Meshfree Methods: Progress Made after 20 Years
Publication: Journal of Engineering Mechanics
Volume 143, Issue 4
Abstract
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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Acknowledgments
The support of this work by the U.S. Army Engineer Research and Development Center under contract W15QKN-12-9-1006 to University of California, San Diego, and the U.S. Army Corps of Engineers SERDP Program under contract W912HQ-16-P-0002 to the University of Illinois at Chicago is greatly acknowledged.
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Information
Published In
Journal of Engineering Mechanics
Volume 143 • Issue 4 • April 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: May 16, 2016
Accepted: Aug 9, 2016
Published ahead of print: Jan 20, 2017
Published online: Jan 23, 2017
Published in print: Apr 1, 2017
Discussion open until: Jun 23, 2017
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