Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
This paper presents the particular solutions for the polyharmonic and the products of Helmholtz partial differential operators with polyharmonic splines and monomials right-hand side. By the application of the Hrmander linear partial differential operator theory, many of the systems can be reduced to a single equation involving the polyharmonic or the product of Helmholtz differential operators. If the inhomogeneous right-hand side of these operators can be removed by the method of particular solutions, then boundary-type numerical methods, such as the boundary element method, the method of fundamental solutions, and the Trefftz method, can be applied to solve these differential equations.
particular solution boundary element method method of fundamental solutions trefftz method polyharmonic equation product of helmholtz equation dual reciprocity boundary element method radial basis function