The research focus and achievements of Distinguished Professor Cheng-Yu Ku are summarized as follows:<\/h1>\nApplication of Numerical Analysis in Geotechnical Engineering<\/h3>\nMeshless Methods<\/h4>\n
Meshless Methods<\/h4>\n
Research Focus<\/strong>: Meshless methods are commonly used to solve various partial differential equations (PDEs), particularly for developing numerical solutions for space and time-related problems, such as heat conduction, subsurface flow, and diffusion problems. The papers explore various meshless methods, such as the Trefftz Method, Radial Basis Function (RBF) method, and Method of Fundamental Solutions (MFS), applied to heat conduction, groundwater flow, and free surface problems. For instance, meshless methods were applied to heat conduction problems (Papers 45, 53, 55) and inverse heat conduction problems (Papers 42, 43). The MFS method was used to solve 3D nonlinear free surface flows (Paper 40) and free surface problems in layered soils (Paper 51). Applications<\/strong>: Soil flow, groundwater flow, inverse problems in diffusion processes, and flow simulations in heterogeneous multilayer materials. For example, the Collocation Trefftz Method was applied to groundwater tidal effect analysis (Paper 21), and the meshless RBF method was used to solve inverse heat conduction problems (Paper 24).<\/p>\n Nonlinear and moving boundary problems are also explored in several of Professor Ku’s studies, particularly in modeling flows in heterogeneous materials (Papers 41, 44). These studies use meshless methods, highlighting their efficiency and adaptability for solving complex problems in heterogeneous systems.<\/p>\n The Trefftz Method is a key numerical method explored in many studies, often combined with other techniques such as MFS (Paper 44) and multi-scale Trefftz methods (Papers 55, 58). These hybrid methods are effectively applied to complex physical problems, including heat conduction and groundwater flow.<\/p>\n Meshless methods and RBF techniques are applied to solve problems such as elliptic boundary value problems, inverse problems in transport and diffusion processes, and groundwater flow in multilayered soils. For example, Ku and Liu (2023) applied the meshless RBF method to solve groundwater problems, and Liu et al. (2024) proposed using RBF to solve unsaturated flow problems.<\/p>\n Research Focus<\/strong>: Improvements and applications of the dynamic Newton method and homotopy methods to solve ill-posed systems and nonlinear problems in numerical analysis, especially for boundary value problems. The studies include the optimization of homotopy methods and adaptive step-size numerical solvers. Ku et al. (2012-2011) proposed a dynamic Newton method applied to solve ill-posed systems. Ku et al. (2010) used the Newton-homotopy continuation method to solve nonlinear algebraic equations. Applications<\/strong>: Meshless methods applied to groundwater flow problems.<\/p>\n Research Focus<\/strong>: Investigating inverse techniques to solve problems in diffusion and heat conduction. These methods are primarily applied to model and reconstruct data for phenomena such as heat transfer, diffusion processes, and geological compression. Many studies focus on solving inverse problems, especially in transport and diffusion processes, using techniques such as RBF, space-time polynomials, and multi-source meshless methods. These provide innovative numerical methods for groundwater flow and heat transfer problems. For example, Xiao et al. (2022) used RBF and polynomials to solve the inverse problem for steady-state convection-diffusion equations. Inverse problems (Inverse Problems) and boundary value problems (Boundary Value Problems) are frequently discussed. Inverse problems often involve reconstructing unknown physical quantities from limited observational data, such as inverse heat conduction problems (Papers 42, 43) solved using space-time meshless methods. The inverse Cauchy problem (Paper 56) was solved using MFS and a scalar homotopy algorithm with exponential convergence.<\/p>\n Research Focus<\/strong>: Numerical simulations of the bearing characteristics and effective soil stress of offshore wind turbine foundations. Applications<\/strong>: Structural safety and stability assessment of offshore wind turbines in Taiwan.<\/p>\n Research Focus<\/strong>: Applying techniques such as random forests and neural networks for soil classification, ground subsidence, fire prediction, and flood susceptibility assessment. Applications<\/strong>: Soil classification, ground subsidence, fire prediction, and risk assessment of flooding and slope stability.<\/p>\n Research Focus<\/strong>: Applying numerical methods and machine learning techniques to simulate triggering conditions for natural disasters such as rainfall, slope instability, and fires. Studies discuss how deep neural networks (DNN), random forests, and other machine learning techniques are used to address complex engineering and environmental problems like soil classification, fire prediction, and ground subsidence. These studies demonstrate the efficiency of machine learning in handling large datasets and nonlinear problems. For example, Liu et al. (2024) applied random forest techniques for soil classification, while Ku et al. (2024) used deep learning to predict fire occurrence. Research Focus<\/strong>: Investigating the causes and simulation of geological disasters, with a particular focus on geological risks (e.g., rockfall and debris flow) in Central Taiwan. These studies aim to develop simulation techniques to enhance prediction and risk management. Ku et al. (2014) explored the causes of geological disasters in Central Taiwan, while Ku (2014) used 3D numerical modeling for rockfall risk assessment. Hsu et al. (2010) applied simulation techniques to delineate debris flow hazard zones. Research Focus<\/strong>: The mechanical behavior of rock fractures and numerical simulation of crack propagation, particularly in anisotropic rock materials. These studies improve understanding of crack propagation in rocks and provide a basis for engineering design. Relevant literature: Ke et al. (2009) used the boundary element method to simulate crack propagation paths in anisotropic rocks. The development of equivalent continuum and discrete models was applied to the mechanical simulation of fractured rock masses. This research provides a new framework for addressing multi-scale mechanical behavior in rock masses. Lin & Ku (2017) focused on multi-scale modeling of fractured rock masses.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\nNonlinear and Moving Boundary Problems<\/h3>\n
Trefftz Method and Hybrid Meshless Methods<\/h3>\n
Radial Basis Function (RBF) Method<\/h3>\n
Homotopy Method and Numerical Solving Techniques<\/h3>\n
Inverse Problems<\/h3>\n
Offshore Wind Turbine Foundation Numerical Analysis<\/h3>\n
Artificial Intelligence in Geotechnical Engineering<\/h3>\n
Application of Machine Learning in Disaster Prevention and Mitigation<\/h4>\n
Machine Learning Integrated with GIS for Disaster Analysis<\/h4>\n
\nApplications<\/strong>: Fire and slope risk prediction studies in Taiwan, along with spatial analysis and GIS technology applications. Research explores the relationship between ground subsidence and hydrological processes, particularly using mathematical models and artificial neural networks to simulate and predict ground subsidence issues caused by groundwater extraction. These studies are applied to areas such as Yunlin County and the Zhuoshui River Delta in Taiwan. For instance, Ku et al. (2022) studied the spatial variability of ground subsidence and groundwater extraction in the Zhuoshui River Delta, using GIS for simulation.<\/p>\nRock Mechanics and Regional Geological Disasters<\/h3>\n