Multidimensional pseudo-spectral methods on lattice grids

[1]  Dominique Maisonneuve Recherche et Utilisation des “Bons Treillis.” Programmation et Résultats Numériques , 1972 .

[2]  G. Kedem,et al.  A table of good lattice points in three dimensions , 1974 .

[3]  M. Bourdeau,et al.  Tables of good lattices in four and five dimensions , 1985 .

[4]  I. Sloan,et al.  Lattice methods for multiple integration: theory, error analysis and examples , 1987 .

[5]  R. Kosloff,et al.  Optimal choice of grid points in multidimensional pseudospectral Fourier methods , 1988 .

[6]  J. N. Lyness An Introduction to Lattice Rules and their Generator Matrices , 1989 .

[7]  J. N. Lyness,et al.  An algorithm for finding optimal integration lattices of composite order , 1992 .

[8]  K. Hallatschek Fouriertransformation auf dünnen Gittern mit hierarchischen Basen , 1992 .

[9]  J. N. Lyness,et al.  Lattice rules by component scaling , 1993 .

[10]  I. Sloan Lattice Methods for Multiple Integration , 1994 .

[11]  Patrick Keast,et al.  Application of the Smith Normal Form to the Structure of Lattice Rules , 1995, SIAM J. Matrix Anal. Appl..

[12]  Ronald Cools,et al.  Minimal cubature formulae of trigonometric degree , 1996, Math. Comput..

[13]  Ronald Cools,et al.  Three- and four-dimensional K-optimal lattice rules of moderate trigonometric degree , 2001, Math. Comput..

[14]  Ian H. Sloan,et al.  Component-by-component construction of good lattice rules , 2002, Math. Comput..

[15]  Ronald Cools,et al.  Five- and six-dimensional lattice rules generated by structured matrices , 2003, J. Complex..

[16]  Tor Sørevik,et al.  Four-dimensional lattice rules generated by skew-circulant matrices , 2004, Math. Comput..

[17]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[18]  Åke Björck,et al.  The calculation of linear least squares problems , 2004, Acta Numerica.

[19]  Harry Yserentant,et al.  On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives , 2004, Numerische Mathematik.

[20]  Harry Yserentant,et al.  Sparse grid spaces for the numerical solution of the electronic Schrödinger equation , 2005, Numerische Mathematik.

[21]  Tor Sørevik,et al.  A search program for finding optimal integration lattices , 2005, Computing.

[22]  I. Sloan,et al.  Lattice Rules for Multivariate Approximation in the Worst Case Setting , 2006 .

[23]  H. Munthe-Kaas On group Fourier analysis and symmetry preserving discretizations of PDEs , 2006 .

[24]  Henryk Wozniakowski,et al.  Good Lattice Rules in Weighted Korobov Spaces with General Weights , 2006, Numerische Mathematik.

[25]  Dirk Nuyens,et al.  Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces , 2006, Math. Comput..

[26]  Tor Sørevik,et al.  Five-dimensional K-optimal lattice rules , 2006, Math. Comput..

[27]  M. Griebel,et al.  Sparse grids for the Schrödinger equation , 2007 .

[28]  Vasile Gradinaru,et al.  Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation , 2007, Computing.

[29]  Vasile Gradinaru,et al.  Strang Splitting for the Time-Dependent Schrödinger Equation on Sparse Grids , 2007, SIAM J. Numer. Anal..

[30]  Henryk Wozniakowski,et al.  Lattice rule algorithms for multivariate approximation in the average case setting , 2008, J. Complex..

[31]  M. Aurada,et al.  Convergence of adaptive BEM for some mixed boundary value problem , 2012, Applied numerical mathematics : transactions of IMACS.