This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being only one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry.
Introduction.- Dual-horizon Peridynamics.- First order nonlocal
operator method.- Nonlocal operator method for waveguides.
Timon Rabczuk is chaired professor of Computational Mechanics at the Bauhaus Universität Weimar, Germany. He has published more than 600 SCI papers, mainly about computational methods for the solution of partial differential equations. He is the editor-in-chief of CMC-Computers, Materials and Continua, an associated editor of International Journal of Impact Engineering and Applied Physics A, and an executive editor of FSCE-Frontiers of Structural and Civil Engineering. He was listed as one of ISI Highly Cited Researchers in Computer Science and Engineering from 2014 up to now.
Huilong Ren is currently a research fellow at the Institut für Photonik of Leibniz Universität Hannover, Germany. He obtained his Ph.D. degree by the thesis Dual-horizon peridynamics and nonlocal operator method at Institut für Strukturmechanik (ISM) of Bauhaus-Universität Weimar. He is interested in nonlocality-based methods (peridynamics, nonlocal operator method), numerical methods (FEM, IGA, meshless methods), and automatic code generation for numerical solutions of partial differential equations.
