On an economic prediction of the finer resolution level wavelet coefficients in electron structure calculations

TL;DR

This paper explores an economic prediction method for finer resolution wavelet coefficients in electron structure calculations, aiming to improve efficiency and accuracy in multi-resolution quantum simulations.

Contribution

It extends previous work by applying the prediction method to higher resolution levels and analyzes the energy and coefficient scaling behavior.

Findings

The prediction method can be effectively applied to higher resolution coefficients.

Predicted wave functions yield accurate energy expectation values.

Coefficient scaling behavior is characterized in the fine resolution limit.

Abstract

In wavelet based electron structure calculations introducing a new, finer resolution level is usually an expensive task, this is why often a two-level approximation is used with very fine starting resolution level. This process results in large matrices to calculate with and a large number of coefficients to be stored. In our previous work we have developed an adaptively refining solution scheme that determines the indices, where refined basis functions are to be included, and later a method for predicting the next, finer resolution coefficients in a very economic way. In the present contribution we would like to determine, whether the method can be applied for predicting not only the first, but also the other, higher resolution level coefficients. Also the energy expectation values of the predicted wave functions are studied, as well as the scaling behaviour of the coefficients in the fine resolution limit.