Sentence examples for layer potentials are from inspiring English sources

Then the layer potentials are regularized and discretized using standard quadratures.

By various examples, we show that all our estimates on layer potentials are sharp.

Layer potentials are evaluated to second-order accuracy, in times which exhibit considerable speedups even over a reasonably sophisticated direct calculation.

In this paper elementary boundary integral equations for the Helmholtz equation in the exterior domain, based on Green's formula or through representation of the solution by layer potentials, are considered.

The abstract single and double layer potentials are defined by begin{aligned} mathcal {S}:{left{ begin{array}{ll} mathcal {H}rightarrow mathfrak {H}, varphi mapsto mathcal {G}Upsilon _0^* varphi, end{array}right.

Accurate evaluation of layer potentials is crucial when boundary integral equation methods are used to solve partial differential equations.

The equations of the form (1) were first considered by SN Kharin: the asymptotics of integrals of the double layer potentials were studied, and approximate solutions of some applied problems were constructed [6, 7].

To account for the effect of the walls the Green's functions are modified and all terms for the double-layer potential are derived.

Meanwhile, the singularity of the double-layer potential is eliminated by recasting the principal-value integral of the double-layer potential when the influence coefficient matrix is calculated.

The right-hand side f = (1 / 2 − K ′ ) (∂ n u ) ∈ H − 1 / 2 with Γ = ∂ Ω and K ′ the adjoint double layer-potential is chosen such that the hyper-singular integral equation (8) is equivalent to some Neumann problem (11) with f = 0.

In borax buffer pH 9.2 no stable image is obtained during the growth of the Cu2O films with d>1 nm whereas the images of the duplex layer formed at higher potentials are stable again.