AUTHOR=Gao Xiao-Wei , Jiang Wei-Wu , Xu Xiang-Bo , Liu Hua-Yu , Yang Kai , Lv Jun , Cui Miao 

TITLE=Overview of Advanced Numerical Methods Classified by Operation Dimensions

JOURNAL=Aerospace Research Communications

VOLUME=Volume 1 - 2023

YEAR=2023

URL=https://www.frontierspartnerships.org/journals/aerospace-research-communications/articles/10.3389/arc.2023.11522

DOI=10.3389/arc.2023.11522

ISSN=2813-6209

ABSTRACT=In this paper, the progresses of the frequently used advanced numerical methods are presented.According to the discretization manner and manipulation dimensionality, these methods can be classified into four categories: volume-, surface-, line-, and point-operations based methods.The volume-operation based methods described in this paper include the finite element method and element differential method; the surface-operation based methods consist of the boundary element method and finite volume method; the line-operation based methods cover the finite difference method and finite line method; and the point-operation based methods mainly include the mesh free method and free element method. These methods have their own distinctive advantages in some specific disciplines. For example, the finite element method is the dominant method in solid mechanics, the finite volume method is extensively used in fluid mechanics, the boundary element method is more accurate and easier to use than other methods in fracture mechanics and infinite media, the mesh free method is more flexible to simulate the varying and distorted geometries, and the newly developed free element and finite line methods are suitable for solving multi-physics coupling problems. This paper will give a detailed conceptual description and typical applications of these promising methods, focused on the developments in recent years.