Sentence examples for boundary integral representation is from inspiring English sources

Specifically, a boundary-integral equation allows one to evaluate the potential distribution around the body; after having obtained this, the corresponding boundary integral representation is used to evaluate the potential and hence the pressure at any point in the field.

The approach to use hybrid FEM and boundary integral representations is not new and our developed model was influenced by such works as Zhou et al.

Lemma 1 Assume that the function q ( x, y ) solves the modified Helmholtz equation (1.1) in the upper half z-plane Ω, and that it satisfies the Dirichlet boundary conditions (1.2), then the integral representation is valid: q = β 2 π ∫ 0 ∞ e i β ( k z − z ¯ k ) ( k + 1 k ) D ( k ) d k k, (2.1).

Lemma 2 Assume that the function q ( x, y ) solves the modified Helmholtz equation (1.1) in the upper half z-plane Ω, and that it satisfies the Dirichlet boundary conditions (1.3), then the integral representation is valid: q ( x, y ) = D 2 π i ∫ l e i β ( k z − z ¯ k ) [ e i β a ( 1 k − k ) − e i β b ( 1 k − k ) ] k 2 + 1 k ( k 2 − 1 ) d k, (2.3).

In the dual BEM, the singular integral representation is written along the boundary elements positioned at one crack surface, whereas the hyper-singular integral representation is applied along the opposite crack surface.

The singular integral representation is applied along the entire external boundaries.

The singular integral representation is applied into the discretization of one crack boundary in such BEM approach.

A new algorithm, derived from an integral representation, is proposed for efficient calculations.

Another integral representation is the following.

whose integral representation is given by (2.6).

This restatement of the original problem is then amenable to boundary integral representation and boundary element solution.