The paper by Graeme Fairweather and Andreas Karageorghis provides an overview of the development and applications of the Method of Fundamental Solutions (MFS) over the past three decades. MFS is a numerical technique for solving elliptic boundary value problems, similar to the Boundary Element Method (BEM) but with some advantages. The method uses fundamental solutions of the differential equation, which are functions that satisfy the equation when integrated over a domain. The approximate solution is expressed as a linear combination of these fundamental solutions, with singularities placed outside the domain. The locations of these singularities are either preassigned or determined through a least squares fit to satisfy the boundary conditions. The paper also discusses extensions of MFS to non-trivial problems and inhomogeneous problems, and highlights its applications in various fields such as elastostatics, potential theory, and inviscid flow around bodies.The paper by Graeme Fairweather and Andreas Karageorghis provides an overview of the development and applications of the Method of Fundamental Solutions (MFS) over the past three decades. MFS is a numerical technique for solving elliptic boundary value problems, similar to the Boundary Element Method (BEM) but with some advantages. The method uses fundamental solutions of the differential equation, which are functions that satisfy the equation when integrated over a domain. The approximate solution is expressed as a linear combination of these fundamental solutions, with singularities placed outside the domain. The locations of these singularities are either preassigned or determined through a least squares fit to satisfy the boundary conditions. The paper also discusses extensions of MFS to non-trivial problems and inhomogeneous problems, and highlights its applications in various fields such as elastostatics, potential theory, and inviscid flow around bodies.