A note on the basis set approach in the constrained interpolation profile method

Takayuki Utsumi; Takashi Yabe; James Koga; Takayuki Aoki; Masatoshi Sekine; Youichi Ogata; Eiichi Matsunaga

doi:10.1016/j.jcp.2003.10.019

A note on the basis set approach in the constrained interpolation profile method

Takayuki Utsumi, Takashi Yabe, James Koga, Takayuki Aoki, Masatoshi Sekine, Youichi Ogata, Eiichi Matsunaga

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We propose a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. By adopting the higher-order derivatives of the master equations as constraints to generate a self-consistent subgrid profile, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schrödinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Journal of Computational Physics
Volume	196
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2003.10.019
State	Published - 1 May 2004
Externally published	Yes

Keywords

Basis sets
CIP method
CIP-BS method
Dirichlet1 boundary conditions
Generalized eigenvalue equation
Neuman boundary conditions
Time-dependent Schrödinger equation

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10.1016/j.jcp.2003.10.019

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title = "A note on the basis set approach in the constrained interpolation profile method",

abstract = "We propose a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. By adopting the higher-order derivatives of the master equations as constraints to generate a self-consistent subgrid profile, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schr{\"o}dinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates.",

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AU - Utsumi, Takayuki

AU - Yabe, Takashi

AU - Koga, James

AU - Aoki, Takayuki

AU - Sekine, Masatoshi

AU - Ogata, Youichi

AU - Matsunaga, Eiichi

PY - 2004/5/1

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AB - We propose a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. By adopting the higher-order derivatives of the master equations as constraints to generate a self-consistent subgrid profile, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schrödinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates.

KW - Basis sets

KW - CIP method

KW - CIP-BS method

KW - Dirichlet1 boundary conditions

KW - Generalized eigenvalue equation

KW - Neuman boundary conditions

KW - Time-dependent Schrödinger equation

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A note on the basis set approach in the constrained interpolation profile method

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Keywords

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