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See the MATLAB central file exchange to download the toolbox (.zip file): FELICITY Download
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This is a MATLAB/C++ code for solving PDEs that are discretized by a finite element method on unstructured simplex grids. It uses a Domain-Specific-Language (DSL) to help streamline implementation of FE discretizations (e.g. matrix assembly) by automatic code generation. The resultant sparse matrices can be manipulated by MATLAB for ease in solving a PDE on a triangular (or tetrahedral) mesh.
- PDEs can be defined on 1-D, 2-D, and 3-D domains. Moreover, the domains can be curves or surfaces embedded in 3-D. For example, you can solve the Laplace-Beltrami equation on a 2-D surface in 3-D.
- Can have multiple interacting sub-domains in a single problem. For example, can have a 1-D curve sub-domain embedded in a 3-D bulk mesh. Can also have a 2-D surface sub-domain embedded in a 3-D bulk-mesh.
- Can define bilinear and linear forms with contributions from multiple embedded sub-domains of different dimensions (i.e. co-dimension >= 0).
- Can do higher order geometry (e.g. quadratic triangle mappings).
- New elements are easily added using a simple ``flat'' m-file.
- Automatically generate custom matrix assembly codes that are callable from MATLAB.
- Automatically generate DoF (Degree-of-Freedom) numbering/allocation for any element implemented in FELICITY.
- Generic mesh classes that implement some useful mesh routines, such as 1-D and 2-D adaptive mesh refinement.
- Some mesh generation utilities (see below).
- MATLAB classes for managing FEM spaces.
- H(div) and H(curl) elements are implemented.
- Support for finite element interpolation in 1-D, 2-D, and 3-D.
- Efficient C++ implementations of bitree, quadtree, and octree; useful for nearest neighbor searching.
- Efficient closest point searching of simplex meshes. This includes finding closest points on surface meshes in 3-D.
Please see the manual (PDF) in the .zip file for more information.
If you use this toolbox in your work, then you must acknowledge it. Please cite the paper on FELICITY (bibtex entry given):
@Article{Walker_SJSC2018,
author = {Shawn W. Walker},
title = {FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling},
journal = {SIAM Journal on Scientific Computing},
year = {2018},
volume = {40},
number = {2},
pages = {C234-C257},
doi = {10.1137/17M1128745},
eprint = {https://doi.org/10.1137/17M1128745},
url = {https://doi.org/10.1137/17M1128745},
}
Note: there is also a supplementary demo file.
Then download the FELICITY package and only keep this sub-directory:
./FELICITY/Static_Codes/Isosurface_Meshing
Next, run compile_mex_2D_mesh_tiger_code, compile_mex_3D_mesh_tiger_code to compile the C++ code.
Then look at the tutorial: Mesh Generation With TIGER: Part 1.
If you use the mesh generator in your work, then you must acknowledge it. Please cite the paper on TIGER (bibtex entry given):
@Article{Walker_SISC2013,
author = {Shawn W. Walker},
title = {Tetrahedralization of Isosurfaces with Guaranteed-Quality by Edge
Rearrangement ({TIGER})},
journal = {SIAM Journal on Scientific Computing},
year = {2013},
volume = {35},
pages = {A294-A326},
number = {1},
doi = {10.1137/120866075},
eprint = {http://epubs.siam.org/doi/pdf/10.1137/120866075}
}