Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.Comment: 61 pages, 5 figure

The KW-boundary hybrid digital waveguide mesh for room acoustics applications

The digital waveguide mesh is a discrete-time simulation used to model acoustic wave propagation through a bounded medium. It can be applied to the simulation of the acoustics of rooms through the generation of impulse responses suitable for auralization purposes. However, large-scale three-dimensional mesh structures are required for high quality results. These structures must therefore be efficient and also capable of flexible boundary implementation in terms of both geometrical layout and the possibility for improved mesh termination algorithms. The general one-dimensional N-port boundary termination is investigated, where N depends on the geometry of the modeled domain and the mesh topology used. The equivalence between physical variable Kirchoff-model, and scattering-based wave-model boundary formulations is proved. This leads to the KW-hybrid one-dimensional N-port boundary-node termination, which is shown to be equivalent to the Kirchoff- and wave-model cases. The KW-hybrid boundary-node is implemented as part of a new hybrid two-dimensional triangular digital waveguide mesh. This is shown to offer the possibility for large-scale, computationally efficient mesh structures for more complex shapes. It proves more accurate than a similar rectilinear mesh in terms of geometrical fit, and offers significant savings in processing time and memory use over a standard wave-based model. The new hybrid mesh also has the potential for improved real-world room boundary simulations through the inclusion of additional mixed modeling algorithms

Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.Comment: 22 pages with 9 figure