Object-oriented modeling and design
Object-oriented modeling and design
Exploiting symmetry in boundary element methods
SIAM Journal on Numerical Analysis
Boundary value problems with symmetry and their approximation by finite elements
SIAM Journal on Applied Mathematics
Exploiting symmetry on parallel architectures
Exploiting symmetry on parallel architectures
Equivariant preconditioners for boundary element methods
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
On the Role of Mathematical Abstractions for Scientific Computing
Proceedings of the IFIP TC2/WG2.5 Working Conference on the Architecture of Scientific Software
A draft description of the group theory language Cayley
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Radial Basis Functions
Eigenvalues for equivariant matrices
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
Journal of Computational and Applied Mathematics
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Symmetry-exploiting software based on the generalized Fourier transform (GFT) is presented from a practical design point of view. The algorithms and data structures map closely to the relevant mathematical abstractions, which primarily are based upon representation theory for groups. Particular care has been taken in the design of the data layout of the performance-sensitive numerical data structures. The use of a vanilla strategy is advocated for the design of flexible mathematical software libraries: An efficient general-purpose routine should be supplied, to obtain a practical and useful system, while the possibility to extend the library and replace the default routine with a special-purpose - even more optimized - routine should be supported. Compared with a direct approach, the performance results show the superiority of the GFT-based approach for so-called dense equivariant systems. The GFT application is found to be well suited for parallelism.