Laplacian in 1D, 2D, or 3D
The code computes the exact eigenpairs of (1-3)D negative Laplacian on a rectangular finite-difference grid for combinations of Dirichlet, Neumann, and Periodic boundary conditions using explicit formulas from
http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative
The code can also compute the sparse matrix itself, using Kronecker sums of 1D Laplacians. For more information on tensor sums, see
http://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians
Example, compute everything for 3D negative Laplacian with mixed boundary conditions:
[lambda,V,A] = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
Compute only the eigenvalues:
lambda = laplacian([100,45,55],{'DD' 'NN' 'P'}, 20);
Compute the matrix only:
[~,~,A] = laplacian([100,45,55],{'DD' 'NN' 'P'});
GNU OCTAVE compatible.
This code is a part of the BLOPEX eigensolver package, see
http://en.wikipedia.org/wiki/BLOPEX
or go directly to
http://code.google.com/p/blopex/
Copyright owners: Bryan C. Smith and Andrew V. Knyazev
Zitieren als
Andrew Knyazev (2024). Laplacian in 1D, 2D, or 3D (https://www.mathworks.com/matlabcentral/fileexchange/27279-laplacian-in-1d-2d-or-3d), MATLAB Central File Exchange. Abgerufen .
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- Mathematics and Optimization > Partial Differential Equation Toolbox > Domain-Specific Modeling > Electromagnetics >
- Mathematics and Optimization > Partial Differential Equation Toolbox > General PDEs > Eigenvalue Problems >
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Version | Veröffentlicht | Versionshinweise | |
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1.2 | Revision 1.1 changes: rearranged the output variables, always compute the eigenvalues, compute eigenvectors and/or the matrix on demand only.
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1.1.0.0 | updated description |
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1.0.0.0 |