The boundary element method is a numerical method for solving a boundary value problem by reformulating its partial differential equation as an integral equation on the boundary of the domain. The boundary is partitioned into elements, and the boundary data or unknown boundary values are approximated on those elements.
Because only the boundary is discretized, a problem in 
dimensions produces a mesh of dimension 
. The resulting matrices are generally dense, since the integral kernel couples distant boundary elements.
The method is particularly natural when a fundamental
solution of the differential operator
is known.
