G I Fann et al 2007 J. Phys.: Conf. Ser. 78 012018 doi:10.1088/1742-6596/78/1/012018
G I Fann1, R J Harrison2, G Beylkin3, J Jia1, R Hartman-Baker1, W A Shelton4 and S Sugiki4
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 quantum chemistry and nuclear physics problems based on Density Functional Theory (DFT). Using low separation rank representations of functions and operators in conjunction with representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation, the Schrodinger equation, and the projector on the divergence free functions provide important examples with a wide range of applications in computational chemistry, nuclear physics, computational electromagnetic and fluid dynamics.
We have implemented this approach along with adaptive representations of operators and functions in the multiwavelet basis and low separation rank (LSR) approximation of operators and functions. These methods have been realized and implemented in a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS).
82.20.-w Chemical kinetics and dynamics
02.60.Nm Integral and integrodifferential equations
03.65.Ge Solutions of wave equations: bound states
07.05.Bx Computer systems: hardware, operating systems, computer languages, and utilities
Instrumentation and measurement
Issue 1 (2007)
G I Fann et al 2007 J. Phys.: Conf. Ser. 78 012018
L Robertsson et al 2005 Metrologia 42 04002
I A Ivanov and A S Kheifets 2008 J. Phys. B: At. Mol. Opt. Phys. 41 095002
F Krząkała and L Zdeborová 2008 J. Phys.: Conf. Ser. 95 012012
F M Hoffman et al 2007 J. Phys.: Conf. Ser. 78 012026
T Osipov et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 091001
Allan Adams et al JHEP10(2001)029
Naoki Sasakura JHEP12(2004)009
Juan Garcia-Bellido and Troels Haugbølle JCAP04(2008)003
Joële Viallon et al 2008 Metrologia 45 08005