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Building Two-Dimensional Meshes
Published in Pavel Sumets, Computational Framework for the Finite Element Method in MATLAB® and Python, 2023
Above, we have considered how to define a domain geometry and build a mesh using MATLAB tools. Now, we explain how to perform mesh building in Python. Again, the approach is to use third-party library for mesh processing rather than discussing particular mesh building algorithm. There is a powerful mesh generation tool, named Gmsh, having its own scripting language allowing creating complex geometries. The library PyGmsh provides a Python interface for the Gmsh scripting language so one can create geometry and generate meshes more easily with excess to Python's features. After installing PyGmsh, the default Gmsh kernel with basic geometry construction functions can be used.
Domain-Modeling Techniques
Published in Alexandru Telea, Data Visualization, 2014
Implementing robust, efficient, and scalable algorithms for these mesh generation methods is a complex task. Fortunately, several high-quality software implementations for Delaunay triangulation and Voronoi diagram computation are available in the open-source arena, such as the Triangle mesh generator [Shewchuk 06, Shewchuk 02]. Triangle provides a rich set of Delaunay triangulation algorithms, including the conforming and area, angle, and geometry constrained variants, as well as the computation of Voronoi diagrams, and is capable of triangulating hundreds of thousands of input points in a few seconds and with high precision on a modern PC. All examples presented in this section are computed with the Triangle software. Another high-quality open-source library providing Delaunay triangulation and Voronoi diagram operations is the Gnu Triangulated Surface Library (GTS) [GTS 13]. The interface of the GTS library is relatively more complex than that of the Triangle library. However, the GTS library offers many extra features, such as set operations on surfaces, multiresolution surface representation capabilities, and kd-trees for fast point location.
Technology CAD Tools
Published in Chinmay K. Maiti, Introducing Technology Computer-Aided Design (TCAD), 2017
The difficulties in mesh generation are a challenging task in TCAD and call for automatic and adaptive grid generation techniques. Mesh definition is important for simulation accuracy and time. A fine mesh gives an accurate solution but increases simulation time. Device simulation involves the solution of coupled PDEs which describe the evolution of either geometry or impurity distribution as a result of manufacturing process steps, or internal physical quantities in response to electrical boundary conditions. Solutions of coupled PDEs can only obtained numerically; thus, a proper discretization (mesh generation) procedure is required. Mesh generation has thus a crucial impact on the convergence, accuracy, and efficiency of the simulation. Also, meshing has become a major issue because device architectures are now essentially 3D. Therefore, automatic grid generation and adaptation are highly desirable, for improving both the trade-off between computational complexity and solution accuracy. To optimizing the mesh grid is the important goal for MOSFET structures. Automated gridding procedures (adaptive meshing) are desirable in process and device simulations. A mesh should be refined in the key areas. These areas are: Around junctions and depletion regionsInversion regionsAreas of high electric fieldAreas of current flow
Magnetized flow of naturally convective viscous fluid in permeable rhombus-shaped annulus by executing FEM simulations
Published in Numerical Heat Transfer, Part A: Applications, 2023
Sardar Bilal, Noor Zeb Khan, Imtiaz Ali Shah, Murad Ali Shah
Grid generation or meshing is one of the most significant phases in calculating numerical solutions of modeled problems in continuum mechanics. Meshes are a set of simulations that have well-defined structures in terms of alignment with square and triangular elements in 2-D domain. Mesh generation is the process of creating an appropriate grid to approximate solution inside various parts. It provides comprehensive picture of fluid flow not only on boundaries but in the domain. Mesh statistics at different refinement level is exhibited in Table 1. In addition, field variables describing the nature of problem are heeded at boundary and intermediate nodes and degrees of freedom are computed as shown in Table 2. Meshing at extra fine grid level is opted to compute simulations for problem as illustrated in Figure 3.
Towards consistent numerical analyses of embankments on soft soils
Published in European Journal of Environmental and Civil Engineering, 2022
Amar Amavasai, Jean-Philippe Gras, Nallathamby Sivasithamparam, Minna Karstunen, Jelke Dijkstra
An essential step after the parameter determination is to compare the stress-strain response of the model simulations and the laboratory data before continuing to the boundary value level simulations of the engineering problem. The test data should reflect the load paths encountered in the engineering problem. Generally as a minimum, 1D compression and triaxial data should be compared. Here, oedometer and triaxial tests are simulated using Tochnog Professional, a finite element code for geotechnical analysis Tochnog Professional User’s manual (2015) and the results are compared against experimental data. Rather uniquely, in addition to single element simulations, multi-element models are generated to properly incorporate coupled flow analysis. In the latter the mesh is generated using GMSH, an open source code for mesh generation and post-processing (Geuzaine & Remacle, 2009). Boundary conditions are applied similar to laboratory conditions regarding displacements, axisymmetrical boundary on the left edge and free drainage on top of the sample. The Creep-SCLAY1S model is incorporated as a user-defined model in Tochnog. In order to better reflect the real laboratory test, the consolidation stage is also included in the simulations. Hence, an initial isotropic effective stress of 5–10 kPa has been applied. This not only increases the numerical stability near the locus of the failure envelope, it also represents some suction remaining in the soft soil samples after sampling. As a result the pre-overburden pressure (POP) is modified accordingly. The results from the oedometer incremental loading (IL) test simulations (Figure 8) show very good agreement with the laboratory data without further tweaking of the model parameters. Also, the triaxial drained tests have been simulated with good agreement to the laboratory data (see Figure 9), using the same parameter set.