triangulated surfaces generated by the well-known matlab package distmesh  (MathWorks Inc)

Journal: Numerical Algorithms

Article Title: VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D

doi: 10.1007/s11075-024-01919-4

Figure Lengend Snippet: Numerical solution at the final time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=10$$\end{document} T = 10 of the S-RDS on the ellipsoid \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} Γ defined in , solved in VEMcomp on a mesh with 3990 nodes and meshsize \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h \le 0.1$$\end{document} h ≤ 0.1 , whose exact value is not provided by DistMesh. Top row: component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 (left) and component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_2$$\end{document} v 2 (right). Bottom row: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} L 2 norm of time derivative of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (left) and spatial average of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (right)

Article Snippet: For example, for the case of triangulated surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3$$\end{document} R 3 with an empty boundary, VEMcomp is fully compatible with the triangulated surfaces generated by the well-known Matlab package DistMesh [ ]; Black-box solvers : For multiple classes of PDE problems, the library provides a black-box interface that allows the user to set the problem parameters, and returns the VEM or FEM numerical solution.

Techniques:

Journal: Numerical Algorithms

Article Title: VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D

doi: 10.1007/s11075-024-01919-4

Figure Lengend Snippet: Numerical solution at the final time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=10$$\end{document} T = 10 of the S-RDS on the ellipsoid \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} Γ defined in , solved in VEMcomp on a mesh with 3990 nodes and meshsize \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h \le 0.1$$\end{document} h ≤ 0.1 , whose exact value is not provided by DistMesh. Top row: component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 (left) and component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_2$$\end{document} v 2 (right). Bottom row: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} L 2 norm of time derivative of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (left) and spatial average of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (right)

Article Snippet: This means that VEMcomp can be used as a FEM solver for surface and bulk-surface PDEs, when provided with triangular/tetrahedral meshes, for which several open-source generators exist, for instance the Matlab package DistMesh [ ] as illustrated in the numerical example in Section .

Techniques:

Journal: Journal of Computational Neuroscience

Article Title: A numerical simulation of neural fields on curved geometries

doi: 10.1007/s10827-018-0697-5

Figure Lengend Snippet: Illustration of the refinement procedure for a general triangulated domain in which the initial mesh is generated using the DistMesh package

Article Snippet: To do this we deployed the DistMesh MATLAB package (Persson and Strang ) to generate a general mesh, that is, one in which the triangle vertices do not lie on a Cartesian grid, as in our previous investigations.

Techniques: Generated

Journal: Journal of Computational Neuroscience

Article Title: A numerical simulation of neural fields on curved geometries

doi: 10.1007/s10827-018-0697-5

Figure Lengend Snippet: Convergence of linear collocation when computing the integral in on a general triangulation constructed using the DistMesh package. The orange and yellow lines indicate the slopes for first and second order methods, respectively

Article Snippet: To do this we deployed the DistMesh MATLAB package (Persson and Strang ) to generate a general mesh, that is, one in which the triangle vertices do not lie on a Cartesian grid, as in our previous investigations.

Techniques: Construct

Journal: Journal of Computational Neuroscience

Article Title: A numerical simulation of neural fields on curved geometries

doi: 10.1007/s10827-018-0697-5

Figure Lengend Snippet: Travelling bump solution of computed on a general DistMesh triangulation

Article Snippet: To do this we deployed the DistMesh MATLAB package (Persson and Strang ) to generate a general mesh, that is, one in which the triangle vertices do not lie on a Cartesian grid, as in our previous investigations.

Techniques:

Journal: Journal of Computational Neuroscience

Article Title: A numerical simulation of neural fields on curved geometries

doi: 10.1007/s10827-018-0697-5

Figure Lengend Snippet: Illustration of a general triangulation of the torus generated using the DistMesh package (Persson and Strang )

Article Snippet: To do this we deployed the DistMesh MATLAB package (Persson and Strang ) to generate a general mesh, that is, one in which the triangle vertices do not lie on a Cartesian grid, as in our previous investigations.

Techniques: Generated