Multiresolution Analysis for Compactly Supported Interpolating Tensor Product Wavelets (long version)

Höynälänmaa, Tommi

doi:10.48550/arxiv.1005.3371

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2021

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“…Compactly supported interpolating wavelets have been generalized to multiple dimensions in Refs. [5], [6], and [7]. Fukuda, Kinoshita, and Suzuki [8] have studied unconditional convergence of wavelet expansions.…”

Section: Introductionmentioning

confidence: 99%

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Electronic structure calculations with interpolating tensor product wavelet basis

Höynälänmaa¹,

Rantala²

2021

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We introduce a basis set consisting of three-dimensional Deslauriers-Dubuc wavelets and numerically solve the Schrödinger equations of hydrogen atom, helium atom, hydrogen molecule ion, hydrogen molecule, and lithium hydride molecule with Hartree-Fock and DFT methods. We also compute the 2s and 2p excited states of hydrogen. The Coulomb singularity at the nucleus is handled by using a pseudopotential. Results are compared with those of CCCBDB and BigDFT. The eigenvalue problem is solved with Arnoldi and Lanczos methods, and the Poisson equation with GMRES and CGNR methods. The various matrix elements are computed using the biorthogonality relations of the interpolating wavelets.

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Section: Introductionmentioning

confidence: 99%

“…The notation for wavelet basis functions and filters is similar to Refs. [5] and [6]. The computation of matrix elements is similar to Ref.…”

Section: Introductionmentioning

confidence: 99%

Electronic structure calculations with interpolating tensor product wavelet basis

Höynälänmaa¹,

Rantala²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Multiresolution Analysis for Compactly Supported Interpolating Tensor Product Wavelets (long version)

Cited by 1 publication

References 0 publications

Electronic structure calculations with interpolating tensor product wavelet basis

Electronic structure calculations with interpolating tensor product wavelet basis

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