Complex Geometrical Optics Solutions and Reconstruction of Discontinuities
نویسنده
چکیده
In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside of a domain filled with known conductivity from local boundary measurements. Computational results demonstrate the versatility of these solutions to determine electrical inclusions.
منابع مشابه
Reconstruction of discontinuities in systems
We survey some recent results on the reconstruction of discontinuities by boundary measurements for elasticity and related systems in two dimensions. Our main tool is a new type of complex geometrical optics solutions.
متن کاملReconstructing Discontinuities Using Complex Geometrical Optics Solutions
In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements. Computational results dem...
متن کاملReconstruction of Obstacles Immersed in an Incompressible Fluid
We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity.
متن کاملReconstruction of Inclusions in an Elastic Body
We consider the reconstruction of elastic inclusions embedded inside of a planar region, bounded or unbounded, with isotropic inhomogeneous elastic parameters by measuring displacements and tractions at the boundary. We probe the medium with complex geometrical optics solutions having polynomial-type phase functions. Using these solutions we develop an algorithm to reconstruct the exact shape o...
متن کاملOn the Quasi-random Choice Method for the Liouville Equation of Geometrical Optics with Discontinuous Wave Speed
We study the quasi-random choice method (QRCM) for the Liouville equation of geometrical optics with discontinuous local wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discontinuities, and measure-valued solutions. The so-cal...
متن کامل