Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation

In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [1] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hierarchical representation of the vector finite elements. The new iterative scheme appears to be an efficient solver for the edge finite element solution of the frequency domain Maxwell equations. The solver can be seen as a variable preconditioner and, thus, accelerated by Krylov subspace techniques (e.g. GCR or FGMRES). We demonstrate the efficiency of our approach on a test problem with strong jumps in the conductivity. [1] R. Hiptmair. Multigrid method for Maxwell's equations. SIAM J. Numer. Anal., 36(1):204-225, 1999

Modal parameter identification of a three-storey structure using frequency domain techniques FDD and EFDD and time domain technique SSI: experimental studies and simulations

The aim of this study is to modal parameter identification of a three-storey structure using operational modal analysis. In this research, available techniques in both time domain and frequency domain have been utilized. In time domain, the Stochastic Subspace Identification (SSI) technique, and in the frequency domain, Frequency Domain Decomposition (FDD) and Extended Frequency Domain Decomposition (EFDD) have been used. The modal parameters of a three-storey structure have been calculated using both experimental and finite element method. For this purpose, first, the three-storey structure was modeled in the ANSYS software and then, using the vibration analysis, structural responses are determined. The structure responses are used as inputs of the operational modal analysis algorithms and the modal parameters are obtained. Then, by constructing and exciting the structure by a variety of external excitation, the responses are measured and then, they are used as inputs to the operational modal analysis algorithm to obtain the modal parameters. Since the input signal in OMA method should be random, random, periodic random, pseudo-random, and burst random signals are used for exciting the structure. Finally, the calculated modal parameters from the finite element method and empirical method are compared with each other

Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation

In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [R. Hiptmair, Multigrid method for Maxwell’s equations, SIAM J. Numer. Anal. 36 (1) (1999) 204–225] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hierarchical representation of the vector finite elements. The new iterative scheme appears to be an efficient solver for the edge finite element solution of the frequency domain Maxwell equations. The solver can be seen as a variable preconditioner and, thus, accelerated by Krylov subspace techniques (e.g. GCR or FGMRES). We demonstrate the efficiency of our approach on a test problem with strong jumps in the conductivity

Efficient domain decomposition algorithms for the solution of the helmholtz equation

The purpose of this thesis is to formulate and investigate new iterative methods for the solution of scattering problems based on the domain decomposition approach. This work is divided into three parts. In the first part, a new domain decomposition method for the perfectly matched layer system of equations is presented. Analysis of a simple model problem shows that the convergence of the new algorithm is guaranteed provided that a non-local, square-root transmission operator is used. For efficiency, in practical simulations such operators need to be localized. Current, state of the art domain decomposition algorithms use the localization technique based on rational approximation of the symbol of the transmission operator. However, the original formulation of the procedure assumed decompositions that contain no cross-points and consequently could not be used in the cross-point algorithm. In the context of the perfectly matched layer problem, we adapt the cross-point technique and combined with the rational approximation of the square root transmission operator to yield an effective algorithm. Furthermore, to reduce Krylov subspace iterations, we present a new, adequate and efficient preconditioner for the perfectly matched layer problem. The new, zero frequency limit preconditioner shows great reduction in the required number of iterations while being extremely easy to construct. In the second part of the thesis, a new domain decomposition algorithm is considered. From theoretical point of view, its formulation guarantees well-posedness of local problems. Its practicality on the other hand is evident from its efficiency and ease of implementations as compared with other, state of the art domain decomposition approaches. Moreover, the method exhibits robustness with respect to the problem frequency and is suitable for large scale simulations on a parallel computer. Finally, the third part of the thesis presents an extensible, object oriented architecture that supports development of parallel domain decomposition algorithms where local problems are solved by the finite element method. The design hides mesh implementation details and is capable of supporting various families of finite elements together with quadrature formulas of suitable degree of precision

Improved DORT for breast cancer detection in low contrast scenarios

© 2015 The Institute of Electronics, Information and Comm. Microwave imaging performance deteriorates with increasing clutter and heterogeneity in the imaging medium. Breast cancer detection becomes increasingly challenging with increasing breast density. Decomposition of the time reversal operator (DORT) uses signal subspace of the multistatic matrix which is perturbed in highly heterogeneous medium. To overcome the problem we propose coherent processing in frequency domain prior to imaging operation. Coherent DORT (C-DORT) provides robust imaging performance compared to conventional non-coherent DORT in cluttered medium as evident from the imaging results obtain using anatomically realistic numerical breast phantoms

Foreground component separation with generalised ILC

The 'Internal Linear Combination' (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.Comment: 11 pages, 6 figures (2 figures added), 1 reference added, introduction expanded, V2: version accepted by MNRA