MRA and low-separation rank approximation with applications to quantum electronics structures computations

We 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 represen...

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Bibliographic Details
Published in:Journal of physics. Conference series 2005-01, Vol.16 (1), p.461-465
Main Authors: Fann, G I, Harrison, R J, Beylkin, G
Format: Article
Language:English
Subjects:
Approximation
Computational chemistry
Differential equations
Divergence
Fluid dynamics
Integral transforms
Mathematical analysis
Numerical methods
Operators (mathematics)
Physics
Poisson equation
Quantum chemistry
Quantum electronics
Representations
Schrodinger equation
Separation
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Summary:We 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).
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/16/1/062