maximum information flow algorithm to optimize relationships between a query disease and candidate protein complexes through a heterogeneous network that is constructed by combining protein-protein interactions and disease phenotypic similarities. Cross-validation experiments on 539 protein complexes show that MAXCOM can rank 382 (70.87%) protein complexes at the top against protein complexes constructed at random. Permutation experiments further confirm that MAXCOM is robust to the network structure and parameters involved. We further analyze protein complexes ranked among top ten for breast cancer and demonstrate that the SWI/SNF complex is potentially associated with breast cancer.
MAXCOM is an effective method for the discovery of disease-related protein complexes based on network optimization. The high performance and robustness of this approach can facilitate not only pathologic studies of diseases, but also the design of drugs targeting on multiple proteins.
Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretization that be used ...to solve PDEs requires care and a deep knowledge of the selected computational method. In this article, we present a novel integrated collocation scheme based on smart clouds. It allows us to transform a CAD geometry into a complete point collocation model, aware of the base geometry, with minimum effort. For this process, only the geometry of the domain, in the form of a STEP file, and the boundary conditions are needed. We also introduce an adaptive refinement process for the resultant smart cloud using an a posteriori error indication. The scheme can be applied to any 2D or 3D geometry, to any PDE and can be applied to most point collocation approaches. We illustrate this with the meshfree Generalized Finite Difference (GFD) method applied to steady linear elasticity problems. We further show that each step of this process, from the initial discretization to the refinement strategy, is connected and is affected by the approach selected in the previous step, thus requiring an integrated scheme where the whole solution process should be considered at once.
•CAD files are used to generate smart point clouds without any intermediate step.•Exact normal vectors and boundary conditions are based on the CAD geometry.•ZZ-type error indicators are the basis for model adaptivity and are quick to compute.•Model adaptivity speeds up the convergence rate of the solution.•Model adaptivity is based on the exact CAD geometry.
We introduce in this article a unified algorithm which allows the selection of collocation stencils, based on the visibility criterion, for convex, concave, and singular problems solved using a ...collocation method. The algorithm can be applied to any 2D or 3D problem. We show the importance of using a threshold angle, in conjunction with the visibility criterion, to assess of the inclusion of a node in the support of a collocation center. We also show how the algorithm can be used to assess the presence of a node in a defined domain. Such algorithm is particularly useful in the context of model refinement.
•A novel simulation method for massive concrete structures with cracks is proposed.•Refined simulation model with irregular cracks is established based on the method.•The method reduces meshing ...difficulty in complex 3D models with cross-scale cracks.•Crack propagation during dam construction and under an earthquake is examined.
The irregular cross-scale cracks in massive concrete structures threat the safety. Due to huge difference in scale between structures and cracks, the stability of the irregular cross-scale cracks (millimeter level) cannot be accurately analyzed in the massive concrete structures (hundred-meter level). The imprecision of the mesh model is incompatible with existing advanced cracking methods. To address the problem, this paper presents a novel numerical simulation method for irregular cross-scale cracks in massive concrete structures with node projection strategy. The elements that the crack passes through are identified on the original mesh model without cracks, and the numerical simulation model with irregular cracks is generated by projecting the corresponding nodes of elements that the crack passes through onto the crack point cloud. The primary advantage of this method is that it does not require modifying the original element types or meshing the geometric model with cracks. To verify the present method, the three-point bending beams of concrete with regular cracks and irregular cracks are examined with experiment and numerical simulation. It demonstrates that the shape characteristics of an irregular crack can result in distinct tension damage patterns compared to a regular crack. In addition, the crack propagation during dam construction and earthquake loading is investigated to demonstrate the applicability of the present method for simulating crack propagation in massive concrete structures.
Besides the pinpointing of individual disease-related genes, associating protein complexes to human inherited diseases is also of great importance, because a biological function usually arises from ...the cooperative behaviour of multiple proteins in a protein complex. Moreover, knowledge about disease-related protein complexes could also enhance the inference of disease genes and pathogenic genetic variants. Here, we have designed a computational systems biology approach to systematically analyse potential relationships between diseases and protein complexes. First, we construct a heterogeneous network which is composed of a disease-disease similarity layer, a tissue-specific protein-protein interaction layer, and a protein complex membership layer. Then, we propose a random walk model on this disease-protein-complex network for identifying protein complexes that are related to a query disease. With a series of leave-one-out cross-validation experiments, we show that our method not only possesses high performance but also demonstrates robustness regarding the parameters and the network structure. We further predict a landscape of associations between human diseases and protein complexes. This landscape can be used to facilitate the inference of disease genes, thereby benefiting studies on pathology of diseases.
We present numerical computation of stresses under fretting fatigue conditions derived from closed form expressions. The Navier-Cauchy equations, that govern the problem, are solved with strong and ...weak form meshless numerical methods. The results are compared to the solution obtained from well-established commercial package ABAQUS, which is based on finite element method (FEM). The results show that the weak form meshless solution exhibits similar behavior as the FEM solution, while, in this particular case, strong form meshless solution performs better in capturing the peak in the surface stress. This is of particular interest in fretting fatigue, since it directly influences crack initiation. The results are presented in terms of von Mises stress contour plots, surface stress profiles, and the convergence plots for all three methods involved in the study.
•Numerical computation of fretting contact.•Navier-Cauchy equations.•Strong and weak form meshless solution.•Strong form performs better in capturing peak stress.
When defects reach a critical size, failure occurs in engineering components. The criticality assessment of defects is hence a key aspect of the structural integrity of gas pipelines in service. ...Fitness-For-Service (FFS) assessments are generally employed for evaluating the criticality of a crack-like flaw in structures using simplified assumptions in relation to geometry and material properties. Whilst the errors resulting from these modelling simplifications prove acceptable in many cases, there are situations where it will be necessary to take into account the nonlinearities in geometry and/or material behaviour. This can be either to avoid excess conservatism or, on the contrary, to ensure the results are safe. In such cases it becomes essential to develop a finite element model of the structure to account for such real-engineering complexity. Welding, the most prevalent technique to join pipe, often brings about a misalignment between two pipes and hence complex crack shape is formed. The aim of this study is to develop an elastoplastic finite element model of a gas pipeline possessing a crack in a misaligned weld. The remaining life of the pipeline is determined using a Failure Assessment Diagram (FAD) and the Paris law. The results obtained from the finite element method to determine the stress intensity factors are compared to results derived using the API-579 for stress intensity factors calculations.
Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretization that be used ...to solve PDEs requires care and a deep knowledge of the selected computational method. In this article, we present a novel integrated collocation scheme based on smart clouds. It allows us to transform a CAD geometry into a complete point collocation model, aware of the base geometry, with minimum effort. For this process, only the geometry of the domain, in the form of a STEP file, and the boundary conditions are needed. We also introduce an adaptive refinement process for the resultant smart cloud using an \textit{a posteriori} error indication. The scheme can be applied to any 2D or 3D geometry, to any PDE and can be applied to most point collocation approaches. We illustrate this with the meshfree Generalized Finite Difference (GFD) method applied to steady linear elasticity problems. We further show that each step of this process, from the initial discretization to the refinement strategy, is connected and is affected by the approach selected in the previous step, thus requiring an integrated scheme where the whole solution process should be considered at once.
PDF
