Enclosure methods for Helmholtz-type equations
نویسندگان
چکیده
The inverse problem under consideration is to reconstruct the shape information of obstacles or inclusions embedded in the (inhomogeneous) background medium from boundary measurements of propagating waves. This article is a survey of enclosure-type methods implementing exponential complex geometrical optics waves as boundary illumination. The equations for acoustic waves, electromagnetic waves and elastic waves are considered for a medium with impenetrable obstacles and penetrable inclusions (characterized by a jump discontinuity in the parameters). We also outlined some open problems along this direction of research.
منابع مشابه
Stable Gaussian radial basis function method for solving Helmholtz equations
Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems. They are often referred to as a meshfree method and can be spectrally accurate. In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion. We develop our approach in two-dimensional spaces for so...
متن کاملCubic spline Numerov type approach for solution of Helmholtz equation
We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...
متن کاملEnclosure Methods for the Helmholtz-type Equations
This paper serves as a survey of enclosure-type methods used to determine the obstacles or inclusions embedded in the background medium from the near-field measurements of propagating waves. A type of complex geometric optics waves that exhibits exponential decay with distance from some critical level surfaces (hyperplanes, spheres or other types of level sets of phase functions) are sent to pr...
متن کاملApplication of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)
A novel element with arbitrary domain shape by using decoupled scaled boundary finite element (DSBFEM) is proposed for eigenvalue analysis of 2D vibrating rods with different boundary conditions. Within the proposed element scheme, the mode shapes of vibrating rods with variable boundary conditions are modelled and results are plotted. All possible conditions for the rods ends are incorporated ...
متن کاملAn efficient method for the numerical solution of Helmholtz type general two point boundary value problems in ODEs
In this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. Method is tested on problems to ensure the computational eciency. We have compared numerical results with results obtained by other method in literature. We conclude that propose method is computationally ecient and eective.
متن کامل