Two-dimensional Mesh Research Articles

Computational Costs of Multi-Frontal Direct Solvers with Analysis-Suitable T-Splines

In this paper, we consider the computational cost of a multi-frontal direct solver used for the factorization of matrices resulting from a discretization of isogeometric analysis with T-splines, and analysis-suitable T-splines. We start from model projection or model heat transfer problems discretized over two-dimensional meshes, either uniformly refined or refined towards a point or an edge. These grids preserve several symmetries and they are the building blocks of more complicated grids constructed during adaptive isotropic refinement procedures. A large class of computational problems construct meshes refined towards point or edge singularities. We propose an ordering that permutes the matrix in a way that the computational cost of a multi-frontal solver executed on adaptive grids is linear. We show that analysis-suitable T-splines with our ordering, besides having other well-known advantages, also significantly reduce the computational cost of factorization with the multi-frontal direct solver. Namely, the factorization with N T-splines of order p over meshes refined to a point has a linear O(Np4) cost, and the factorization with T-splines on meshes refined to an edge has O(N2pp2) cost. We compare the execution time of the multi-frontal solver with our ordering to the Approximate Minimum Degree (AMD) and Cuthill–McKee orderings available in Octave.

Chimney Height, a Determining Factor in the Dispersion of Pollutants and Their Concentration

This work proposes a way of modelling two-dimensional complex meshes using elliptic equations, which the computational grid coincides with the problem geometry, making computational processing more suitable. A multiblock technique was used in order to achieve a better representation of the problem domain. In this way, numerical simulations of the movement and dispersion of pollutant emissions in the atmosphere are presented in the generated domains, using the Navier-Stokes pollutant transport equations. The curvilinear coordinates and the finite difference method are used for the discretization. The model was verified in two tests. In the first test, three cases were proposed, with geometries containing a chimney followed by an obstacle, using different chimney heights, and the obstacle height was fixed. The test aims to verify the vortices appearance, in the blocks, to obtain agreement with as presented in the literature. In the second test, the geometry is described by a chimney and an obstacle that represents one of the mountains in the valley. The performed tests made possible to verify that the height of the chimney can be considered a determining factor to describe the dispersion of pollutants, as well as their concentration in the proximity of industrial areas.

Numerical simulation of adiabatic shear bands formation processes on two-dimensional eulerian meshes

In this work we suggest a mathematical model of motion of the elasto-plastic materials with nonlinear plasticity constitutive law; we also propose an effective numerical method for numerical simulations of such tasks on two-dimensional eulerian meshes. Based on the method, we research formation of multiple adiabatic shear bands (ASB) at high-speed shear deformations. We test our approach on two-dimensional problem where the initial heterogeneity of temperature leads to formation of adiabatic shear band.

Improved Transmission Line Parameter Calculation Through TCAD Process Modeling for Superconductor Integrated Circuit Interconnects

The Florida Object-Oriented Device, Process and Reliability Simulator (FLOOXS) technology computer-aided design process modeling tools developed at the University of Florida have been adapted under the Intelligence Advanced Research Projects Activity SuperTools program to support the MIT Lincoln Laboratory SFQ5ee fabrication process. We use FLOOXS to build meshed models of passive transmission lines from superconductor integrated circuit layouts. We have previously developed a numerical solver that extracts transmission line parameters from the meshed model. In this work, we convert a layout slice to FLOOXS inputs, generate two-dimensional meshes of cross-sectional geometries from simulated process steps, and then extract the transmission line parameters from the meshes. Results are shown compared against the results for simplified transmission lines that do not utilize process modeling. The results confirm that process modeling alters the extracted parameter values and suggest that process modeling will become more important as cell density of superconducting electronics increases. We conclude with a discussion on the necessity of process modeling for high-quality parameter extraction.

The Axial Hartree–Fock + BCS Code SkyAx

The nuclear mean-field model based on Skyrme forces can predict a variety of properties of nuclear ground states. We present the Code SkyAx solving the Hartree–Fock equations in two spatial dimensions assuming axial symmetry. Pairing can be included in the BCS approximation. The code is implemented with a view on computational speed. Program summaryProgram title: SkyAxCPC Library link to program files:http://dx.doi.org/10.17632/fd453hc4jb.1Licensing provisions: GPLv3Programming language: Fortran 90 and parallel version with OpenMP.External routines/libraries: BLAS, LAPACK.Nature of problem: The Hartree–Fock equations can be used to determine static properties of nuclei all over the nuclear chart, e.g., nuclear masses, charge radii and deformations. This code implements the widely used Skyrme forces as interaction model and offers in addition to include the pairing interaction through the BCS theory. Due to its two-dimensional nature, the code allows only for axial deformations, which is suitable for most nuclei in the chart of nuclides.Solution method: The nucleonic wave functions are represented on a two-dimensional mesh assuming axial symmetry. The Coulomb potential is calculated for an isolated charge distribution by splitting the problem into a short-range and a long-range part. All spatial derivatives are evaluated using the finite Fourier transform method. The code solves the static Hartree–Fock equations with a damped gradient iteration method. It also allows for constraint iterations, where the monopole, quadrupole, octupole and hexadecapole moments can be fixed.Additional comments including restrictions and unusual features: The current implementation is restricted to even–even nuclei. Furthermore the Hartree–Fock + BCS model is valid only for well-bound nuclei. For nuclei near the neutron and proton drip lines, a full Hartree–Fock–Bogolyubov treatment would be more suitable.The code allows for multipole constraints up to l=4. Furthermore the code can be used to calculate fission paths or landscapes of deformations (potential energy surfaces) in one single run.

Improved Algorithm to Trace Boundary Curves on Two-Dimensional Square Meshes

In the contoured cutter path computation of a mold part, the Minkowski sum shape of the mold part CAD model and an inverted cutter model is sliced by a horizontal plane at a specific height. The cutter path can be obtained by tracing the boundary curve of the cross-sectional figure in the two-dimensional (2D) square mesh model. In the boundary curve tracing of the square mesh, the 2D marching cubes method based on the classification of the cell pattern of the mesh is typically used. We extended the classification pattern so that the existence of very small shapes in the cell, which is ignored by the conventional 2D marching cubes method, is evaluated in tracing the boundary curve. By using this technology, a robust and accurate contoured cutter path can be obtained without any increase in the computation time.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 52077203 and 61701467) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY19E070003).

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

Computational design of skintight clothing

We propose an optimization-driven approach for automated, physics-based pattern design for tight-fitting clothing. Designing such clothing poses particular challenges since large nonlinear deformations, tight contact between cloth and body, and body deformations have to be accounted for. To address these challenges, we develop a computational model based on an embedding of the two-dimensional cloth mesh in the surface of the three-dimensional body mesh. Our Lagrangian-on-Lagrangian approach eliminates contact handling while coupling cloth and body. Building on this model, we develop a physics-driven optimization method based on sensitivity analysis that automatically computes optimal patterns according to design objectives encoding body shape, pressure distribution, seam traction, and other criteria. We demonstrate our approach by generating personalized patterns for various body shapes and a diverse set of garments with complex pattern layouts.

High-order point-value enhanced finite volume method for two-dimensional hyperbolic equations on unstructured meshes

Presently, an approximate delta function (ADF) is defined in multi-dimensional space in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand spanning a finite domain. By using this ADF over a two-dimensional unstructured mesh, a compact high-order point-value enhanced finite volume method (PFV) is constructed. The corresponding scheme is capable of storing and updating cell-averaged values inside each element as well as the unknown quantities and their derivatives (when needed) on vertex points. The sharing of vertex information with surrounding elements reduces the number of degrees of freedom relative to other compact and high-order methods of comparable convergence rate. To ensure conservation, cell-averaged values are updated using an identical approach to the one traditionally followed in the finite volume method. To verify the performance of the PFV scheme at successive orders, its accuracy and stability are vetted using benchmark problems associated with the two-dimensional wave and Euler equations encompassing a total of six standard test cases.

Spectral graph wavelet regularization and adaptive wavelet for the backward heat conduction problem

This paper proposes a new regularization technique using spectral graph wavelet for backward heat conduction problem (BHCP) on the graph. The method uses the fourth-order compact difference for an approximation of differential operators. Meanwhile, the error estimate between the exact and wavelet regularized solution is derived. Adaptive node arrangement is obtained using spectral graph wavelet. The essence of the method is that the same operator can be used for the construction of the spectral graph wavelet and the approximation of the differential operator. The proposed method is applied to solve BHCP on graph arising from regular one-dimensional and two-dimensional mesh. Numerical results show that we can obtain a stable solution using spectral graph wavelet regularization. Moreover, spectral graph wavelet adaptivity and fourth-order compact difference scheme lead to a very efficient solution.

Numerical investigations of the flow around four non-aligned circular cylinders

This works aims at numerically investigating the flow around a group of four non-aligned cylinders, for two different angles of incidence, β = 0° and 180° at Reynolds number (Re) equal to 200. The influence of the proximity between the cylinders is investigated by means of the numerical analysis based on Computational Fluid Dynamics (CFD), using a finite volume method with two-dimensional unstructured meshes. The distance between cylinders and the angle of incidence has a great influence on the flow behavior, which is reflected on the analysis of the force coefficients and the Strouhal number. At β = 0°, it is observed the presence of two regimes in the time series of the lift coefficient, which lifespan of the first regime is reduced with increase of the spacing ratio. Also, different drag coefficients were seen at spacing ratio equals to 3.5 D for the rear cylinders. Regarding to the results with β = 180°, they showed multiple peaks on the lift coefficient amplitude spectrum for the rear cylinders. This work contributes to enhance the understanding of the flow around multiple cylinders, mainly regarding non-traditional configurations such as tandem and side-by-side arrangements.

On the aerodynamic fog collection efficiency of fog water collectors via three-dimensional numerical simulations

Fog water collection gained interest in recent years as an emerging solution for water scarcity in arid and semi-arid areas. During a fog event, a porous mesh screen of plastic polymer retains the water through droplet impaction, where the droplets coalesce and trickle into a gutter for collection. This type of collecting system has existed since the 1960s; however, a substantial lack of understanding remains as to the aerodynamics that dominates the collection phenomena. The Aerodynamic Collection Efficiency (ηa) is the determining factor in the overall performance of such systems. This paper aims to further the fundamental knowledge on the aerodynamic behavior during fog collection. For this, a three-dimensional computational fluid dynamics model was developed, where the collector's mesh was modeled as a porous medium, which simulates a conventional two-dimensional double layer mesh. A parametric study was carried out varying the mesh's geometric characteristics (flat and concave), mesh-to-ground distance, and wind speed. The effect of wind speed on aerodynamic collection efficiency is mainly determined by the relative relationship between the viscous and inertial pressure drop in the porous medium. A greater curvature reduces the mesh's airflow impedance, leading to a significant improvement of the aerodynamic collection efficiency. Within the parameter range of our study, we found a maximum aerodynamic collection efficiency of 35% for the largest curvature (1.1 m), the highest mesh-to-ground distance (2 m), and the maximum wind speed (5 to 7 m s−1).

Method for automatically generating a two-dimensional triangular mesh of a bone from a CT image considering its density heterogeneity

To perform numerical analyses, such as bio-mechanical analyses, on bones, it is necessary to construct the mesh model of the shape of the bone. In previous studies, the mesh has been generated by assuming that bones are homogeneous in terms of material distribution. However, bones are inherently heterogeneous. Therefore, the mesh has to be generated by considering the variation of the properties of bones. In this study, we propose a method for automatically generating a bone mesh by considering its heterogeneity. However, only two-dimensional triangular meshes are considered. In the proposed method, the boundary polylines of a bone are extracted from its computed tomography (CT) image using the marching squares method. Nodes are randomly generated on and inside the boundary polylines, and triangles are generated from the nodes by Delaunay triangulation. When the nodes are generated on and inside the boundary polylines, the density of the nodes is controlled by threshold functions defined by the magnitude of the gradient vector of the Hounsfield unit values of the CT image. The proposed method was implemented using C++ and visualization toolkit, and experiments were performed using CT images on the right femur, hip bones, and vertebra. We also verified that the proposed method can generate meshes reflecting the variation of the properties of bones.

Three-dimensional numerical modelling of multi-layered shell structures using two-dimensional plane mesh

The article presents a full three-dimensional (3D) numerical analysis of curved laminated shell structures using only a two-dimensional (2D) planar finite element mesh. The applied numerical method is called FEM23, which stands for the 2D finite element method for a full 3D analysis. FEM23 makes it possible to perform a numerical analysis of a multi-layered shell, utilising a numerical model based on a 2D finite element mesh. FEM23 ensures exact shell geometry since a pure mathematical description of a geometry is applied in the numerical model. Examples provided in the following paper prove FEM23 to be accurate and flexible. They involve the analysis of a special laminated structure - laminated glass, which comprises of glass panes bonded by thin polymer films. A full 3D description is provided for the glass panes as well as polymer films, even though the film thickness is over ten times smaller than the glass layers. The results are verified by the analytical solution and those obtained by standard 3D FEM. A unique post-processing procedure developed specially for FEM23 enables visualisation of the full 3D results.

An arbitrary Lagrangian-Eulerian RKDG method for multi-material flows on adaptive unstructured meshes

In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) method for solving compressible multi-material flows on two-dimensional adaptive unstructured triangular meshes. We couple a conservative equation related to a γ-model (or a mass fractional model) with the system of fluid equations for obtaining the specific heat ratio of the multi-material flows. The discretization of the coupling system is implemented by Runge-Kutta Discontinuous Galerkin (RKDG) method and the vertex velocity is obtained by the variational approach. The new meshes can be automatically redistributed and concentrated on regions with large gradient values. This work is a new development of our previous research for solving single-material flow with ALE-RKDG method. The proposed method is more concise compared to many other methods and robust for the simulations of multi-material flows. Numerical examples are presented to verify this method, and the results show that our scheme is not only efficient but also with the anticipative accuracy.

Automatic triangular and triangular-prism mesh generation for overland and subsurface water flow simulations

In this paper, an automatic mesh generator is developed to simulate density-dependent water flow and transport problems in watershed systems. The two-dimensional (2D) triangular mesh is generated by global Delaunay triangulation, and the three-dimensional (3D) triangular-prism mesh is generated by vertical stretch. The implementation procedures of mesh generation are adjusted according to the interaction options of one-dimensional (1D) river, 2D overland, and 3D subsurface flows. An improved boundary point generation algorithm is proposed to maintain appropriate correspondence of points and edges according to the discrete patterns of river reaches and dead ends. Overlapped nodes are generated on zero-width river reaches and zero-width junctions without storage to construct the numerical models for 2D overland simulations. An additional triangular mesh generation method is proposed to create additional triangles for filling the empty water zones of finite-width river reaches, junctions with storage, finite-width ponds, lakes, and dead ends. The boundary loops bounding each water area are identified correctly, and the additional grids are created compatibly, aiming at the finite-depth and zero-depth patterns of storage zones. The computation equations of relevant parameters used for 3D stretch from triangles to triangular-prisms are built, and the 1D/2D/3D correspondence on river reaches, junctions, ponds, lakes, dead ends, and control structures is established. Finally, practical examples for discretizing real-world water areas are provided to demonstrate the robustness and effectiveness of our developed mesh generator by using the skewness as the mesh quality metric.

Tasks mapping in the network on a chip using an improved optimization algorithm

PurposeA set of routers that are connected over communication channels can from network-on-chip (NoC). High performance, scalability, modularity and the ability to parallel the structure of the communications are some of its advantages. Because of the growing number of cores of NoC, their arrangement has got more valuable. The mapping action is done based on assigning different functional units to different nodes on the NoC, and the way it is done contains a significant effect on implementation and network power utilization. The NoC mapping issue is one of the NP-hard problems. Therefore, for achieving optimal or near-optimal answers, meta-heuristic algorithms are the perfect choices. The purpose of this paper is to design a novel procedure for mapping process cores for reducing communication delays and cost parameters. A multi-objective particle swarm optimization algorithm standing on crowding distance (MOPSO-CD) has been used for this purpose.Design/methodology/approachIn the proposed approach, in which the two-dimensional mesh topology has been used as base construction, the mapping operation is divided into two stages as follows: allocating the tasks to suitable cores of intellectual property; and plotting the map of these cores in a specific tile on the platform of NoC.FindingsThe proposed method has dramatically improved the related problems and limitations of meta-heuristic algorithms. This algorithm performs better than the particle swarm optimization (PSO) and genetic algorithm in convergence to the Pareto, producing a proficiently divided collection of solving ways and the computational time. The results of the simulation also show that the delay parameter of the proposed method is 1.1 per cent better than the genetic algorithm and 0.5 per cent better than the PSO algorithm. Also, in the communication cost parameter, the proposed method has 2.7 per cent better action than a genetic algorithm and 0.16 per cent better action than the PSO algorithm.Originality/valueAs yet, the MOPSO-CD algorithm has not been used for solving the task mapping issue in the NoC.

Mesh Coarsening for Fast Simulation on Low Resource Machine

Mesh-based application uses a mesh to discretely represent a real physical system and then calls appropriate algorithm over the mesh to solve equation for simulation. Mesh-based application is usually developed by domain programmers and it runs with very large mesh on super computer. It takes a long time to run with such a large mesh on low resource machine. In this paper, we propose an algorithm designed for coarsening two-dimensional quadrilateral mesh aiming to reduce the size of the mesh so that the application could run with the smaller coarse mesh on low resource machine in a short time. This makes it more convenient for domain programmers to develop and debug the application on low resource machine. The algorithm first generates cells of the coarse mesh by agglomerating cells of the original mesh. Then it constructs internal edges, boundary edges, nodes and all mappings of the coarse mesh. At last, the algorithm constructs datasets of the coarse mesh according to the datasets of the original mesh. The experimental result shows that it takes much less time to run application over the coarse mesh produced by our algorithm, and the error of fast simulation results is within the acceptable range.

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

This paper focuses on efficiently numerical investigation of two-dimensional heat conduction problems of material subjected to multiple moving Gaussian point heat sources. All heat sources are imposed on the inside of material and assumed to move along some specified straight lines or curves with time-dependent velocities. A simple but efficient moving mesh method, which continuously adjusts the two-dimensional mesh dimension by dimension upon the one-dimensional moving mesh partial differential equation with an appropriate monitor function of the temperature field, has been developed. The physical model problem is then solved on this adaptive moving mesh. Numerical experiments are presented to exhibit the capability of the proposed moving mesh algorithm to efficiently and accurately simulate the moving heat source problems. The transient heat conduction phenomena due to various parameters of the moving heat sources, including the number of heat sources and the types of motion, are well simulated and investigated.

Three-Dimensional Analysis of Laminated Plates with Functionally Graded Layers by Two-Dimensional Numerical Model

This work presents a three-dimensional (3D) numerical analysis of multi-layered laminated plates in which selected layers may be made of functionally graded material (FGM), in which the Young’s modulus may change along the thickness as a consequence of a continuous and graded mixture of two materials. For the analysis, the method, known as FEM23, is applied, which uses a two-dimensional (2D) mesh, yet enables obtaining full 3D results for the layered structure. In FEM23, the layered structure may be a combination of thin and thick layers made of materials with significantly different properties. This paper presents two examples comparing the results to other numerical or analytical solutions. The examples confirm the correctness and flexibility of FEM23 for laminated plates with functionally graded layers.