G I Fann et al 2005 J. Phys.: Conf. Ser. 16 461 doi:10.1088/1742-6596/16/1/062
MRA and low-separation rank approximation with applications to quantum electronics structures computations
G I Fann1, R J Harrison2 and G Beylkin3
Show affiliationsWe describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving problems in computational chemistry (the so-called multiresolution quantum chemistry).
Using low separation rank representations of functions and operators and representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation and the Schrodinger equation, the projector on the divergence free functions, provide important examples with a wide range of applications in computational chemistry, computational electromagnetic and fluid dynamics.
We have implemented these ideas that include adaptive representations of operators and functions in the multiwavelet basis and low separation rank approximation of operators and functions. These methods have been implemented into a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS).
- PACS
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03.67.Lx Quantum computation architectures and implementations
02.60.Lj Ordinary and partial differential equations; boundary value problems
03.65.Ge Solutions of wave equations: bound states
- MSC
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35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 1 (2005)
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MRA and low-separation rank approximation with applications to quantum electronics structures computations
G I Fann et al 2005 J. Phys.: Conf. Ser. 16 461
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Dissipative particle dynamics with energy conservation
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Mesoscopic two-phase model for describing apparent slip in micro-channel flows
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A maximum a posteriori reconstruction method for plasma tomography
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C Armendáriz-Picón and Vikram Duvvuri 2004 Class. Quantum Grav. 21 2011
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V Voss 1930 J. Sci. Instrum. 7 389
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Direct thermal dose control of constrained focused ultrasound treatments: phantom and in vivo evaluation
Dhiraj Arora et al 2005 Phys. Med. Biol. 50 1919
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The SI unit of mass
Richard Davis 2003 Metrologia 40 299
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Magnetic properties of weights, their measurements and magnetic interactions between weights and balances
R Davis and M Gläser 2003 Metrologia 40 339
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