## Laplacian in 1D, 2D, or 3D

Version 1.2 (5.27 KB) by
Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs.

Updated 15 May 2015

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

Copyright owners: Bryan C. Smith and Andrew V. Knyazev

### Cite As

Andrew Knyazev (2023). Laplacian in 1D, 2D, or 3D (https://www.mathworks.com/matlabcentral/fileexchange/27279-laplacian-in-1d-2d-or-3d), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.2

Revision 1.1 changes: rearranged the output variables, always compute the eigenvalues, compute eigenvectors and/or the matrix on demand only.
added a conversion to a toolbox

1.1.0.0

updated description

1.0.0.0