This paper presents an overview of the singular boundary method (SBM) and its various
engineering applications. The basic concepts of the singular boundary method are first …

During the construction of mass concrete structures, the embedded water pipe cooling
system is regarded as a standard tool to control temperature. Prediction of thermal field in …

We present a new localized boundary knot method (LBKM) for the solution of large-scale
partial differential equations based on the non-singular general solutions. The proposed …

In this paper, a localized space-time method of fundamental solutions (LSTMFS) is proposed
to solve the diffusion and convection-diffusion problems. The proposed LSTMFS only …

A new space–time meshless method is proposed for solving the nonhomogeneous
convection–diffusion equations with variable coefficients. From the perspective of the space …

Gas convection transport in porous media plays a pivotal role in various engineering and
natural systems, such as oil and gas reservoir behavior and carbon dioxide sequestration. In …

In this paper, the generalized finite difference method (GFDM) combined with the Newton–
Raphson method is proposed to accurately and efficiently simulate the steady-state double …

The efficient numerical method for simulating unsteady convection–diffusion problems is a
crucial research topic in the field of numerical heat transfer. However, the state in which …

This paper presents a simple empirical formula of origin intensity factor in singular boundary
method (SBM) solution of Hausdorff derivative Laplace equations. The SBM with the …

In this paper, a novel spatial-temporal radial Trefftz collocation method (STRTCM) is
proposed to solve 2D and 3D backward heat conduction equations with time-dependent …