Investigation of the three-dimensional Helmholtz equation for a wedge using the block element method

For boundary-value problems, the Helmholtz equations in wedge-shaped domains, it is shown that in packed block elements corresponding to the same boundary-value problem can be combined taking into account the type of boundary conditions, also forming a packed block element. The result is verified using another method. It is shown that in the presence of corner points in the domain in which the boundary-value problem is considered, combining block elements does not involve additional complications. It is found that since the solutions of some boundary-value problems in continuum mechanics and physics can be represented as a combination of solutions of boundary-value problems of the Helmholtz equation, this approach can be used to study more complex boundary-value problems and design materials with mosaic structure.