WeChat Mini Program
Old Version Features

Numerical Analysis of the Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation.

APPLIED MATHEMATICS LETTERS(2023)

Shandong Normal Univ

Cited 3|Views11
Abstract
This paper gives a numerical analysis of the optimal 9-point finite difference format proposed in Chen et al. (2013) for the two-dimensional Helmholtz equation with constant wavenumber. The basic idea of the proof is to transform the 2D error equation into a series of 1D difference equations. For each 1D difference equation, the existence, uniqueness, and stability of its solution can be proved. Based on the results of the one-dimensional problems, the uniqueness and convergence of the solution of the optimal 9-point scheme are derived. Numerical experiments confirm that the optimal 9-point difference scheme has second-order convergence.(c) 2023 Elsevier Ltd. All rights reserved.
More
Translated text
Key words
Helmholtz equation,Finite difference method,Convergence analysis
求助PDF
上传PDF
Bibtex
AI Read Science
AI Summary
AI Summary is the key point extracted automatically understanding the full text of the paper, including the background, methods, results, conclusions, icons and other key content, so that you can get the outline of the paper at a glance.
Example
Background
Key content
Introduction
Methods
Results
Related work
Fund
Key content
  • Pretraining has recently greatly promoted the development of natural language processing (NLP)
  • We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
  • We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
  • The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
  • Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance
Upload PDF to Generate Summary
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Data Disclaimer
The page data are from open Internet sources, cooperative publishers and automatic analysis results through AI technology. We do not make any commitments and guarantees for the validity, accuracy, correctness, reliability, completeness and timeliness of the page data. If you have any questions, please contact us by email: report@aminer.cn
Chat Paper
Summary is being generated by the instructions you defined