Fast Method of Particular Solutions for Solving Partial Differential Equations

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the large-scale problems are some of the challenges which need to overcome. In this dissertation, we have used several techniques to overcome such challenges. The closed-form particular solutions for the Matérn and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matérn and Gaussian RBFs for the Laplace and biharmonic operators in 2D and 3D. These derived particular solutions play an important role in solving inhomogeneous problems using MPS and boundary methods such as boundary element methods or boundary meshless methods. In this dissertation, to select the good shape parameter, various existing variable shape parameter strategies and some well-known global optimization algorithms have also been applied. These good shape parameters provide high accurate solutions in many RBFs collocation methods. Fast method of particular solutions (FMPS) has been developed for the simulation of the large-scale problems. FMPS is based on the global version of the MPS. In this method, partial differential equations are discretized by the usual MPS and the determination of the unknown coefficients is accelerated using a fast technique. Numerical results confirm the efficiency of the proposed technique for the PDEs with a large number of computational points in both two and three dimensions. We have also solved the time fractional diffusion equations by using MPS and FMPS

Meshless Modeling of Flow Dispersion and Progressive Piping in Poroelastic Levees

Performance data on earth dams and levees continue to indicate that piping is one of the major causes of failure. Current criteria for prevention of piping in earth dams and levees have remained largely empirical. This paper aims at developing a mechanistic understanding of the conditions necessary to prevent piping and to enhance the likelihood of self-healing of cracks in levees subjected to hydrodynamic loading from astronomical and meteorological (including hurricane storm surge-induced) forces. Systematic experimental investigations are performed to evaluate erosion in finite-length cracks as a result of transient hydrodynamic loading. Here, a novel application of the localized collocation meshless method (LCMM) to the hydrodynamic and poroelastic problem is introduced to arrive at high-fidelity field solutions. Results from the LCMM numerical simulations are designed to be used as an input, along with the soil and erosion parameters obtained experimentally, to characterize progressive piping

Numerical Simulation of Soil Water Movement under Subsurface Irrigation

By constructing a radial basis function collocation method combined with a difference method, a two-dimensional mathematical model with boundary conditions of soil water movement under irrigation is proposed. The nonlinear term is dealt with a difference method and the equation is solved using an implicit scheme. In addition, the existence and uniqueness of the solution to the soil water movement equation are proven. Numerical results show that the proposed method has high precision and is easier to use than traditional methods. Moreover, the selection of parameter c plays an important role in guaranteeing calculation precision. It lays the foundation for the numerical solutions to high-dimensional soil water movement equations

Coastal Geohazard and Offshore Geotechnics

With rapid developments being made in the exploration of marine resources, coastal geohazard and offshore geotechnics have attracted a great deal of attention from coastal geotechnical engineers, with significant progress being made in recent years. Due to the complicated nature of marine environmnets, there are numerous natural marine geohazard preset throughout the world’s marine areas, e.g., the South China Sea. In addition, damage to offshore infrastructure (e.g., monopiles, bridge piers, etc.) and their supporting installations (pipelines, power transmission cables, etc.) has occurred in the last decades. A better understanding of the fundamental mechanisms and soil behavior of the seabed in marine environments will help engineers in the design and planning processes of coastal geotechnical engineering projects. The purpose of this book is to present the recent advances made in the field of coastal geohazards and offshore geotechnics. The book will provide researchers with information reagrding the recent developments in the field, and possible future developments. The book is composed of eighteen papers, covering three main themes: (1) the mechanisms of fluid–seabed interactions and the instability associated with seabeds when they are under dynamic loading (papers 1–5); (2) evaluation of the stability of marine infrastructure, including pipelines (papers 6–8), piled foundation and bridge piers (papers 9–12), submarine tunnels (paper 13), and other supported foundations (paper 14); and (3) coastal geohazards, including submarine landslides and slope stability (papers 15–16) and other geohazard issues (papers 17–18). The editors hope that this book will functoin as a guide for researchers, scientists, and scholars, as well as practitioners of coastal and offshore engineering

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference