Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright (C) 2009 John Wiley & Sons, Ltd.

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

A brief survey of some of the fundamental algorithms in unstructured mesh generation is presented.Included is a discussion and categorization of triangle, tetrahedral, quadrilateral and hexahedral meshgeneration methods currently in use in academia and industry. Also included is a brief discussion ofsmoothing, cleanup and refinement algorithms. An informal survey of currently available mesh generationsoftware is also provided comparing some of their main features.1. IntroductionAutomatic unstructured mesh generation is a relatively new field. Within its short life span we have seentremendous advances in many diverse fields. Once in a while, it is useful to step back from our ownexpertise and look at the entire picture of what is going on in the field. The purpose of this survey is togive some perspective to what the current trends are in mesh generation and outline some of the majortechnology areas, who is working in these fields and what software is available.Probably the simplest approach is to first break down the technology based on the shape of elementgenerated. We will consider triangle and quad generation methods in 2D and tetrahedral and hexahedralmethods in 3D. Straddled between 2D and 3D, we have surface meshing, which has it’s own set of issues.In addition we have another set of issues dealing with post processing of the mesh including smoothing,cleanup and refinement. Within each of these issues, have emerged a few clear categories of algorithms,which tend to dominate much of the literature and software. Not included in this survey are a wide varietyof equally important related topics such as adaptive, anisotropic and parallel mesh generation as well asdata structure and geometry management issues. Because of the immense scope of the field of unstructuredmesh generation, I have limited this survey to include what I consider the more fundamental aspects of thefield. Since I do not purport to be an expert in all fields of mesh generation, this will be at best, a cursorylook at the main issues in each category.1.1 Software SurveyAs part of this paper, I conducted an informal survey of software vendors, research labs and educationalinstitutions that develop mesh and grid generation software. The purpose was to get a broad picture of whowas currently involved in developing software and what common algorithms were employed. The resultsof the survey are included as an appendix to this paper. They are also posted on the World Wide Web

A Survey of Unstructured Mesh Generation Technology.

1 Partially supported by the Deutsche Forschungsgemeinschaft, grant Kl 655 2-2.

Chapter 5 – Voronoi Diagrams*

Local mesh smoothing algorithms have been shown to be effective in repairing distorted elements in automatically generated meshes. The simplest such algorithm is Laplacian smoothing, which moves grid points to the geometric center of incident vertices. Unfortunately, this method operates heuristically and can create invalid meshes or elements of worse quality than those contained in the original mesh. In contrast, optimization-based methods are designed to maximize some measure of mesh quality and are very effective at eliminating extremal angles in the mesh. These improvements come at a higher computational cost, however. In this article the author proposes three smoothing techniques that combine a smart variant of Laplacian smoothing with an optimization-based approach. Several numerical experiments are performed that compare the mesh quality and computational cost for each of the methods in two and three dimensions. The author finds that the combined approaches are very cost effective and yield high-quality meshes.

/pdf/on-combining-laplacian-and-optimization-based-mesh-smoothing-1cmzuehwl3.pdf

On combining Laplacian and optimization-based mesh smoothing techniques

https://www.cell.com/biophysj/pdf/S0006-3495(03)70065-4.pdf

Heterogeneity of ADP Diffusion and Regulation of Respiration in Cardiac Cells

GEOMPACK — a software package for the generation of meshes using geometric algorithms☆

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

B. Joe

Author Tools

Chat about Author

Papers

GEOMPACK — a software package for the generation of meshes using geometric algorithms☆