Trefftz method, method of fundamental solutions, and method of particular solutions belong to a class of numerical methods that utilize special solutions of partial differential equation, such as general solutions, fundamental solutions, and particular solutions, as basis functions. The purpose is to reduce the discretization dimension of the numerical solution system from that of the domain to that of the boundary. These, and other similar methods, can be called the boundary collocation methods. These methods are generally “meshless”, that is, without the element for integration, which is required by methods such the finite element method. Although these boundary methods have a long history of development, there seems to be a recent resurgence in their popularity. By this joint conference, we hope to bring together the communities of applied mathematicians and engineering researchers to share information and to seek collaboration in the development and application of these methods.