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This code demonstrates vectorization concepts from the paper:
Talal Rahman and Jan Valdman: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements, Applied Mathematics and Computation 219, 7151–7158 (2013).
A link to the paper can be found at the author web page located at http://sites.google.com/site/janvaldman/publications
Please cite the paper if you find the code useful.
Available scripts from the paper:
"start_compute_areas"
"start_assembly_P1_2D"
"start_assembly_P1_3D"
"start_assembly_P1_2D_elasticity"
"start_assembly_P1_3D_elasticity"
Additional script (provided by Tien Dat Ngo from EFPL Lausanne):
"start_assembly_Q1_3D_elasticity"
Cite As
Jan Valdman (2026). Fast FEM assembly: nodal elements (https://in.mathworks.com/matlabcentral/fileexchange/27826-fast-fem-assembly-nodal-elements), MATLAB Central File Exchange. Retrieved .
Acknowledgements
Inspired: Fast FEM evaluation of nonlinear energies: hp elements, Efficient vectorization techniques for FEM computations, p-Laplace equation solver using 1D, 2D FEM, Element-based Solvers, Fast FEM evaluation of nonlinear energies: nodal elements, Fast FEM assembly: edge elements, Evolutionary model for shape memory alloys, Hyper elasticity with a non-penetration condition, Implementation of C1 FEM, Simulation of von Kármán viscoelastic plates, Linear elasticity with a non-penetration surface condition, Hierarchical hp FEM on rectangles in 2D
General Information
- Version 1.17.0.0 (813 KB)
MATLAB Release Compatibility
- Compatible with any release
Platform Compatibility
- Windows
- macOS
- Linux
| Version | Published | Release Notes | Action |
|---|---|---|---|
| 1.17.0.0 | Description simplified, 'stifness' changed to 'stiffness'. |
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| 1.16.0.0 | Title and summary update. |
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| 1.15.0.0 | P1 coefficients for mass matrices (both 2D and 3D) added |
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| 1.14.0.0 | P0 coefficients added to assemblies of mass matrices in both 2D and 3D
|
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| 1.13.0.0 | paper info completed |
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| 1.12.0.0 | improved description |
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| 1.11.0.0 | Q1 assembly in 3D for linear elasticity added thanks to Tien Dat Ngo. |
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| 1.10.0.0 | Paper information added |
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| 1.4.0.0 | report link add, extended to work for linear elasticity |
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| 1.3.0.0 | tested for both linux and windows |
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| 1.2.0.0 | added start_calculate_areas |
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| 1.1.0.0 | 2D functionality added |
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| 1.0.0.0 |
