INVESTIGATION OF THE THREE-DIMENSIONAL HELMHOLTZ EQUATION FOR A WEDGE USING THE BLOCK ELEMENT METHOD

摘要

For boundary-value problems for the Helmholtz equation in wedge-shaped domains, it has been shown that packed block elements corresponding to the same boundary-value problem can be combined taking into account the type of boundary conditions also to form a packed block element. This result has been verified using another method. It has been shown that in the presence of corner points in the domain in which the boundary-value problem is considered, there are no additional difficulties in combining block elements. It has been 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 for the Helmholtz equation, this approach can be used to study more complex boundary-value problems and design materials with a mosaic structure.