Multilevel Quasi-Interpolation on Chebyshev Sparse Grids

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2024-07-18 DOI:10.3390/computation12070149

Faisal Alsharif

引用次数: 0

Abstract

This paper investigates the potential of utilising multilevel quasi-interpolation techniques on Chebyshev sparse grids for complex numerical computations. The paper starts by laying down the motivations for choosing Chebyshev sparse grids and quasi-interpolation methods with Gaussian kernels. It delves into the practical aspects of implementing these techniques. Various numerical experiments are performed to evaluate the efficiency and limitations of the multilevel quasi-sparse interpolation methods with dimensions two dimension and three dimension. The work ultimately aims to provide a comprehensive understanding of the computational efficiency and accuracy achievable through this approach, comparing its performance with traditional methods.

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切比雪夫稀疏网格上的多级准内插法

本文研究了在切比雪夫稀疏网格上利用多级准插值技术进行复杂数值计算的潜力。论文首先阐述了选择切比雪夫稀疏网格和高斯核准插值方法的动机。论文深入探讨了实施这些技术的实际问题。通过各种数值实验来评估二维和三维多级准稀疏插值方法的效率和局限性。这项工作的最终目的是全面了解这种方法的计算效率和精确度，并将其性能与传统方法进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.