TY - JOUR
T1 - Meshfree methods
T2 - Progress made after 20 years
AU - Chen, Jiun Shyan
AU - Hillman, Michael
AU - Chi, Sheng Wei
N1 - Publisher Copyright:
© 2017 American Society of Civil Engineers.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - In the past two decades, meshfree methods have emerged into a new class of computational methods with considerable success. In addition, a significant amount of progress has been made in addressing the major shortcomings that were present in these methods at the early stages of their development. For instance, essential boundary conditions are almost trivial to enforce by employing the techniques now available, and the need for high order quadrature has been circumvented with the development of advanced techniques, essentially eliminating the previously existing bottleneck of computational expense in meshfree methods. Given the proper treatment, nodal integration can be made accurate and free of spatial instability, making it possible to eliminate the need for a mesh entirely. Meshfree collocation methods have also undergone significant development, which also offer a truly meshfree solution. This paper gives an overview of many classes of meshfree methods and their applications, and several advances are described in detail.
AB - In the past two decades, meshfree methods have emerged into a new class of computational methods with considerable success. In addition, a significant amount of progress has been made in addressing the major shortcomings that were present in these methods at the early stages of their development. For instance, essential boundary conditions are almost trivial to enforce by employing the techniques now available, and the need for high order quadrature has been circumvented with the development of advanced techniques, essentially eliminating the previously existing bottleneck of computational expense in meshfree methods. Given the proper treatment, nodal integration can be made accurate and free of spatial instability, making it possible to eliminate the need for a mesh entirely. Meshfree collocation methods have also undergone significant development, which also offer a truly meshfree solution. This paper gives an overview of many classes of meshfree methods and their applications, and several advances are described in detail.
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U2 - 10.1061/(ASCE)EM.1943-7889.0001176
DO - 10.1061/(ASCE)EM.1943-7889.0001176
M3 - Article
AN - SCOPUS:85015925792
SN - 0733-9399
VL - 143
JO - Journal of Engineering Mechanics
JF - Journal of Engineering Mechanics
IS - 4
M1 - 04017001
ER -