Computer Methods in Applied Mechanics and Engineering
Boundary value problems with symmetry and their approximation by finite elements
SIAM Journal on Applied Mathematics
Generalized FFTS - A Survey of Some Recent Results
Generalized FFTS - A Survey of Some Recent Results
Designing for geometrical symmetry exploitation
Scientific Programming - Parallel/High-Performance Object-Oriented Scientific Computing (POOSC '05), Glasgow, UK, 25 July 2005
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
Journal of Computational and Applied Mathematics
Mesh generation for symmetrical geometries
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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An equivariant matrix A commutes with a group of permutation matrices. Such matrices often arise in numerical applications where the computational domain exhibits geometrical symmetries, for instance triangles, cubes, or icosahedra.The theory for block diagonalizing equivariant matrices via the generalized Fourier transform (GFT) is reviewed and applied to eigenvalue computations. For dense matrices which are equivariant under large symmetry groups, we give theoretical estimates that show a substantial performance gain. In case of cubic symmetry, the gain is about 800 times, which is verified by numerical results.It is also shown how the multiplicity of the eigenvalues is determined by the symmetry, which thereby restricts the number of distinct eigenvalues. The inverse GFT is used to compute the corresponding eigenvectors. It is emphasized that the inverse transform in this case is very fast, due to the sparseness of the eigenvectors in the transformed space.