Operating system

Machine learning

Physics

Basis (linear algebra)

Mathematical analysis

Finite element method

Singularity

Boundary value problem

Vibration

Collocation method

Acoustics

Geometry

Space (punctuation)

Mathematics

Domain (mathematical analysis)

Computer science

Method of fundamental solutions

Ordinary differential equation

Boundary (topology)

Boundary element method

Discretization

Differential equation

Collocation (remote sensing)

Singular boundary method

Half-space

Thermodynamics

Applied Mathematical Modelling

In this study, the singular boundary method (SBM) is extended to simulate the dynamic response of the half-space saturated soils in the frequency domain. The SBM employs the fundamental solutions of the governing equations as basis functions. Thus, the domain of interest can be discretized into several source points merely on the boundary, which makes the SBM available to describe the wave propagation in the half-space soil medium. The source singularity caused by the coincidence of collocation points and source points is overcome by the origin intensity factors (OIFs), which is given for the unclosed boundary. Two numerical examples exhibit the feasibility and advantages of the proposed SBM.

A half-space singular boundary method for predicting ground-borne vibrations