A program for accurate solutions of two-electron atoms

Edvardsson, Sverker; Åberg, Daniel; Uddholm, P

doi:10.1016/j.cpc.2004.01.007

Cited by 7 publications

(6 citation statements)

References 26 publications

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“…As in Ref. [30], these values can be extrapolated to continuum (i.e., ^,0, -+ 00). This extrapolated value is listed in the last line.…”

Section: (25)mentioning

confidence: 99%

“…The total number of particles is thus given by N^. However, due to the symmetry of 5-states only a triangular domain needs to be applied [30]. The total number of panicles /V,", in this triangle, including the diagonal, is given by Niat = N{N -\-l)/2.…”

Section: (25)mentioning

confidence: 99%

“…Tr" d where in this case the pair function <1>^, (;'i, /•2) = í'no(''i i '"2) and 1/;-^ = l/n if i-| > r2, else !/;•> = l/;-2, see Ref, [30], The interaction functional of a certain particle / is written as Ti = [(4'(í)|//|*F(í)) -ff\\¡ii i.e,, for the present case we have for a particle p,y at position {r\i,r2¡) that:…”

Section: Dfpm For the Helium Atommentioning

confidence: 99%

“…The boundary conditions ^(-cx)) = T(oo) = 0 are applied for a sufficiently large domain ±L. The parameter w may simultaneously be obtained during the time iterations through dx (30) The normalization (4'(J:)|4'(X)) = 1 is also applied. The groundstate *Fo(.v) and co are then readily obtained by applying DFPM.…”

Section: Dfpm For a Nonlinear Schrödinger Equationmentioning

confidence: 99%

“…In the case of ARPACK [32], it is based on the implicitly restarted amoldi method (IRAM). The ARPACK CPU times in Table 2 was also verified by using a highly optimized computer code [30]. All tests were performed on a Linux computer with 1 GB primary memory and the CPU was an AMD Sempron 3600-I-2.0 GHz.…”

Section: (25)mentioning

confidence: 99%

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The Dynamical Functional Particle Method: An Approach for Boundary Value Problems

Edvardsson

Gulliksson

Persson

2012

Journal of Applied Mechanics

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The present work is concerned with new ideas of potential value for solving differential equations. First, a brief introduction to particle methods in mechanics is made by revisiting the vibrating string. The full case of'nonlinear motion is studied and the corresponding nonlinear differential equations are derived. It is suggested that the particle origin of these equations is of more general interest than usually considered. A novel possibility to develop particle methods for solving differential equations in a direct way is investigated. The dynamical functional particle method (DFPM) is developed as a solution method for boundary value problems. DFPM is based on the concept of an interaction functional as a dynamical force field acting on quasi particles. The approach is not limited to linear equations. We e.xemptify by applying DFPM to several linear Schrodinger type of problems as welt as a nonlinear case. It is seen that DFPM performs veiy well in comparison with some standard numerical libraries. In all cases, the convergence rates are exponential in time.

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“…As in Ref. [30], these values can be extrapolated to continuum (i.e., ^,0, -+ 00). This extrapolated value is listed in the last line.…”

Section: (25)mentioning

confidence: 99%

Section: (25)mentioning

confidence: 99%

Section: Dfpm For the Helium Atommentioning

confidence: 99%

Section: Dfpm For a Nonlinear Schrödinger Equationmentioning

confidence: 99%

Section: (25)mentioning

confidence: 99%

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The Dynamical Functional Particle Method: An Approach for Boundary Value Problems

Edvardsson

Gulliksson

Persson

2012

Journal of Applied Mechanics

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Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission

Rizea

Ledoux

Daele

et al. 2008

Computer Physics Communications

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A general spectral method for the numerical simulation of one-dimensional interacting fermions

Clason

Winckel

2012

Computer Physics Communications

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is work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. e approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An e cient M program for the assembly of the sti ness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. is program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e. g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the timedependent Schrödinger equation. * is work was supported by the Austrian Science Fund (FWF) under grant SFB F (SFB "Mathematical Optimization and Applications in Biomedical Sciences").

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A program for accurate solutions of two-electron atoms

Cited by 7 publications

References 26 publications

The Dynamical Functional Particle Method: An Approach for Boundary Value Problems

The Dynamical Functional Particle Method: An Approach for Boundary Value Problems

Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission

A general spectral method for the numerical simulation of one-dimensional interacting fermions

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