On the numerical solution of the direct scattering problem for an open sound-hard arc

Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

“…Based on the identified structure, we determined why inaccurate locations/shapes of cracks were appeared and developed a simple algorithm for finding the exact locations/shapes of cracks by generating small or extended crack on the basis of the tendency of the inaccurate result. Our current research considers cracks with Dirichlet boundary conditions; we plan to extend our research to cracks with Neumann boundary conditions (soundhard arc in inverse acoustic scattering problem), refer to [11,12]. Furthermore, motivated by [2,7,10,18,20], extending our research to the limited-view inverse scattering problem will be an interesting research topic.…”

An integral equation method for a boundary value problem in superconductivity

“…Now we can read o regularity, form and asymptotics by standard arguments (cf. Reference [3,Chapters 6,7]). Furthermore, using the jump relations for the normal derivative of the double-layer potential, we see that the Neumann boundary conditions (4) are already fulÿlled by construction.…”

“…Substituting A m1; m2; n for in the collocation method formulation yields a fully discrete approximation scheme that can be easily implemented. Following Reference [7], we ÿnally observe that we can reduce the linear system that originates from the integrals over , by half since we seek solutions in even functions on T n;e , i.e. the densitỹ ' and the interpolation points are symmetric with respect to .…”

Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency

“…Then, the retrieval of the arc itself is carried out via a Newton-type iterative scheme. This approach works as well for a Neumann inverse scattering problem, using the material proposed in [19] on the direct problem in this case, and one then refers to [20].…”