31,497 research outputs found
Tensor factorizations of local second-order M{\o}ller Plesset theory
Efficient electronic structure methods can be built around efficient tensor
representations of the wavefunction. Here we describe a general view of tensor
factorization for the compact representation of electronic wavefunctions. We
use these ideas to construct low-complexity representations of the doubles
amplitudes in local second order M{\o}ller-Plesset perturbation theory. We
introduce two approximations - the direct orbital specific virtual
approximation and the full orbital specific virtual approximation. In these
approximations, each occupied orbital is associated with a small set of
correlating virtual orbitals. Conceptually, the representation lies between the
projected atomic orbital representation in Pulay-Saeb{\o} local correlation
theories and pair natural orbital correlation theories. We have tested the
orbital specific virtual approximations on a variety of systems and properties
including total energies, reaction energies, and potential energy curves.
Compared to the Pulay-Saeb{\o} ansatz, we find that these approximations
exhibit favourable accuracy and computational times, while yielding smooth
potential energy curves
Rigorous Simulations of 3D Patterns on Extreme Ultraviolet Lithography Masks
Simulations of light scattering off an extreme ultraviolet lithography mask
with a 2D-periodic absorber pattern are presented. In a detailed convergence
study it is shown that accurate results can be attained for relatively large 3D
computational domains and in the presence of sidewall-angles and
corner-roundings.Comment: SPIE Europe Optical Metrology, Conference Proceeding
Rigorous Simulation of 3D Masks
We perform 3D lithography simulations by using a finite-element solver. To
proof applicability to real 3D problems we investigate DUV light propagation
through a structure of size 9 microns times 4 microns times 65 nm. On this
relatively large computational domain we perform rigorous computations (No
Hopkins) taking into account a grid of 11 times 21 source points with two
polarization directions each. We obtain well converged results with an accuracy
of the diffraction orders of about one percent. The results compare well to
experimental aerial imaging results. We further investigate the convergence of
3D solutions towards quasi-exact results obtained with different methods.Comment: 8 pages, 5 figures (see original publication for images with a better
resolution
A literature survey of low-rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as
a new tool in scientific computing to address large-scale linear and
multilinear algebra problems, which would be intractable by classical
techniques. This survey attempts to give a literature overview of current
developments in this area, with an emphasis on function-related tensors
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